WO2017121473A1 - Turbocodes entrelacés à fenêtre (wi) - Google Patents

Turbocodes entrelacés à fenêtre (wi) Download PDF

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Publication number
WO2017121473A1
WO2017121473A1 PCT/EP2016/050570 EP2016050570W WO2017121473A1 WO 2017121473 A1 WO2017121473 A1 WO 2017121473A1 EP 2016050570 W EP2016050570 W EP 2016050570W WO 2017121473 A1 WO2017121473 A1 WO 2017121473A1
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Prior art keywords
input
interleaver
sequence
output
decoder
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Wen Xu
Onurcan ISCAN
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Huawei Technologies Duesseldorf GmbH
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Huawei Technologies Duesseldorf GmbH
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Priority to CN201680078962.6A priority Critical patent/CN108476027B/zh
Priority to PCT/EP2016/050570 priority patent/WO2017121473A1/fr
Publication of WO2017121473A1 publication Critical patent/WO2017121473A1/fr
Anticipated expiration legal-status Critical
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    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/27—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes using interleaving techniques
    • H03M13/2771—Internal interleaver for turbo codes
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/29—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes combining two or more codes or code structures, e.g. product codes, generalised product codes, concatenated codes, inner and outer codes
    • H03M13/2957—Turbo codes and decoding
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/37—Decoding methods or techniques, not specific to the particular type of coding provided for in groups H03M13/03 - H03M13/35
    • H03M13/39—Sequence estimation, i.e. using statistical methods for the reconstruction of the original codes
    • H03M13/3972—Sequence estimation, i.e. using statistical methods for the reconstruction of the original codes using sliding window techniques or parallel windows
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/27—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes using interleaving techniques
    • H03M13/2739—Permutation polynomial interleaver, e.g. quadratic permutation polynomial [QPP] interleaver and quadratic congruence interleaver
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/27—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes using interleaving techniques
    • H03M13/2742—Irregular interleaver wherein the permutation pattern is not obtained by a computation rule, e.g. interleaver based on random generators
    • H03M13/2746—S-random interleaver
    • H—ELECTRICITY
    • H03—ELECTRONIC CIRCUITRY
    • H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
    • H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
    • H03M13/27—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes using interleaving techniques
    • H03M13/2771—Internal interleaver for turbo codes
    • H03M13/2775—Contention or collision free turbo code internal interleaver

Definitions

  • the present invention generally relates to the field of interleaver design, and specifically relates to an interleaver and to an interleaving method having a band structure.
  • the present invention relates further to obtaining such an interleaver and using such an interleaver in a communication system, e.g. for channel encoding and decoding.
  • a delay or latency caused by the channel encoder or decoder there is a delay or latency caused by the channel encoder or decoder.
  • the delay may have a big influence on the quality of service (QoS) and the quality of experience (QoE).
  • QoS quality of service
  • QoE quality of experience
  • a structural delay may be seen as the cause of the latency that depends on the system design and not on the processing power and memory of transmitter or receiver.
  • One aspect that causes large structural delay is the block-wise processing of the signals in the transmitter and receiver chains.
  • FEC forward error correction
  • the channel decoder requires coded symbols corresponding to the whole codeword in order to start the decoding operation.
  • Coded symbols may relate to both binary and non- binary symbols, wherein in case of a binary code, a symbol is a bit.
  • the decoder cannot start as long as the whole codeword is not received. For long codewords, this may cause a large delay.
  • Certain channel codes have special structures that allow the decoder to start the decoding operation even if the whole codeword is not available.
  • This kind of codes may be decoded with a so-called sliding window decoder (SWD), where the availability of only a part of the codeword is enough to start the decoding process.
  • SWD sliding window decoder
  • a sliding window decoder SWD the decoding is performed over the symbols within a window, said window having a length w. After the decoding of m targeted symbols inside the window (m ⁇ vv) is completed, the window is shifted to a new location, where new targeted symbols are then decoded. This procedure is repeated until the whole codeword is decoded.
  • the sliding window decoder SWD allows more flexibility in latency: The decoder may indeed start decoding the first targeted symbols as soon as the symbols within a certain window are available.
  • Convolutional codes may be given as an example for codes that may be decoded with a sliding window decoder SWD, wherein each encoded symbol only depends on certain previously encoded symbols.
  • Another example of convolutional codes may be the low-density parity-check convolutional codes (LDPC-CC) that have a parity check matrix with a band diagonal structure, which also allows using a sliding window decoder SWD.
  • LDPC-CC is known for example from A. J. Felstrom, and K. S. Zigangirov, "Time- varying periodic convolutional codes with low-density parity-check matrix" IEEE Transactions on Information Theory, 45.6 ( 1999): 2181 -2191.
  • An interleaver is a deterministic function that takes a sequence as input and outputs the same sequence with a different order. Interleaving is a technique that is usually used to improve the performance of channel codes.
  • An interleaver of length k in particular a block interleaver, can be described by a bijective function f(j) with j and f(j) taking integer values from 0 to k— 1.
  • the function f(j) defines the order that the samples or symbols are read from the input vector, i.e., the / h output of the interleaver is read from the location /(/) in the input vector.
  • Turbo codes as parallel concatenated convolutional codes, are powerful error correction codes first introduced in C. Berrou, A. Glavieux. "Near optimum error correcting coding and decoding: Turbo-codes", IEEE Transactions on Communications, 44.10 ( 1996): 1261 -1271.
  • the encoder of a turbo code used e.g., in 3GPP WCDMA or LTE, consists of two
  • convolutional encoders (constituent encoders), and an interleaver /(. ).
  • turbo interleavers used in turbo codes, i.e. the turbo interleavers, are usually designed in a way such that the input is shuffled as much randomly as possible. It is indeed desired to have interleavers with large spread factors.
  • the spread Sf of an interleaver with interleaving function is defined as the minimum distance of any two different indices: where is the distance metric between the indices i and j defined as:
  • interleavers with large spreads are desired due to their better error correction performance. Therefore, during the design of an interleaver for a turbo code, one normally tries to build interleavers where the spread is maximized.
  • an LTE turbo code is constructed using two constituent convolutional codes with 8 states, i.e. with the generators 15 and 13 (in octal) for feedforward and feedback, respectively.
  • the decoder of a turbo code consists of two Soft-In-Soft-Out (SISO) decoders, i.e. one SISO decoder for each constituent convolutional code.
  • SISO Soft-In-Soft-Out
  • the two SISO decoders are connected via an interleaver and a deinterleaver
  • the decoding operation occurs in an iterative way, such that extrinsic information is exchanged between the constituent decoders during each iteration.
  • turbo codes in general cannot be decoded with a sliding window decoder SWD.
  • the interleaver and the deinterleaver connecting both SISO decoders make the use of a sliding window decoder SWD impossible or at least difficult.
  • the sliding window decoder SWD may be used to decode the constituent convolutional codes, however the focus here is the sliding window decoding of the turbo codewords. If a sliding window decoder SWD is used with a turbo code, the following problem occurs. Assume a window with w symbols, where the first m symbols are the targeted symbols. The first SISO decoder may process the first w symbols and produce extrinsic information about those symbols.
  • the present invention aims to improve the state of the art.
  • the object of the present invention is to provide an improved interleaver with the distance between input sequence and output sequence limited in a pre-defined range, so that turbo codes can be interleaved in such way that it can be decoded by using sliding window decoding. In this way, a latency caused by interleaver and decoding can be reduced.
  • a first aspect of the present invention provides an interleaver, parti cularly for channel coding, for mapping an input sequence of k indexed input symbols to an output sequence of k indexed output symbols, k being a positive integer, comprising means for mapping an input index of the input sequence to an output index of the output sequence according to an interleaving function,
  • a distance between the input index and the output index defined by the interleaving function is smaller than or equal to a threshold p, p being a positive integer smaller than k.
  • p a threshold
  • deinterleaver can be defined by the inverse of the interleaving function, i.e., it is an interleaver with the interleaving function / ⁇ 1 (. ) .
  • the interleaver is advantageous in that it shows a band structure, such that a sliding window decoder may be used for a decoder for reducing the decoder latency.
  • the interleaver may particularly be an interleaver for a channel encoder or decoder, especially as for forward error correction (FEC).
  • FEC forward error correction
  • the k input symbols of the input sequence are indexed in that the order of the k input symbols in the input sequence is determined by respective input indices. In other words, the k input symbols have an order that is determined by their respective input index.
  • the k output symbols of the output sequence are indexed in that the order of the k output symbols in the output sequence is determined by respective output indices. In other words, the k output symbols have an order that is determined by their respective output index.
  • the interleaver is configured for turbo codes or turbo codewords.
  • the distance between the input index and the output index defined by the interleaving function is smaller than or equal to the threshold p for all k input indices.
  • the distance between the input index and the output index may relate to the absolute value of the difference between the input index and the output index.
  • the interleaving function may fulfill the condition for all k input
  • deinterleaver as a deinterleaver is an interleaver with the interleaving function In fact, it can be shown that when . Therefore, we may not di fferentiate unless otherwise stated.
  • the distance between the input index and the output index defined by the interleaving function is smaller than or equal to the threshold p only for a subset of all k input indices.
  • the distance between the input index and the output index may relate to the absolute value of the difference between the input index and the output index.
  • a second aspect of the present invention provides an interleaving method, particularly for channel coding, for mapping an input sequence of k indexed input symbols to an output sequence of k indexed output symbols, k being a positive integer,
  • a distance between the input index and the output index defined by the interleaving function is smaller than or equal to a threshold p, p being a positive integer smaller than k.
  • b ⁇ ffc/4] where [.
  • a third aspect of the present invention provides a channel encoder comprising at least one interleaver according to the first aspect of the present invention.
  • the channel encoder may be a turbo encoder.
  • the interleaver may be used in any channel code that can be decoded with the turbo principle.
  • convolutional codes as well as other types of codes like repeat-accumulate codes (Jin, Hui, Aaniod Khandckar, and Robert McEliece. "Irregular repeat-accumulate codes.” Proc. 2nd Int. Symp. Turbo codes and related topics. 2000.),, accumulate-repeat-accumulate codes (Abbasfar, Aliazam, Dariush Divsalar, and Kung Yao. " A ccumul at e-repeat-accumul ate codes.” IEEE Transactions on Communications 55.4 (2007): 692-702) and other kind of serial and parallel concatenated codes connected via an interl eaver where the constituent codes may be any block code or convolutional code.
  • the proposed interleavers may also be used as interleavers between the channel code and the symbol mapper in any bit interleaved coded modulation (BICM) system (Caire, Giuseppe, Giorgio Taricco, and Ezio Biglieri. "Bit- interleaved coded modulation," IEEE Transactions on Information Theory, 44.3 (1998): 927- 946), where the second constituent code is a symbol mapper.
  • BICM bit interleaved coded modulation
  • a constituent code can be any channel code, including the conventional turbo code, convolutional code, LDPC code, or LDPC-eonvolutional code.
  • the channel encoder for encoding the input sequence into an encoded sequence, is a turbo encoder further comprising:
  • the first constituent encoder being adapted to generate a first constituent codeword from the input sequence
  • the second constituent encoder being adapted to generate a second constituent codeword from the output sequence of the interl eaver
  • - a combination unit adapted to combine the input sequence, the first constituent codeword and the second constituent codeword into the encoded sequence.
  • the channel encoder comprises:
  • an identification unit adapted to identify, from among all k input indices, the input indices for which the distance between the input index and the output index defined by the
  • a computing unit adapted to set to known symbols the input symbols located at the identified input indices in the input sequence.
  • the channel encoder comprises:
  • an identification unit adapted to identify, from among all k input indices, the input indices for which the distance between the input index and the output index defined by the
  • a fourth aspect of the present invention provides a channel decoder for decoding a received encoded sequence codeword into a sequence of decoded symbols
  • the channel decoder for decoding a received encoded sequence into a sequence of decoded symbols, is a turbo decoder further comprising a first and a second concatenated constituent decoders,
  • the first and second constituent decoders being connected by the interleaver.
  • the first and second constituent decoders are sliding window decoders.
  • the first constituent decoder is adapted to perform soft output decoding of the received encoded codeword so as to generate the sequence of decoded symbols and a first extrinsic information
  • the second constituent decoder is adapted to perform soft output decoding of the received encoded codeword so as to generate second extrinsic information
  • interleaver is adapted to map the first extrinsic information to side information for the second constituent decoder
  • a deinterleaver is adapted to map the second extrinsic information to side information for the first constituent decoder according to the opposite function of the interleaving function.
  • the channel decoder is adapted to decode an encoded sequence encoded by a channel encoder according to the third aspect of the present invention in that the first and second constituent decoders of the channel decoder are adapted to use perfect a-priori information about the known symbols. Particularly, the first and second constituent decoders of the channel decoder are adapted to use perfect a-priori information about the known symbols set by the computing unit of the channel encoder.
  • a fifth aspect of the present invention provides a method for obtaining the interleaving function according to any of the claims 1 to 5, said interleaving function being adapted to be used in a turbo encoder or turbo decoder,
  • the method comprising: - randomly or pseudo-random ]y generating a plurality of input interleaving functions respectively satisfying the condition that, for at least a subset of the set of all k input indices, a distance between the input index and an output index defined by the input interleaving function is smaller than or equal to the threshold p,
  • k is a positive integer and p is a positive integer smaller than k
  • a sixth aspect of the present invention provides a method that may be referred to as s-random construction method for obtaining the interleaving function according to any of the claims 1 to 5, said interleaving function being adapted to be used in a turbo encoder or turbo decoder, the method comprising:
  • the method further comprising recursively performing following steps:
  • the steps B to E are performed recursively until the input set / is empty.
  • the distance between the input index and the output index defined by the interleaving function is smaller than or equal to the threshold p for all k input indices.
  • the steps B to E are performed recursively until no input value A from the input set / fulfils the criteria i. and ii., wherein the input set / is not empty.
  • the steps B to E may be further performed recursively by ignoring the condition ii .
  • the distance between the input index and the output index defined by the interleaving function may be smaller than or equal to the threshold p only for a subset of all k input indices.
  • the steps B to E are performed recursively until no input value A from the input set / fulfils the criteria i. and ii., wherein the input set / is not empty.
  • the interleaving function is obtained by performing again the step A and the recursive steps B to
  • a seventh aspect of the present invention provides a method that may be referred to as base interleaver construction method for obtaining an interleaving function , said interleaving
  • turbo encoder 100
  • turbo decoder 200
  • the base interleaver may be chosen as an LTE turbo interleaver.
  • helper function may be chosen according to the following equation:
  • obtained interleaving function defines a zigzag-window interleaver.
  • helper function may be chosen according to the following equation:
  • An eight aspect of the present invention provides an interleaving device comprising:
  • a serial to parallel converter to write the input sequence to a matrix M of size L by k ⁇ a base interleaver to be applied on each row of M, where the output is written to the corresponding rows of a matrix R of the same size
  • a parallel to serial converter to read the matrix S row by row to generate the interleaved output of length k'L.
  • the base interleaver may be chosen as LTE interleaver.
  • the base interleaver may be a Quadratic Permutation Polynomial (QPP) interleaver.
  • QPP Quadratic Permutation Polynomial
  • a ninth aspect of the present invention provides a channel encoder for encoding an input sequence into an encoded sequence
  • the channel encoder comprising at least one interleaver
  • interleaver is defined such that the encoded sequence is adapted to be decoded by a channel decoder comprising concatenated constituent decoders in the form of sliding window decoders.
  • a tenth aspect of the present invention provides a computer program having a program code for performing the method according to the second, fifth, sixth or seventh aspect of the present invention, when the computer program runs on a computing device.
  • Fig. 1 shows a turbo encoder according to an embodiment of the present invention
  • Fig. 2 shows a turbo decoder according to an embodiment of the present invention
  • Fig. 3 shows a turbo encoder according to a further embodiment of the present invention
  • Fig. 4 shows a turbo decoder according to a further embodiment of the present invention
  • Fig. 5 shows an interleaving function of an interleaver according to the state of the art
  • Fig. 6 shows an interleaving function of an interleaver according to an embodiment of the present invention
  • Fig. 7 shows an interleaving function of an interleaver according to another embodiment of the present invention
  • Fig. 8 shows a zigzag window interleaver according to an embodiment of the present invention
  • Fig. 9 shows a smoothed window interleaver according to an embodiment of the present invention
  • Fig. 10 shows a smoothed window interleaver according to another embodiment of the present invention
  • Fig. 1 1 shows a sliding window decoding according to an embodiment of the present invention
  • Fig. 12 shows performance results of wi-turbo codes with smoothed window interleavers according to an embodiment of the present invention
  • Fig. 13 shows performance results of wi-turbo codes with zigzag window interleavers according to an embodiment of the present invention
  • Fig. 14 shows performance results of wi-turbo codes with smoothed-window interleavers according to an embodiment of the present invention
  • Fig. 15 shows possible gains due to the flexible latency adjustment according to the present invention.
  • Fig. 16 shows an interleaving device with an interleaving function according to an embodiment of the present invention.
  • the present invention proposes an interleaver, particularly for channel coding, for mapping an input sequence of k indexed input symbols to an output sequence of k indexed output symbols, k being a positive integer.
  • the interleaver comprises means for mapping an input index of the input sequence to an output index of the output sequence according to an interleaving function. For at least a part of all k input indices, a distance between the input index and the output index defined by the interleaving function is smaller than or equal to a threshold p, k and the threshold p being positive integer.
  • the k input symbols of the input sequence are i ndexed in that the order of the k input symbols in the input sequence is determined by respective input indices. In other words, the k input symbols have an order that is determined by their respective input index.
  • the k output symbols of the output sequence are indexed in that the order of the k output symbols in the output sequence is determined by respective output indices. In other words, the k output symbols have an order that is determined by their respective output indices.
  • the means for mapping may e.g. be a computing unit adapted to map the input index of the input sequence to the output index of the output sequence according to the interleaving function.
  • the input symbols and output symbols of the respective input sequence and output sequence may be values or coded symbols related to either binary and non-binary codes. Particularly, in case of a binary code, a symbol may be a bit.
  • the threshold p may be a positive integer.
  • the threshold p may be set such that 2p+l is smaller than the value k, the value k reflecting the total length of input sequence or the total number of input symbols of the input sequence.
  • the threshold p may verify or fulfill the equation p ⁇ (k- ⁇ )/2, with p and k being positive integers.
  • p can be typically chosen as p ⁇ (k- ⁇ )/4.
  • the proposed interleaver may be an interl eaver for turbo codes, i.e. a turbo code interl eaver.
  • Figs. 1 and 2 show two embodiments for using the interl eaver according to the present invention.
  • Fig. 1 shows a turbo encoder 100 according to an embodiment of the present invention.
  • the turbo encoder 100 comprises an interleaver 104 according to the present invention.
  • Fig. 1 shows the interleaver 104, particularly for channel coding, for mapping an input sequence 101 of k indexed input symbols to an output sequence 105 ot ' k indexed output symbols, k being a positive integer.
  • the interleaver 104 comprises means for mapping an input index of the input sequence 101 to an output index of the output sequence 105 according to an interleaving function.
  • a distance between the input index and the output index defined by the interleaving function is smaller than or equal to a threshold p, p being a positive integer smaller than k.
  • the said means may be implemented through a module, unit or on a software basis.
  • the input of the turbo encoder 100 is the sequence of information symbols to be encoded 101 corresponding to the input sequence 101 of k indexed input symbols.
  • Output of the encoder contains systematic symbols 101 - i.e. the sequence of information symbols itself-, parity symbols 103 generated by a first constituent encoder 102, and parity symbols 107 generated by a second encoder 106 after interleaving 104.
  • the turbo encoder 100 is adapted to encode the input sequence 101 into an encoded sequence or codeword 109.
  • the turbo encoder 100 comprises the interleaver 104, as well as first 102 and second 106 concatenated constituent encoders.
  • the first constituent encoder 102 is adapted to generate a first constituent codeword 103 from the input sequence 101
  • the second constituent encoder 106 is adapted to generate a second constituent codeword 107 from the output sequence 105 of the interleaver 104.
  • the turbo encoder 100 also comprises a combination unit, like a serial/parallel unit 108, adapted to combine the first constituent codeword 103 and the second constituent codeword 107 into the encoded sequence 109.
  • the combination unit 108 may be adapted to combine the input sequence 101 , the first constituent codeword 103, and the second constituent codeword 107 into the encoded sequence 109.
  • first and second constituent encoders 102, 106 of the turbo encoder 100 may be respectively in the form of convolutional encoders as shown in Fig. 1.
  • Fig. 2 shows a turbo decoder 200 according to an embodiment of the present invention.
  • the turbo decoder 200 comprises an interleaver 205 according to the present invention.
  • FIG. 2 shows the interleaver 205, particularly for channel coding, for mapping an input sequence 204 of k indexed input symbols to an output sequence 206 of k indexed output symbols, k being a positive integer.
  • the interleaver 205 comprising means for mapping an input index of the input sequence 204 to an output index of the output sequence 206 according to an interleaving function.
  • a distance between the input index and the output index defined by the interleaving function is smaller than or equal to a threshold p, the threshold p being a positive integer smaller than k.
  • the said means may be implemented through a module, unit or on a software basis.
  • the input of the turbo decoder 200 is the received symbols 201 in form of reliability values, e.g. log-likelihood values or L-values, or soft values.
  • the output 210 corresponds to the decoded symbols.
  • the turbo decoder 200 comprises first and second constituent decoders 202, 203 that are connected by the interleaver 205.
  • the two constituent decoders 202, 203 are also connected by a de-interleaver 208 corresponding to interleaver 205, i.e. being the opposite of the interleaver 205.
  • the two constituent decoders 202, 203 perform a soft output decoding, and generate respective extrinsic information 204, 207 about each symbol of the information sequence 201.
  • the extrinsic information 204 of the first constituent decoder 202 is then interleaved by the interleaver 205 and fed 206 to the second constituent decoder 203 as side information.
  • the extrinsic information 207 of the second constituent decoder 203 is de- interleaved by the de-interleaver 208 and fed 209 to the first constituent decoder 202 as side information.
  • the respective extrinsic information 204, 207 of one constituent decoder is fed iteratively to the other constituent decoder.
  • This iterative procedure is repeated a certain amount of times before making a final decision on the decoded symbols 210. If decoding is successful, the decoded symbols 210 are equivalent to the transmitted information sequence 101.
  • the channel encoder and channel decoder of Figs. 1 and 2 comprise respectively constituent encoders 102, 106 and constituent decoders 202, 203 that are parallel concatenated.
  • Figs. 1 and 2 show parallel concatenated turbo codes in form of parallel concatenated binary convolutional codes.
  • the invention is also applicable to channel encoder and channel decoder having alternative structures, see for example Figs. 3 and 4.
  • the invention is also applicable to non- binary and/or to serially concatenated codes.
  • the invention may be used with parallel or serially concatenated codes containing more constituent codes, i.e. containing more than the two constituent encoders 102, 106 of Fig. 1 and more than the two constituent decoders 202, 203 of Fig. 2.
  • a parallel or serial concatenated code according to the invention may then be a turbo code consisting of at least two constituent codes and at least one interleaver.
  • the intcrleaver may be referred to as the turbo interleaver.
  • the symbols are the output 109 of the channel encoder, i.e. the encoded sequence
  • K and N are positive integers.
  • the present invention is advantageous in that the encoded symbols c, may be generated even if only a part of the input sequence is available.
  • the output symbol c n is called the delay-d and window-w encoded, if c legally may be generated using with Further on, when c legally is delay-d and window-w encoded for all n, then the channel code is called delay-d and window-w
  • a code is delay-d and window-w encodable, then it is also d and window-(w+l) encodable. Since we are interested only in the minimum of d and w, unless otherwise stated, the delay-i/ and window-w encodable channel code is referred to as the code which is not delay -(d- 1) and window-(w-l) encodable. Thus, without considering the processing delay, the delay d is dependent only on the structural delay of the channel encoder.
  • bk is called the delay-d and window-w decodable, if b* can be decoded using with w > d ⁇ 0.
  • the channel code is called the delay-d and window-w decodable
  • the corresponding decoder is called the delay-d and window-w decoder. Since any delay-d and window-w decodable code is also delay-(d+l) and window-(w+J) decodable, unless otherwise stated, d and w are the minimum delay d and window w of the delay-d and window-w code, respectively.
  • the delay d is dependent only on the structural delay of the channel decoder, and may serve as a structure delay parameter.
  • a known non-recursive convolutional encoder may consist of s memory elements - shift registers - and the output at each time instant may be a linear combination of the values in the memory elements.
  • the input sequence is fed to the memory elements and shifted by one symbol after the outputs are generated. Due to this structure, one can say that a non-recursive convolutional code with s memory elements is delays windows encodable.
  • Recursive convolutional codes are similar to non-recursive codes, except their output may also depend on the previous outputs due to the feedback connection. For recursive convolutional codes, the encoding delay is the same as the non-recursive codes, but as the output depends also on the previous outputs, the window size may be regarded as infinity.
  • the decoder can be regarded as delay-is window-is decoder.
  • the turbo codes respectively use
  • a known encoder requires the whole input sequence in order to produce its encoded sequence.
  • a known decoder requires the whole input sequence in order to start decoding.
  • a turbo code is delay-k window-k encodable and delay-k window-k decodable.
  • the constituent codes of a turbo code can be any kind of codes (like block codes or convolutional codes), however one usually uses convolutional codes as constituent codes with parallel concatenated turbo codes due to their advantages such as performance and simplicity.
  • the invention proposes particularly a new interleaver, a new channel encoder and channel decoder and new turbo codes generated by using the new interleaver having band
  • Such kind of turbo codes according to the present invention may be called window interleaved turbo codes, i. e. Wi -Turbo or wi-turbo codes.
  • the proposed interleaver having band structure or properties may be referred to as Window Interleaver.
  • delay-d and window-w encoder can be extended to many devices, including the (de)interleavers.
  • an interleaver of length k can be interleavcd/deinterleaved with a delay of k symbols.
  • interleavcrs with special structures such as window interleavcrs, WI
  • WI window interleavcrs
  • the Wi -Turbo encoder or decoder has a reduced structural latency or delay, i.e. a reduced waiting time for encoding or decoding.
  • the proposed new coding method allows the generated codewords to be encoded or decoded using a sliding window encoder or decoder. In other words, their encoding or decoding time is dependent on the chosen WI parameters.
  • Wi -Turbo codes are more flexible in supporting rate matching and incremental redundancy, compared to other modern codes such as the LDPC-CC.
  • the proposed Wi-turbo codes according to the present invention have special interleavcrs, like window interleavers, that allow them to be decoded using a sliding window decoder.
  • a window interleaver is defined by the parameter p that defines the maximum distance between the input and the output of the interleaver. Therefore, assuming that the convolutional encoders of the turbo code, i.e. of the turbo encoder, has s memory elements, the encoding delay of the wi-turbo codes can be regarded as s+p ⁇ k. Note that s is usually small compared to p and can be neglected.
  • the main advantage of the present invention i.e. of the wi-turbo codes compared to conventional turbo codes is their suitability to sliding window decoder (SWD). If an SWD is used, the decoding latency can be as small as p symbols, similar to the encoder. However to obtain good error correction performance, one usually defines a number of target symbols m - number of symbols to be decoded in each window - and chooses a window of size greater than m+p. Experimental evaluations suggest that, for example, choosing m-p and the window size w ⁇ 5m usually leads to good results.
  • SWD sliding window decoder
  • Figs. 3 and 4 show two embodiments for using the interleaver according to the present invention in respectively a turbo encoder and a turbo decoder having an alternative structure.
  • Fig. 3 shows a turbo encoder 300 according to a further embodiment of the present invention.
  • the turbo encoder 300 comprise an interleaver 304 according to the present invention.
  • the turbo encoder 300 is a serial concatenated encoder.
  • Two constituent codes 302, 306 are connected serially with the interleaver 304. Repeat-accumulate codes, wherein the first constituent code 302 is a repetition code and the second one 306 is an accumulator, and accumulate-repeat-accumulate codes, wherein the first constituent code 302 is an
  • accumulator/repetition code and the second one 306 is an accumulator can be given as examples for serially concatenated codes.
  • the turbo encoder 300 of Fig. 3 generates an encoded sequence or encoded symbols 309 from an input sequence or input symbols 301.
  • the input sequence 301 is applied to a first constituent code, i.e. a first constituent encoder 302, to obtain a first constituent codeword 303.
  • the interleaver of the present invention generates an output sequence 305 from the first constituent codeword 303.
  • the output sequence 305 is applied to a second constituent code, i.e. a second constituent encoder 306, to obtain a second constituent codeword 307.
  • a combination unit 308 is adapted to combine the input sequence 301 and the second constituent codeword 307 into the encoded sequence 309.
  • Fig. 4 shows a turbo decoder 400 according to a further embodiment of the present invention.
  • the turbo decoder 400 comprise an interleaver 405 according to the present invention.
  • the turbo decoder 400 of Fig. 4 may be used to decode the encoded sequence 309, 401 generated by the turbo encoder 300 of Fig. 3 so as to obtain decoded symbols 410.
  • the turbo decoder 400 comprises a first 403 and a second constituent decoder 402 that are connected by the interleaver 405 and by a de-interleaver 408 being the opposite of the interleaver 405.
  • the input sequence 401 of the turbo decoder 400 is applied to the second constituent decoder 402 and the decoded symbols 410 is generated by the first constituent decoder 403.
  • the distance between the input and the output of the interleaver is limited. Since both constituent codes 302, 306 may be chosen as codes with low latency - like accumulators, for example memory- 1 convolutional codes, and repeaters -, the overall latency may be characterized by the interleaver latency. Therefore, if a window interleaver with parameter p is used, the encoder latency may be regarded as p, and is reduced with respect to known interleaves.
  • the interleaver according to the present invention may be realized by several constrained interleavers.
  • the folio wings two embodiments for the interleaver are presented, as well as two interleaver construction methods.
  • Fig. 6 shows an interleaving function of an interleaver according to a first embodiment of the interleaver.
  • the first proposed interleaver shown in Fig. 6 is called -window interleaver, or It is defined with the interleaving function of length k, where the absolute
  • the interleaving function f defines the order that the samples or values are read from the
  • the interleaving function has a length k, and the values j and p are integer values between 0 and k In this way, the distance between the input and the output indices are limited by p for all
  • Fig. 6 correspondingly presents an interleaver function having a band structure with a width of In comparison, Fig. 5 shows an interleaving function of
  • Th )- window interleaver of length k according to the embodiment of Fig. 6 is a
  • the interleaving function is the threshold or parameter defining the maximum distance between input and the output of the interleaving function. It is proportional to the interleaver size and has an influence on the possible window- sizes if this interleaver is used as the turbo interleaver of a wi -turbo code. As shown previously, should hold, wherein m is the number of targeted symbols and w is
  • FIG. 7 shows an interleaving function of an interleaver according to a second embodiment of the interleaver.
  • the interleaver of the second embodiment may be called P( - window interleaver or -WI. It is defined with the interleaving function of length k,
  • the distance between the input and the output indices is limited by the threshold p for only a subset of all possible input indices.
  • the distance between the input and the output indices is limited by p for only the input indices comprised between
  • the / WI has the advantage of a simple construction. However, it has to be noted that
  • the -window interleaver of length k according to the embodiment of Fig. 7 is a
  • k and p being positive integers
  • d being a nonnegative integer: wherein J d is a subset of / with cardinality k-d.
  • d is the parameter specifying the number that shows at how many input indices of the interleaving function do not fulfill the constraint given in equation (4). It is desired to have a small d - because for these indices other measures have to be taken during decoding, like setting systematic bits to known values or puncturing systematic bits corresponding to these known values, as explained below -, but its value mainly depends on the construction methods explained in the next sections. Note that the d indices are located in the first or in the last b locations.
  • a -window interleaver fulfills the same conditions as a window interleaver
  • This first construction method may be called random construction method.
  • the first proposed construction method is a brute force method to construct a random WI.
  • this method one basically generates a large number of length- A: random or pseudo random interleavers such that enough number of Wis can be also generated.
  • the best performing WI may be selected among the generated interleavers.
  • One option to select the best performing one is to evaluate the performance of turbo codes constructed with the stored interleavers in terms of bit error rate (BER) or block error rate (BLER) and then select the interleaver that give the best error correction performance.
  • BER bit error rate
  • BLER block error rate
  • Wi-Turbo encoder and decoder By alternating the selected Wis employed in Wi-Turbo encoder and decoder, different BLERs (block error rates) or BERs (bit error rates) can be measured at the Wi-Turbo decoder. The best performing Wis are then the Wis - used in Wi-Turbo - which lead to the lowest FER or BER.
  • This second construction method may be called s-random construction method, and is based on the method proposed by S. Dolinar, D. Divsalar, "Weight distributions for turbo codes using random and nonrandom permutations," TDA Progress Report 42.122, 1995, with the modification that during the construction of the interleaving function / the constraint is also considered.
  • This second method describes how to construct a window interleaver of length k with a modified s-random construction method.
  • the inputs of the following algorithm are interleaver length k, minimum spread s of the interleaver and the threshold p - being a constraint for SWD -, where all of the inputs are non-negative integers.
  • the second construction method comprises:
  • step 1 again from the beginning, i.e. from step 1.
  • This second construction method may be called base interleaver construction method.
  • a helper function is generated by modifying the base interleaver function, which is then concatenated L times using a deterministic method to obtain a Theoretically, L can approach infinity such that
  • the encoder/decoder can work for infinite size of data streams.
  • the obtained WI can have a
  • helper function For the constraction, first the following helper function is defined wherein is an integer.
  • This method can be seen as concatenating the base interleaver L times where the connection between each interleaver is defined by the helper function.
  • the interleaving method for mapping an input sequence of k'L indexed input symbols to an output sequence of k'L indexed output symbols, k' and L being positive integers can be defined. Accordingly, the interleaving function will be
  • a first example of the third construction method from a base interleaver is presented together with Fig. 8.
  • a Zigzag Window Interleaver may be constructed, as shown in the right diagram of Fig. 8.
  • Fig. 8 shows the helper function and the right diagram shows the resulting zigzag window interleaver, wherein is a randomly selected subset of J with cardinality
  • the indices of ] are depicted with red markers.
  • a SWD with window size w can be used.
  • the codeword can be
  • a smoothed Window Interleaver may be constructed, as shown in the right diagram of Fig. 9. It is proposed to construct the smoothed window interleaver with the third construction method, using the following helper function:
  • a third example of the third construction method from a base interleaver is presented together with Fig. 10.
  • a smoothed Window Interleaver may be constructed, as shown in the right diagram of Fig. 10.
  • This third example also yields a smoothed window interleaver, as depicted in Fig. 10.
  • the left diagram of Fig. 10 shows the helper function while the resulting smoothed window interleaver is presented in the right diagram of Fig. 10, wherein
  • contention-free QPP interleavers one can construct contention free Wis with good spread factor by using LTE Turbo code interleavers as base interleavers.
  • Decoding starts by processing the first w systematic bits and their corresponding parity bits, where the first m systematic bits in the window are the targeted symbols.
  • Turbo codes with an / p fi (;)-Wi may be decoded by using the same method in the previous part, i.e. may be decoded by a Sliding Window Decoding for Turbo Codes using an - Window Interleaver.
  • a performance loss due to the d indices of the interleaver which do not fulfill the condition (4) and hence will lie outside of the window.
  • the systematic bits corresponding to d indices are set to known values - e.g., zeros, whose corresponding log-likelihood value equals such that no information is transmitted over these indices.
  • the systematic bits corresponding to these known values are punctured, i.e. not transmitted.
  • a sliding window decoder is used with the following modification.
  • the known values of the d indices are fed to the decoder as perfect a-priori information - e.g., with a log-likelihood value of
  • Fig. 16 shows an interleaver or an interleaving device 1600 with an interleaving function according to an embodiment of the present invention.
  • the interleaving device 1600 is adapted to generate an output sequence or interleaved sequence 1609 from the input sequence 1601.
  • the input sequence 1601 and the output sequence 1609 have a length
  • the interleaving device 1600 comprises a serial to parallel converter 1602 to write the input sequence 1601 to a matrix M 1603 of size L by k '.
  • the serial to parallel converter 1602 is adapted to reshape the input sequence 1601 into the matrix M 1603.
  • the interleaving device 1600 comprises a base interleaver 1604 to be applied on each row of M 1603, wherein the output of the base interleaver 1604 is written to the corresponding rows of the matrix R 1605 of the same size. Each row is interleaved using the base interleaver 1604.
  • the cyclic shift operator 1606 performs a cyclic shift in vertical dimension according to tj.
  • the interleaving device 1600 comprises a parallel to serial converter 1608 to read the matrix S 1607 row by row so as to generate the interleaved output 3609 of length k 'L.
  • the base interleaver 1604 may be an LTE interleaver.
  • Fig. 12 shows performance results of wi-turbo codes - in terms of required Et/No to achieve a target error probability - with smoothed window interleavers according to the present invention.
  • the performance of the wi-turbo codes decoded with a sliding window decoder is shown in Fig. 12.
  • the window-interleavers are generated by using the third construction method and using the LTE QPP interleavers of different lengths as base interleavers.
  • latency is defined as the number of required symbols to start decoding, i.e. for SWD the latency equals the window length.
  • the performance metric is the required SNR or Et/No to reach a target error bit probability of 0.0001.
  • Each square marker in Fig. 12 corresponds to the performance of an LTE Turbo code with different interleaver lengths. It may be noted that, for providing a fair comparison, the decoding latency of the LTE turbo codes where no SWD is possible are considered as the message length, i.e.
  • Fig. 14 shows the bit error rate (BER) performance of wi-turbo codes with smoothed-window interleavers constructed from LTE QPP interleavers, i.e. constructed from different LTE QPP interleaver lengths k and different values L.
  • BER bit error rate
  • Fig. 15 shows an example scenario where the wi-turbo codes can have a significant advantage compared to LTE turbo codes. Assume that the receiver has to wait for ⁇ seconds due to some other processing tasks, where it receives additional 750 symbols. Traditional turbo decoder would not be able to use this information to improve the decoding performance, but wi-turbo code can make use of these symbols to increase the performance, in this example by up to 0.4 IdB. Note that due to the special structure, any latency can be supported such that the decoder can work with nearly no idle periods.
  • the present invention is advantageous in that, by using the turbo codes with the proposed interleaver, the transmitter and receiver can have lower latency in channel encoding and decoding.
  • One can adjust its decoding latency easily according to its latency budget by changing the window size of e.g. an SWT). This is not possible if a conventional interleaver is used because in known communication systems utilizing turbo codes, the latency cannot be adjusted at the transmitter or receiver side.
  • the present invention is advantageous in that, by using the proposed wi-turbo codes, the same codeword can be decoded with low latency in case of a good channel realization, and hence if a small window is enough for successful decoding.
  • the present invention is advantageous in that, by using the proposed wi-turbo codes, the latency can be increased by the transmitter or by the receiver to improve the error correction performance.
  • the present invention is advantageous in that, by using the third construction method, one can build Wis that can have some good properties of the base interleaver, like contention-free property and the spread factor.
  • the present invention is advantageous in that, by using the third construction method, one can build Wis with a periodic structure, such that the storage need for the interleaver function does not increase with the interleaver length.
  • the present invention is advantageous in that, by using the third construction method, one can build Wis of any length that are integer multiples of base interleaver length.
  • the present invention may be implemented in hardware and/or software.
  • the proposed wi -turbo codes and interleaver may be used in optical, wireline or wireless

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  • Physics & Mathematics (AREA)
  • Probability & Statistics with Applications (AREA)
  • Engineering & Computer Science (AREA)
  • Theoretical Computer Science (AREA)
  • Error Detection And Correction (AREA)
  • Detection And Prevention Of Errors In Transmission (AREA)

Abstract

La présente invention porte sur un entrelaceur (104), en particulier pour un turbocodeur (100), pour le mappage d'une séquence d'entrée de k symboles d'entrée (101) indexés en une séquence de sortie de k symboles de sortie (105) indexés, k étant un entier positif, comprenant des moyens de mappage d'un indice d'entrée de la séquence d'entrée en un indice de sortie de la séquence de sortie en fonction d'une fonction d'entrelacement, tel que, pour un sous-ensemble particulier de k indices d'entrée, une distance entre l'indice d'entrée et l'indice de sortie définie par la fonction d'entrelacement est inférieure ou égale à un seuil (p), p étant un entier positif inférieur à k. Cet entrelaceur peut être appliqué avantageusement en combinaison à un décodage à fenêtre glissante.
PCT/EP2016/050570 2016-01-13 2016-01-13 Turbocodes entrelacés à fenêtre (wi) Ceased WO2017121473A1 (fr)

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