CN106941394B - Joint detection decoding method and device for SCMA (sparse code multiple access) coded by polarization code - Google Patents

Abstract

The invention discloses a joint detection and decoding method and device for sparse code multiple access (Sparse code multiple access, SCMA) detection and polar code (polar code) decoding based on belief proportion (BP), To further improve the stability of the communication system and reduce the bit error rate. The method combines the factor graph detected by SCMA BP and the factor graph decoded by polar codes, so that the probability information between them can be circulated, so that the probability information can have higher accuracy and faster convergence speed.

Description

Joint detection and decoding method and device for SCMA encoded by polar codes

technical field

The invention belongs to the technical field of space-time coding and channel coding, and in particular relates to a method and device for joint detection and decoding of polar code coded SCMA.

Background technique

In the face of the increasing requirements of 5G communication for all aspects of transmission, Sparse Code Multiple Access (SCMA) is undergoing extensive research. Since SCMA technology can improve the utilization efficiency of spectrum resources and mediate the interference between users to a certain extent, it has become a very promising air interface technology for 5G communication. Polar codes have been attracting attention since they were proposed in 2008. Polar code is the first code that can theoretically reach the Shannon limit, and now polar code is listed as a 5G standard code for use in enhanced mobile broadband scenarios. For the Polar SCMA system, the traditional separated detection and decoding (SDD) first performs SCMA detection on the received signal, and then sends the detected soft information to the decoder for decoding to obtain the decoding result. The joint detection and decoding method (Iterative detection and decoding, IDD) proposed by the present invention can further improve the reliability of the polar SCMA system, thereby reducing the bit error rate.

SUMMARY OF THE INVENTION

Purpose of the invention: In order to meet some occasions that have higher requirements on the bit error rate, the present invention proposes a SCMA joint detection and decoding method and device based on polar code coding, by combining the factor graphs of SCMA detection and polar code decoding. , so that the probability information in the two graphs can be transferred to each other, which can reduce the bit error rate and improve the convergence speed.

Technical scheme: In order to realize the above-mentioned purpose of the invention, the present invention adopts the following technical scheme:

A joint detection and decoding method for SCMA encoded by polar codes, which combines the factor graphs of SCMA detection and polar code decoding, so that the probability information between detection and decoding can be transferred to each other. The iteration includes the following steps:

(1) At least one iterative update is performed between user nodes and functional nodes in the SCMA detection factor graph to obtain the symbol probability information of the user nodes;

(2) Transfer the symbol probability information detected by SCMA to the MAP node and map it to bit probability information, and transfer the bit probability information to the polar code decoding factor map;

(3) After at least one iteration update is performed inside the decoding factor graph, the bit probability information is sent to the MAP node to be mapped into symbol probability information, and then sent back to the SCMA detection factor graph for the next iteration.

In a specific embodiment, the calculation formula of the symbol probability information transmitted by the functional node to the user node in step (1) is:

表示SCMA第z次传输，第k个FN传给第j个UN关于符号m的概率信息，c1,c2,..c_dr-1表示dr-1个的符号，dr是LDPC每行为1的元素个数，c_τj(l)这串符号中给第l个UN的符号，N(k)是所有与的第k个FN相连的UN的集合，

是一个常数因子，其表达式为

其中N0是噪声功率，y_j是接收向量的第j个符号，h_k,l是调节系数。in,

Indicates the zth transmission of SCMA, the kth FN transmits the probability information of the symbol m to the jth UN, c1, c2, _{..c dr-1} represents the symbol of dr-1, and dr is the element of 1 in each row of LDPC number, c _τj (l) the symbol for the l-th UN in this string of symbols, N(k) is the set of all UNs connected to the k-th FN,

is a constant factor whose expression is

where N0 is the noise power, y _j is the j-th symbol of the received vector, and h _k,l are the adjustment coefficients.

将SCMA检测得到的符号概率信息映射给译码模块的左信息，

是归一化后的第j个UN符号为m的概率信息，n为译码因子图的级数，z＝1,2,..Z,d＝1,2,…B,其中Z是SCMA传输的次数，B是一个SCMA符号所代表的比特数，MAP^-1表示将符号概率信息转换为比特概率信息。In step (2), follow the formula

Map the symbol probability information detected by SCMA to the left information of the decoding module,

is the probability information that the jth UN symbol is m after normalization, n is the series of the decoding factor graph, z=1,2,..Z,d=1,2,...B, where Z is SCMA The number of transmissions, B is the number of bits represented by an SCMA symbol, and MAP ^-1 represents the conversion of symbol probability information into bit probability information.

In a specific embodiment, in step (3), according to the formula

The bit probability information obtained by the decoding module is transmitted to the user node of the SCMA detection module, where MAP indicates that the bit probability information is converted into symbol probability information, which is between 0 and 1.

In a specific embodiment, in step (3), according to the formula

Update the probability information passed by the user node to the function node and enter the next iteration.

The device for realizing the above-mentioned joint detection and decoding method of polar code-encoded SCMA includes:

SCMA detection factor graph module, including several user node units and functional node units;

Polar code decoding factor graph module, including several basic calculation units for iterative operations;

a first probability information mapping module, including several first mapping units, for converting symbol-based probability information into bit-based probability information;

A second probability information mapping module, including several second mapping units, for converting bit-based probability information into symbol-based probability information;

a first intrinsic information exchange memory for storing bit probability information iteratively updated by the decoded factor graph;

and a second intrinsic information exchange memory for storing the converted bit probability information outgoing from the SCMA detection factor map.

Beneficial effect: The present invention combines SCMA detection (belief propagation (BP) detection) with polar code decoding (BP decoding) for the first time. In the present invention, the factor graphs of SCMA detection and polar code decoding are combined, so that the information between detection and decoding can be transferred to each other. Different from the previous separated detection and decoding (SDD), this method allows the soft information obtained by polar code decoding to be sent back to the MIMO detector through the network, and then sent back after the soft information is updated. That is, information can flow in both directions in the network, while SDD only allows information to flow from the detector to the decoder. The present invention can be applied to the current 5G enhanced mobile broadband scenario using polar codes, and can further improve the reliability of the polar SCMA system.

Description of drawings

FIG. 1 is a system block diagram of joint detection and decoding.

Figure 2 is a factor plot of SCMA detection.

Figure 3 is a factor graph of Polar decoding.

Figure 4 is a factor plot of the joint detection of polar SCMA.

Figure 5 is a graph of the bit error rate results of various methods.

FIG. 6 is a schematic diagram of the overall hardware architecture.

FIG. 7 is a schematic diagram of a partial hardware architecture.

Detailed ways

Below in conjunction with specific embodiments, the present invention will be further illustrated, and it should be understood that these embodiments are only used to illustrate the present invention and not to limit the scope of the present invention. The modifications all fall within the scope defined by the appended claims of this application.

In order to facilitate the understanding of the technical content of the embodiments of the present invention, a channel model of a polar code-encoded SCMA system and an existing separate SCMA detection algorithm and polar code decoding algorithm are briefly described first.

channel model

In a polar code coded SCMA system (see Figure 1), a string of bits to be transmitted is first polar code coded. It may be assumed that the length of the code is N=2 ⁿ , the length of the information bits is K, and the sequence number set of the information bits is A. This encoding process can be expressed as x=uG

SCMA传输模型如下，where x is an N×1 coded sequence, u is an N×1 uncoded sequence in which the information bits are placed according to A, and G is an N×N generator matrix. In a SCMA system with J users, each user code set has M _s codewords and K _s resources. Each codeword is equivalent to B=log _{2 Ms} bits of information, so that each user needs Z=N/B transmissions to transmit N bits. For example, the encoded information x of the jth user is mapped into a series of code words in a code set

The SCMA transmission model is as follows,

都是K_s×1的向量。接收端接收到y^z，根据它求得发送端的序列。Where z is used to record the serial number of the transmission, and w is additive white Gaussian noise. y ^z and

are all K _s × 1 vectors. The receiver receives y ^z , and obtains the sequence of the sender according to it.

SCMA detection

The BP detection of SCMA is a process in which the symbol probability is iteratively converged. The user node (User Node, UN) and the function node (Function Node, FN) transmit probability information about the symbol to each other, so that the symbol probability converges (as shown in Figure 2). . The general process of SCMA's BP detection algorithm is as follows:

为1/M_s，即令1) Initialize the probability information that the user node transmits to the functional node (UN-to-FN). Initialize the zth transmission of SCMA and pass it to the ith FN at the jth UN to think that the symbol is m.

is 1/M _s , that is,

2) Perform iterative detection, and each iteration process includes the following steps:

(2.1) The functional node calculates the probability information that FN transmits to the UN (FN-to-UN) according to the UN-to-FN information, and transmits the information to the user node. The calculation formula is:

表示SCMA第z次传输，第k个FN传给第j个UN关于m的概率信息，c1,c2,..c_dr-1表示dr-1个的符号、c_τj(l)这串符号中给第l个UN的符号，N(k)是所有与的第k个FN相连的UN的集合，

是一个常数因子，其表达式为

其中N0是噪声功率，y_j是接收向量的第j个符号，h_k,l是调节系数。in,

Indicates the zth transmission of SCMA, the kth FN transmits the probability information of m to the jth UN, c1, c2, _{..c dr-1} represents the symbol of dr-1, c _τj (l) in this string of symbols The symbol for the l-th UN, N(k) is the set of all UNs connected to the k-th FN,

is a constant factor whose expression is

where N0 is the noise power, y _j is the j-th symbol of the received vector, and h _k,l are the adjustment coefficients.

(2.2) The user node calculates the UN-to-FN according to the FN-to-UN information, and normalizes it and transmits it to the function node for the next round of calculation. The calculation formula of the UN-to-FN probability information is:

where M(j) is the set of all FNs connected to the jth UN,

3) After the iteration, the probability information that the jth UN symbol is m is obtained as

The pseudo code of the algorithm is as follows:

表示SCMA第z次传输，在第j个UN传给第k个FN认为该符号是m的概率；

表示SCMA第z次传输，第k个FN传给第j个UN关于m的概率信息；

表示第j个UN符号为m的概率信息。In the above algorithm,

Indicates the zth transmission of SCMA, the probability that the symbol is m when it is transmitted to the kth FN at the jth UN;

Indicates the zth transmission of SCMA, and the kth FN transmits the probability information about m to the jth UN;

Represents the probability information that the jth UN symbol is m.

Polar code decoding

The decoding process of polar codes is a process of iteratively updating the left and right information with each other, the left information is transmitted from right to left, and the right information is transmitted from left to right. Finally, the codeword is hard-decided based on the left information of the last stage. Figure 3 is a diagram of polar decoding factors, and the general decoding process is as follows

(1) Initialization: Initialize the left information of the n+1 layer and the right information of the first layer, and initialize the left information of the n+1 layer as the channel input information. For the right information of the first layer, if the bit is information Bits are initialized to 0, otherwise initialized to +∞.

L _n+1,t =I _t

For a polar code with a code length of 2 ⁿ , the factor graph has n levels in total, and each level has N bits of information, so k=1, 2...n, t=1,2,...N.

(2) Iterative decoding, each iteration performs the following operations:

(2.1) The left information is updated sequentially from the n+1th layer to the first layer. The update method is as follows, where g is a function, expressed as g(a,b)=sign(a)sign(b)min(| a|,|b|)

L _k,t =g(L _k+1,2t-1 ,L _k+1,2t +R _k,t+N/2 )

L _k,t+N/2 =g(R _k,t ,L _k+1,2t-1 )+L _k+1,2t

(2.2) The right information is updated once from the first layer to the n+1th layer, and the update method is as follows:

R _k+1,2t-1 =g(R _k,t ,L _k+1,2t +R _k,t+N/2 )

R _k+1,2t =g(R _k,t ,L _k+1,2t-1 )+R _k,t+N/2

After updating the right information, return to update the left information until the maximum number of iterations is reached.

(3) Output, make a hard decision on the left information of the first level and output

In the above algorithm, L _k,t represents the left information of the k-th level t-th bit in the polar code factor graph. R _k,t represents the right information of the k-th t-th bit in the polar code factor graph.

The algorithm pseudo code is:

joint detection and decoding

A method for joint detection and decoding of polar code-encoded SCMA disclosed in an embodiment of the present invention combines the factor graphs of SCMA detection and polar code decoding (as shown in FIG. 4 ), so that the probability between detection and decoding is Information can be transferred to each other. In one iteration of joint detection and decoding, the following steps are included:

(1) At least one iterative update is performed between user nodes and functional nodes in the SCMA detection factor graph to obtain the symbol probability information of the user nodes;

(2) Transfer the symbol probability information detected by SCMA to the MAP node and map it to bit probability information, and transfer the bit probability information to the polar code decoding factor map;

(3) After at least one iteration update is performed inside the decoding factor graph, the bit probability information is sent to the MAP node and mapped into symbol probability information, and then sent back to the SCMA detection factor graph for the next iteration.

For example, in an SCMA system with (N=2 ^r , K _p ) the number of polar code coded users is J and the resource length is K, the specific flow of the joint detection algorithm in the embodiment of the present invention is as follows:

1) Initialize UN-to-FN information

2) Perform iterative detection and decoding, and the specific operations include:

a) First, perform one or several iterations between UN and FN to obtain UN-to-FN probability information. The calculation formula is:

b) Prepare inherent information for decoding, the calculation formula is:

c) mapping the inherent information to the left information of the decoding module, and initializing the right information of the first layer;

where z=1,2,..Z,d=1,2,...B, where Z is the number of SCMA transmissions and B is a

The number of bits represented by the SCMA symbol.

d) The decoding module performs one or several iterations. In each iteration, the left information is updated from the n+1th level to the first level according to the following formula, and the right information is updated from the 1st level to the n+1th level. ;

L _{k, t} =g(L _{k+1, 2t-1} , L _{k+1, 2t} +R _{k, t+N/2} )

_Lk,t+N/2 =g( _Rk,t , _Lk+1,2t-1 )+ _Lk+1,2t

_Rk,t =g( _Rk,t , _Lk+1,2t +Rk _,t+N/2 )

L _k,t =g(R _k,t ,L _k+1,2t-1 )+R _k,t+N/2

e) Polar code network transmits inherent information back

Among them, α is an adjustable parameter, between 0-1.

f) Update the UN-to-FN probability information, and re-iterate until a certain number of times

3) Make a decision based on the last soft information to obtain an estimate for the codeword

The pseudo code of the algorithm is as follows:

In the above algorithm, MAP is a function for converting the symbol probability information detected by SCMA into bit probability information. It is described as follows, the log-likelihood ratio of the input B bits, or the probability that each bit is 0 or 1. Since B bits can produce 2 ^B symbols, each of which can be represented by B bits, the symbol probability is the product of the probabilities of the ratios of each bit that make it up. The symbol probabilities can be reconverted to log-likelihood ratios on output. The selection of _Ip and _Id can be determined according to the convergence of separate detection and decoding. This choice enables detection and decoding to converge in I _p ×iternum iterations and I _d ×iternum decoding to converge.

Figure 5 is the comparison result of the bit error rate under various methods. It can be seen from Figure 5 that the algorithm greatly improves the bit error rate of the system. When the bit error rate is 10 ^-4 , the gain of the bit error rate Can reach 2.5dB.

An apparatus for joint detection and decoding of polar code-encoded SCMA disclosed in an embodiment of the present invention includes: an SCMA detection factor graph module, including several user node units and functional node units; a polar code decoding factor graph module, including several A basic computing unit for iterative operations; a first probability information mapping module, including a number of first mapping units, for converting symbol-based probability information into bit-based probability information; a second probability information mapping module, including a number of first Two mapping units for converting bit-based probability information into symbol-based probability information; a first intrinsic information exchange memory for storing bit probability information iteratively updated by the decoded factor graph; and a second intrinsic information exchange A memory for storing the converted bit probability information transmitted from the SCMA detection factor graph. The hardware architecture of this embodiment is shown in FIG. 6 . After obtaining the vector y ^z from the channel, FN and UN start to perform iterative detection and decoding. After several cycles of detection, the symbol probabilities detected by SCMA are converted into probability-likelihood ratios of bits by Mapper, and then stored in the intrinsic information exchange memory 2 . This information is then used in subsequent iterations of polar code decoding. The hardware of polar code decoding is mainly composed of a basic calculation block (Basic Calculation Block, BCB). The internal storage of polar codes is used to store the left information or right information updated in the previous cycle, because they are needed for the iteration of this cycle. At the end of the decoding process, the left information and right information of the last stage are stored in the inherent information exchange memory 1 after a weighted average. Used to provide initial information for the next SCMA iteration. The whole iterative process is a process of alternating detection and decoding, and finally the final result is output by the decoding part.

Among them, the polar code hardware architecture is composed of a basic calculation block (Basic Calculation Block, BCB), and each BCB has two adders and two modules that implement the g function. BCB can realize the iterative formula in polar decoding, and the specific implementation is shown in Figure 7.

Claims (4)

1. the joint detection and decoding method of the SCMA of polar code coding is characterized in that, the factor graph of SCMA detection and polar code decoding is merged, so that the probability information between detection and decoding can be transmitted to each other, In the iteration of joint detection and decoding, the following steps are included: (1) Multiple iterations are performed between the user node UN and the function node FN in the SCMA detection factor graph to obtain the symbol probability information of the user node; the calculation formula of the symbol probability information transmitted by the function node to the user node is:

in,

Indicates the zth transmission of SCMA, the probability information of the symbol m transmitted by the kth FN to the jth UN,

Indicates the zth transmission of SCMA, the probability that the symbol is m is transmitted to the kth FN at the lth UN, c1, c2, _{..c dr-1} represents the symbol of dr-1, and dr is 1 for each row of LDPC The number of elements, c _τj (l) represents the symbol for the l-th UN in this string of symbols, N(k) is the set of all UNs connected to the k-th FN,

is a constant factor whose expression is

where N0 is the noise power, y _j is the j-th symbol of the received vector, and h _k,l are the adjustment coefficients; (2) Transfer the symbol probability information detected by SCMA to the MAP node to map it into bit probability information, and transfer the bit probability information to the polar code decoding factor map;

Map the symbol probability information detected by SCMA to the left information of the decoding module,

is the probability information that the jth UN symbol is m after normalization, n is the series of the decoding factor graph, z=1,2,..Z,d=1,2,...B, where Z is SCMA The number of transmissions, B is the number of bits represented by an SCMA symbol, and MAP ^-1 represents the conversion of symbol probability information into bit probability information; (3) After multiple iterations are performed inside the decoding factor graph, the bit probability information is sent to the MAP node and mapped into symbol probability information, and then sent back to the SCMA detection factor graph for the next iteration. 2. the joint detection and decoding method of the SCMA of a kind of polar code coding according to claim 1, is characterized in that, in step (3), according to formula

Pass the bit probability information obtained by the decoding module to the user node of the SCMA detection module, where R _{n+1, B(z-1)+d} is the right information, MAP represents the conversion of the bit probability information into symbol probability information, α is in between 0-1. 3. the joint detection and decoding method of the SCMA of a kind of polar code coding according to claim 2, is characterized in that, in step (3), according to formula

Update the probability information passed by the user node to the function node and enter the next iteration. 4. the device that realizes the joint detection and decoding method of the SCMA of a kind of polar code encoding described in any one of claim 1-3, is characterized in that, comprising: SCMA detection factor graph module, including several user node units and functional node units; Polar code decoding factor graph module, including several basic calculation units for iterative operations; a first probability information mapping module, including several first mapping units, for converting symbol-based probability information into bit-based probability information; A second probability information mapping module, including several second mapping units, for converting bit-based probability information into symbol-based probability information; a first intrinsic information exchange memory for storing bit probability information iteratively updated by the decoded factor graph; and a second intrinsic information exchange memory for storing the converted bit probability information outgoing from the SCMA detection factor map.

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