Joint detection and decoding method and device for polar code coded multiple-input multiple-output system

Abstract

The present invention provides a joint detection and decoding method and apparatus for a polar code coded multi-input multi-output (MIMO) system. The method comprises: in a MIMO system using polar code coding and multi-ary quadrature amplitude modulation, setting an initial radius and a bit flip threshold, and searching in a search space in a detection order from the N / mth layer to the first layer, with the initial radius determined based on the noise variance; during the search process, pruning search paths that do not meet a first preset condition, determining the first search path that meets the first preset condition as the reference path; and pruning search paths that meet a second preset condition until a valid path is output as the path with the shortest Euclidean distance to the received signal, and obtaining a decoding result based on the valid path. Based on depth-first spherical detection and decoding, the present invention implements bidirectional pruning by setting an initial radius and a bit flip threshold, thereby improving the error correction performance and convergence speed of the detection and decoding.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technologies, and in particular to a joint detection and decoding method and device for a polar code coded multiple-input multiple-output system. Background Art

[0002] In related technologies, detection and decoding of Multiple Input Multiple Output (MIMO) systems mainly include three methods: one is separation of detection and decoding, the second is iterative detection and decoding, and the third is joint detection and decoding.

[0003] Current joint detection and decoding methods are generally based on the sphere decoding (SD) algorithm using a breadth-first search (BFS) strategy. Compared to separate detection and decoding, or iterative detection and decoding, joint detection and decoding methods based on the breadth-first sphere decoding algorithm achieve better results in terms of complexity.

[0004] However, the fixed number of paths pruned at each layer in this method limits the size of the search space, resulting in a gap between the error correction performance and the maximum likelihood estimation (ML). Summary of the Invention

[0005] To address the above-mentioned problems in related technologies, embodiments of the present invention provide a joint detection and decoding method and apparatus for a polar code coded multiple-input multiple-output (MIMO) system, which improves the error correction performance of the polar code coded MIMO system while ensuring low complexity.

[0006] In a first aspect, an embodiment of the present invention provides a joint detection and decoding method for a polar code MIMO system, including:

[0007] In a multiple-input multiple-output system with polar coding and multi-ary quadrature amplitude modulation, an initial radius and a bit flip threshold are set, and a search is performed in a search space in a detection order from the N / mth layer to the first layer. The initial radius is determined based on the noise variance.

[0008] During the search process, the search paths that do not meet the first preset condition are pruned, and the first search path that meets the first preset condition is determined as the reference path;

[0009] Pruning the search paths that meet the second preset condition until a valid path is output as the path with the shortest Euclidean distance to the received signal, and obtaining a decoding result according to the valid path;

[0010] Wherein, N is the codeword length of the polar code, and m is the number of bits corresponding to each real number symbol;

[0011] The first preset condition includes: when searching to the i-th layer, the partial Euclidean distance of the search path is less than the initial radius, and when searching to the first layer, the total Euclidean distance of the search path is less than the initial radius; the value range of i is 1 to N / m;

[0012] The second preset condition includes: a ratio of the number of flipped bits of the search path to the number of flipped bits of the reference path is greater than the bit flip threshold.

[0013] In some embodiments, before performing the polar code encoding on the information bits, the transmitting end in the MIMO system further performs cascaded CRC encoding;

[0014] The first preset condition also includes:

[0015] When searching to the first layer, the search path passes the CRC check and the total Euclidean distance is less than the initial radius;

[0016] The second preset condition also includes:

[0017] The search path failed the CRC check when searching to layer 1.

[0018] In some embodiments, the method further comprises:

[0019] In the case that the valid path cannot be found, the initial radius is adjusted according to a preset step value.

[0020] In some embodiments, the initial radius is the product of the noise variance and the number of real symbols.

[0021] In some embodiments, the total Euclidean distance of the search path is equal to the sum of the increments of the partial Euclidean distances corresponding to each layer.

[0022] In some embodiments, the partial Euclidean distance corresponding to the i-th level of the search path is determined by the following steps:

[0023] Determine the information bits and frozen bits corresponding to the i-th layer of the search path according to the information bit set after bit flipping and permutation;

[0024] Determine M based on the information bits and the frozen bits i There are m candidate bits, where M i ∈{1,2,4,...,2 m};

[0025] Determine the M corresponding to the i-th layer i Codewords, and modulation mapping is Mi A real number symbol;

[0026] Determine the M i The partial Euclidean distance corresponding to the real number symbol.

[0027] In a second aspect, an embodiment of the present invention further provides a joint detection and decoding apparatus for a polar code MIMO system, including:

[0028] a setting module, configured to set an initial radius and a bit flip threshold in a multiple-input multiple-output system using polar coding and multi-ary quadrature amplitude modulation, and to search in a search space in a detection order from the N / mth layer to the first layer, wherein the initial radius is determined based on the noise variance;

[0029] A first pruning module is used to prune the search paths that do not meet the first preset condition during the search process, and determine the first search path that meets the first preset condition as the reference path;

[0030] a second pruning module, configured to prune search paths that meet a second preset condition until a valid path is output as a path with the shortest Euclidean distance to the received signal, and obtain a decoding result according to the valid path;

[0031] Wherein, N is the codeword length of the polar code, and m is the number of bits corresponding to each real number symbol;

[0032] The first preset condition includes: when searching to the i-th layer, the partial Euclidean distance of the search path is less than the initial radius, and when searching to the first layer, the total Euclidean distance of the search path is less than the initial radius; the value range of i is 1 to N / m;

[0033] The second preset condition includes: a ratio of the number of flipped bits of the search path to the number of flipped bits of the reference path is greater than the bit flip threshold.

[0034] In a third aspect, an embodiment of the present invention further provides a receiver, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the joint detection and decoding method for a polar code coded MIMO system described in any one of the first aspects above is implemented.

[0035] In a fourth aspect, an embodiment of the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor, the joint detection and decoding method for any polar code coded MIMO system described in the first aspect above is implemented.

[0036] In a fifth aspect, an embodiment of the present invention further provides a computer program product, including a computer program. When the computer program is executed by a processor, the joint detection and decoding method for the polar code coded MIMO system described in any one of the first aspects above is implemented.

[0037] The joint detection and decoding method and apparatus for a polar code MIMO system provided in embodiments of the present invention implement bidirectional pruning by setting an initial radius and a bit flip threshold, based on depth-first sphere detection and decoding. This improves the error correction performance and convergence speed of the joint detection and decoding of the polar code MIMO system. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] In order to more clearly illustrate the technical solutions in the present invention or the prior art, a brief introduction will be given below to the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0039] Figure 1 This is a flow chart of a joint detection and decoding method for a polar code MIMO system provided by an embodiment of the present invention;

[0040] Figure 2 This is a second flow chart of the joint detection and decoding method for a polar code MIMO system provided by an embodiment of the present invention;

[0041] Figure 3 2 is a schematic diagram comparing the frame error rate performance of different detection and decoding methods for a MIMO system provided by an embodiment of the present invention;

[0042] Figure 4 1 is a schematic diagram comparing the computational complexity of different detection and decoding methods for a MIMO system provided by an embodiment of the present invention;

[0043] Figure 5 1 is a schematic structural diagram of a joint detection and decoding device for a polar code MIMO system provided by an embodiment of the present invention;

[0044] Figure 6 It is a schematic diagram of the hardware structure of the receiver provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0045] In order to better describe the technical solutions in the embodiments of the present invention, relevant knowledge is introduced below.

[0046] (1) MIMO system

[0047] As data communication requirements continue to increase, traditional communications are approaching the Shannon limit under certain channel coding conditions. The Shannon limit, or Shannon capacity, of a channel refers to the maximum transmission rate for error-free transmission over a channel subject to random bit errors. MIMO technology effectively increases channel capacity and has been a core technology since the third generation of mobile communications.

[0048] To significantly increase channel capacity, MIMO uses multiple antennas at both the transmitter and receiver, forming multiple channels between the transmitter and receiver. In practical applications, to improve error performance, MIMO systems are often combined with error correction coding techniques. At the transmitter, information bits are first source-channel coded and then modulated into symbols in a complex constellation. At the detector, the MIMO detector estimates the transmitted symbols from the received signal. The decoder then recovers the information bits from the estimated symbols. While error correction coding can effectively improve error performance, the additional decoding module significantly increases the overall receiver implementation complexity.

[0049] MIMO detection is a technique used by a receiver to recover the transmitted signal based on the received signal. Linear detection algorithms include zero forcing (ZF) and minimum mean squared error (MMSE). ZF detection can completely eliminate inter-antenna interference but increases noise power. MMSE strikes a balance between the two, maximizing the signal-to-noise ratio at the receiver and achieving greater coding gain than ZF. Both methods have low algorithmic complexity and are relatively simple to implement, but they suffer from poor bit error rate performance. ML detection is the optimal detection method, achieving better bit error rate performance, but is more complex and difficult to implement.

[0050] In small-scale scenarios, the SD algorithm can achieve bit error rate performance close to that of ML while maintaining a certain level of complexity. The SD algorithm's concept is to limit the search area using a sphere in the multidimensional constellation space. When the sphere is sufficiently large, it can achieve performance comparable to ML detection. While the complexity of the ML detection algorithm, which uses an exhaustive search, increases exponentially with the number of antennas, the complexity of the SD algorithm scales polynomially with the number of antennas over a wide range of signal-to-noise ratios. The SD algorithm can achieve ML decoding performance with less computational effort.

[0051] (2) Polarization code

[0052] Polar codes are an error-correcting coding scheme used for signal transmission. Polar codes can implement capacity code construction for symmetric binary discrete memoryless channels and binary erasure channels, offering low encoding and decoding complexity and high hardware implementation capabilities. Polar codes have been selected as the downlink and uplink short code control channel scheme for enhanced mobile broadband (eMBB) scenarios for fifth-generation mobile communications (5G).

[0053] The core of polar code construction lies in channel polarization processing. On the encoding side, each subchannel exhibits different reliability. As the code length continues to increase, some channels approach perfect channels with a capacity close to 1, meaning no errors; others approach pure noise channels with a capacity close to 0. Information is transmitted between channels with a capacity close to 1, thereby improving information transmission efficiency. On the decoding side, the polarized channels can be decoded using simple successive interference cancellation, achieving performance similar to ML decoding with lower complexity.

[0054] Polar codes are currently the only method rigorously proven to reach the Shannon limit. Common polar code decoding algorithms include Successive Cancellation (SC) and Belief Proporg (BP), both of which suffer from performance penalties due to limited block lengths in short code scenarios. In such cases, the SD algorithm can approach ML performance. However, selecting the initial radius in the SD algorithm is a challenge; an inappropriate initial radius can lead to significant computational complexity.

[0055] (3) Detection and decoding of MIMO systems

[0056] Currently, the detection and decoding of MIMO systems mainly include the following three methods:

[0057] The first approach is to separate detection and decoding. A MIMO detector is used to recover the transmitted modulated signal from the received signal, and a decoder is then used to recover the detector output into signal bits. This approach optimizes both the detection and decoding modules to maximize the MIMO system structure and coding architecture, respectively. Information is transmitted unidirectionally from the detector to the decoder, and both operate independently, lacking overall optimization and exhibiting limitations in both complexity and operational efficiency.

[0058] The second approach is an iterative detection and decoding method, which feeds the decoder output back to the detector input to iterate information. This improves the system's error correction performance compared to the separate detection and decoding methods. However, iteration increases the system's time resource consumption and latency.

[0059] The third approach is the combined detection and decoding method, which leverages the properties of the channel and coding to integrate the detection and decoding algorithms, achieving both detection and decoding in a single step. Compared to separate detection and decoding methods, the combined detection and decoding method can leverage the structural information of the code to directly recover the signal bits from the received symbols, thereby improving error correction performance and reducing complexity. Compared to iterative detection and decoding methods, the combined detection and decoding method can omit the repeated iteration of information between the detector and decoder, reducing the consumption of time resources and the storage space required for information iteration.

[0060] (4) Joint detection and decoding based on breadth-first sphere decoding algorithm

[0061] For polar-coded MIMO systems, current joint detection and decoding methods generally use the breadth-first sphere decoding algorithm. This method exploits the similar properties of MIMO detection and polar-coded encoding, as follows:

[0062] The channel matrix undergoes orthogonal and rectangular matrix decomposition (QR decomposition) to obtain a unitary matrix and an upper triangular matrix. By eliminating the unitary matrix, the signal can be recovered from the product of the upper triangular matrix and the transmitted signal. Polar code encoding can be expressed as the product of the information vector, the bit-flip permutation matrix, and the lower triangular matrix.

[0063] Utilizing the bijective nature of modulation, a single-stage tree search algorithm is used to simultaneously implement MIMO detection and channel decoding. The permuted information bits are grouped and mapped to each level of the tree according to the modulation order. Path extensions at each level are determined by constructing the permuted information bits and frozen bits, leading to a hierarchical tree search. Finally, the path with the smallest Euclidean distance to the received signal is output. After path extension, the search is performed in ascending order of the Euclidean distance between each path and the received signal.

[0064] The sphere decoding algorithms for polar code encoding and MIMO detection are introduced as follows:

[0065] ① Polarization code encoding

[0066] Polar codes create polarization by separating and merging channels, causing some channel capacities to approach 1 while the remaining channels approach 0. The higher the channel capacity, the higher the credibility.

[0067] for Polar code, where N is the codeword length and K is the information bit length, K ≤ N. The polar code construction process is the process of selecting the most reliable K polarization channels from N polarization channels. Polar code places K information bits at the most reliable positions, and the remaining NK positions are frozen bits (usually set to 0). The K positions with high reliability constitute the information bit set gather The cardinality is K, where the elements Satisfy 1≤a i ≤N,1≤i≤K, Represents an integer set. The remaining NK positions constitute the frozen bit set gather The cardinality is NK, where the elements Satisfy 1≤a i c ≤N, 1≤i≤NK, Represents a set of integers.

[0068] Define the code rate R = K / N, information vector u = [u1,u2,...,u N ], codeword x=[x1,x2,...,x N ]. K information bits are arranged according to the set The index in is put into the information vector u, and the remaining NK frozen bits are set The index in is put into the information vector u. In the information vector u=[u1,u2,...,u N ], the element element

[0069] The polar code encoding process can be expressed as:

[0070]

[0071] Where x=[x1,x2,...,x N ] is the codeword generated after polar code encoding, x i ∈{0,1}, 1≤i≤N; u is the information vector; To generate the matrix, is a set of real numbers; B is a bit-flip permutation matrix, is a lower triangular matrix The nth-order Kronecker product, n = log2N.

[0072] ② Sphere decoding algorithm in MIMO detection

[0073] For a N t transmit antennas and N r For a flat MIMO channel with multiple receiving antennas, the MIMO channel model can be expressed as:

[0074]

[0075] in, To receive the signal, is the Gaussian channel matrix, To send a signal, is Gaussian white noise, The i-th row and j-th column of the channel matrix represent the complex channel gain from the j-th transmitting antenna to the i-th receiving antenna.

[0076] For ease of processing, the above complex model is generally decomposed into real values ​​(RVD) to obtain the equivalent real domain channel model as follows:

[0077] y=Hs+n

[0078] in, To receive the signal, is the channel matrix, To send a signal, is Gaussian white noise, represents the set of real numbers.

[0079] After the conversion from the complex domain to the real domain, a real symbol set can be obtained, which contains the orthogonal components and in-phase components of all symbols in the original complex constellation. The cardinality of the real symbol set is M is the size of the complex constellation, and each real number symbol corresponds to bits. Perform QR decomposition on the real channel matrix H:

[0080] H=QR

[0081] The unitary matrix can be obtained:

[0082]

[0083] And the upper triangular matrix:

[0084]

[0085] Multiply both sides of the channel equation by Q H ,get:

[0086] z=Q H y=Rs+Q H n=Rs+v

[0087] Among them, because Q is a unitary matrix, v = Q H n is still Gaussian white noise.

[0088] At this time, MIMO maximum likelihood detection can be expressed as:

[0089]

[0090] Based on the above formula, sphere decoding algorithm can be used to implement MIMO detection.

[0091] Compared with the detection and decoding separation and detection and decoding iterative methods, the detection and decoding joint method based on the breadth-first sphere decoding algorithm has achieved better results in terms of complexity. However, the fixed number of paths pruned at each layer in this method limits the size of the search space, and there is still a gap between the error correction performance and ML.

[0092] To address the aforementioned problems in related technologies, embodiments of the present invention provide a joint detection and decoding method and apparatus for a polar-coded multiple-input multiple-output (MIMO) system. Based on sphere detection and decoding based on a depth-first search (DFS) strategy, this method and apparatus improve the error correction performance of detection and decoding in a polar-coded MIMO system while ensuring low complexity by properly setting the initial radius and bit-flip threshold.

[0093] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0094] Figure 1 FIG. 1 is a flow chart of a joint detection and decoding method for a polar code MIMO system provided by an embodiment of the present invention. Figure 1 As shown, the joint detection and decoding method for a polar code MIMO system provided in an embodiment of the present invention includes at least the following steps:

[0095] Step 101: In a multiple-input multiple-output system with polar coding and multi-ary quadrature amplitude modulation, an initial radius and a bit flip threshold are set, and a search is performed in a search space in a detection order from the N / mth layer to the first layer. The initial radius is determined based on the noise variance.

[0096] Wherein, N is the codeword length of the polar code, and m is the number of bits corresponding to each real number symbol.

[0097] Specifically, when there is N t transmit antennas and N r In a flat MIMO uplink system with multiple receiving antennas, multiple quadrature amplitude modulation (M-QAM) is used, and each symbol occupies M c=log2M bits, channel coding uses Polar code encoding, code length N bits, information bits K bits. The channel has n c =N / (M c N t ), the channel can be expressed as:

[0098]

[0099] Let u rev =uB, where u is the information vector and B is the bit flip permutation matrix. The modulation process is:

[0100] s=map{x}

[0101] The polar code encoding process is:

[0102]

[0103] The ML detection and decoding are jointly expressed as:

[0104]

[0105] in, and χ K They represent the information bits, frozen bits and K-dimensional GF(2) fields after bit flipping and permutation, respectively.

[0106] Step 102: During the search process, prune the search paths that do not meet the first preset condition, and determine the first search path that meets the first preset condition as the reference path.

[0107] The first preset condition includes: when searching to the i-th layer, the partial Euclidean distance of the search path is less than the initial radius, and when searching to the first layer, the total Euclidean distance of the search path is less than the initial radius; the value range of i is 1 to N / m;

[0108] Step 103: Prune the search paths that meet the second preset condition until a valid path is output as the path with the shortest Euclidean distance to the received signal, and obtain a decoding result based on the valid path.

[0109] The second preset condition includes: the ratio of the number of flipped bits of the search path to the number of flipped bits of the reference path is greater than a bit flip threshold.

[0110] Specifically, the bijective property of modulation is utilized, and the flipped and permuted information bits are grouped and mapped to each level of the tree according to the modulation order. The path extension of each level is determined by constructing the flipped information bits and frozen bits, thereby realizing the tree search by hierarchical enumeration, and finally outputting the path with the smallest Euclidean distance to the received signal.

[0111] Under Gaussian white noise, the received signal has a Gaussian distribution centered around the transmitted signal in the search space. Therefore, in the embodiments of the present invention, the initial radius is set based on the noise variance. This setting not only reduces the search space but also improves the performance of pruning based on noise bit flipping.

[0112] In addition to setting the initial radius, the embodiment of the present invention also sets a bit flip threshold. After the reference path is determined, in the subsequent search process, those paths whose ratio of flipped bits exceeds the bit flip threshold compared with the reference path are discarded.

[0113] Theoretically, the path with the shortest Euclidean distance to the received signal should be used as the reference path. However, finding the shortest path using a complete SD algorithm can introduce significant latency, and due to inherent algorithmic errors, the resulting path may not necessarily be the shortest. Therefore, in this embodiment of the present invention, the first path found during the search whose total Euclidean distance falls within the initial radius is used as the reference path.

[0114] Therefore, in some embodiments of the present invention, the following pruning method is adopted: an initial radius is set based on the noise variance, and a bit flip threshold is set. The search space is searched in the order of detection from layer N / m to layer 1, and the search is performed in ascending order of the Euclidean distances between each search path and the received signal. During the search process, for any search path, if the partial Euclidean distance at layer i is greater than or equal to the initial radius, the path is discarded. This process continues until a path is found for the first time, and if the partial Euclidean distance at layer i is less than the initial radius, and the total Euclidean distance at layer 1 is less than the initial radius, the path is determined as the reference path. After determining the reference path, the search radius corresponding to the reference path (i.e., the Euclidean distance between the reference path and the received signal) can be updated for subsequent Euclidean distance comparisons. In subsequent searches, for any search path, if the ratio of the number of flipped bits to the number of flipped bits in the reference path is greater than the set bit flip threshold, the path is discarded. This continues until a valid path is output as the path with the shortest Euclidean distance to the received signal. Then the decoding result is obtained according to the valid path.

[0115] The joint detection and decoding method for a polar code MIMO system provided in an embodiment of the present invention implements bidirectional pruning by setting an initial radius and a bit flip threshold based on depth-first sphere detection and decoding, thereby improving the error correction performance and convergence speed of the joint detection and decoding.

[0116] In some embodiments, before the transmitting end in the MIMO system performs polar code encoding on the information bits, it also performs cascaded CRC encoding;

[0117] The first precondition also includes:

[0118] When searching to the first layer, the search path passes the CRC check and the total Euclidean distance is less than the initial radius;

[0119] The second precondition also includes:

[0120] The search path failed the cyclic redundancy check when searching to layer 1.

[0121] Specifically, a cascaded cyclic redundancy check (CRC) can further improve the error correction performance of joint detection and decoding. On the one hand, under noise interference, the path with the shortest Euclidean distance to the received signal found by the depth-first sphere decoding algorithm is not necessarily the correct shortest path. On the other hand, the error correction performance of the sphere decoding algorithm is only related to the distance between each path. Therefore, adding a CRC to the short code and long polar code does not incur the same performance loss as the cyclic redundancy check assisted successive cancellation list (CA-SCL).

[0122] Therefore, in some embodiments of the present invention, before polar code encoding is performed at the transmitter, K information bits are concatenated with L CRC bits via a CRC encoder. These K+L bits are then used to construct an N-bit bit vector via the polar code encoder. At the receiver, when the sphere decoding search reaches layer 1, a CRC check is performed on the search path. Only paths that pass the check are retained. Correspondingly, the first preset condition also includes: the search path passes the CRC check when the search reaches layer 1, and the total Euclidean distance is less than the initial radius.

[0123] It is conceivable that, in the subsequent search process, only search paths that pass the CRC check and whose ratio of flipped bits to the number of flipped bits of the reference path is less than the bit flip threshold will be retained. Correspondingly, the second preset condition also includes: the search path fails the CRC check when searching to layer 1.

[0124] The joint detection and decoding method for a polar code MIMO system provided in an embodiment of the present invention further improves the error correction performance of the joint detection and decoding by adding CRC concatenated coding before polar code encoding and adding a CRC check step when determining the reference path and valid path.

[0125] In some embodiments, the joint detection and decoding method for a polar code MIMO system further includes:

[0126] If a valid path cannot be found, the initial radius is adjusted according to the preset step value.

[0127] Specifically, if a valid path cannot be found, the initial radius is increased by a step value, and pruning is performed based on the adjusted initial radius. The step value is pre-set. Selecting an appropriate step value to correct the initial radius can improve detection performance. The step value can be a simple value increase or a step that represents the total error probability when Gaussian noise falls outside a threshold. For example, a step value of 0.1 times the initial radius can be used to compensate for the initial radius.

[0128] In some embodiments, the initial radius is the product of the noise variance and the number of real symbols.

[0129] Specifically, the initial radius is set based on the noise variance and is determined by weighting the noise variance. Selecting appropriate weights can not only reduce the search space but also improve pruning performance. In some embodiments, the initial radius can be set as the product of the noise variance and the number of real symbols.

[0130] In some embodiments, the total Euclidean distance of the search path is equal to the sum of the increments of the partial Euclidean distances corresponding to each layer.

[0131] Specifically, for any search path, the total Euclidean distance to the first layer is equal to the sum of the incremental partial Euclidean distances for each layer. For the path to the first layer, the relationship between its total Euclidean distance and the current search radius must be determined.

[0132] Since R and They are all triangular matrices, so the calculation of the total Euclidean distance can be decomposed into the sum of the partial Euclidean distance increments corresponding to each real number symbol, satisfying the following calculation formula:

[0133]

[0134] Among them, f i,j express The number of bits corresponding to the real number symbol m=M c / 2, divide N bits into N / m=2n c N t Layer, when searching, i goes from layer N / m to layer 1, and every time a real number symbol is determined, that is, m consecutive bits, its partial Euclidean distance PED can be determined. i Therefore, the information bits can be recovered using a joint detection and decoding method based on a depth-first sphere decoding algorithm, referred to as SD-JDD in this paper.

[0135] In some embodiments, the partial Euclidean distance corresponding to the i-th level of the search path is determined by the following steps:

[0136] Determine the information bits and frozen bits corresponding to the i-th layer of the search path according to the information bit set after bit flipping and permutation;

[0137] Determine M based on the information bit and frozen bit i There are m candidate bits, where M i ∈{1,2,4,...,2 m};

[0138] Determine the M corresponding to the i-th layer i Codewords, and modulation mapping is M i A real number symbol;

[0139] Determine M i The partial Euclidean distance corresponding to the real number symbol.

[0140] Specifically, the ultimate goal of joint detection decoding is to Directly recover the information vector u after bit flipping and permutation rev =uB.

[0141] After QR decomposition of the real channel matrix H, the unitary matrix is ​​obtained and the upper triangular matrix Multiply both sides of the channel equation by Q H ,get:

[0142] z=Q H y=Rs+Q H n=Rs+v

[0143] Transform the problem from receiving signal y to starting from z. Through the information bit set obtained above Frozen bit set And the bit flip permutation matrix B, we can get the set after bit flip permutation and The polar code has a code length of N, with each real number symbol corresponding to m bits. Joint detection and decoding is divided into N / m layers, with detection performed in order from layer N / m to layer 1.

[0144] For the i-th layer, the calculation process of its partial Euclidean distance is as follows:

[0145] According to the information bit set after bit flipping The information bits and frozen bits corresponding to the i-th layer can be determined, thereby determining M i There are m candidate bits, where M i ∈{1,2,4,...,2 m This is because the information bit can be 0 or 1, while the frozen bit is fixed to 0.

[0146] Furthermore, the current M i The polar code corresponding to this extended calculation is:

[0147]

[0148] That is, the information bits from layer i to layer N / m are The product of the GF(2) fields of the corresponding columns of .

[0149] Thus we get M of the i-th layer i Possible codewords p=1,2,...,M i Then the modulation is mapped to the M of the i-th layer i Real number symbols p=1,2,...,M i . The final calculation is from [z i ,z i+1 ,...,z N / m ]arrive The partial Euclidean distance of the product with the upper triangular matrix R.

[0150] The technical solution provided by the present invention is further described below with reference to a specific embodiment.

[0151] In the case of N t transmit antennas and N r In a flat MIMO uplink system with multiple receiving antennas, M-QAM modulation is used, and each symbol occupies M c =log2M bits, channel coding uses Polar code encoding, code length N bits, information bits K bits. The channel has n c =N / (M c N t ), the channel can be expressed as:

[0152]

[0153] Let u rev =uB, the modulation process is s=map{x}, then The ML detection and decoding are jointly expressed as:

[0154]

[0155] in, and χ K represent the information bit, frozen bit and K-dimensional GF(2) field after bit flipping and permutation respectively. They are all triangular matrices, so the calculation of the total Euclidean distance can be decomposed into the sum of the partial Euclidean distance increments corresponding to each symbol:

[0156]

[0157] Among them, fi,j express The number of bits corresponding to the real number symbol is m=M c / 2, divide N bits into N / m=2n c N t When searching, the value of i is from the N / mth layer to the 1st layer. Every time a real number symbol is determined, that is, m consecutive bits, its partial Euclidean distance PED can be determined. i Therefore, the depth-first sphere decoding method, namely SD-JDD, can be used to recover the information bits.

[0158] Furthermore, a cascaded CRC is used to improve the error correction performance of the combined detection and decoding method, called CA-SD-JDD. On the one hand, under noise interference, the path with the shortest Euclidean distance found by SD-JDD may not always be the correct path. On the other hand, the error correction performance of the SD algorithm is only related to the distance spectrum of each path. Therefore, adding a CRC to the short code and long polar code does not result in the same performance loss as CA-SCL.

[0159] At the transmitter, before the polar code encoder, K information bits are concatenated with L CRC bits through the CRC encoder. These K + L bits are then passed through the polar code encoder to construct an N-bit bit vector. The transmitter structure remains the same as above. At the receiver, when the SD search reaches layer 1, the path undergoes a CRC check, and only those paths that pass the check are retained.

[0160] Furthermore, based on the CA-SD-JDD method, a bidirectional pruning strategy can be used to accelerate the convergence speed while maintaining near-ML performance, which is called CA-SFD-JDD.

[0161] When the search space is very large, pruning is performed based on the noise pattern. Under Gaussian white noise, the received signal has a Gaussian distribution centered around the transmitted signal in the search space. Therefore, pruning is performed by using the first path whose Euclidean distance is within the initial radius as the reference path. A bit flip threshold is set, and in subsequent searches, paths whose bit flip ratio exceeds the bit flip threshold compared to the reference path are discarded.

[0162] Under the above conditions, setting the initial radius not only reduces the search space but also improves the performance of pruning methods based on noise bit flipping. Similarly, based on Gaussian white noise, the initial radius can be set to the product of the noise variance and the number of symbols. If no valid path is found, the initial radius is increased by a step value.

[0163] In summary, CA-SFD-JDD sets the initial radius and the bit flip threshold based on the noise variance. After searching the SD layer from layer N / m to layer 1, it performs a CRC check and uses the first valid path as the reference path. In subsequent searches, only paths that pass the CRC check and have a bit flip count below the threshold are retained.

[0164] To further verify the effectiveness of the joint detection and decoding method for the MIMO system proposed in the embodiment of the present invention, Figure 2 FIG2 is a second flow chart of the joint detection and decoding method for a polar code MIMO system provided by an embodiment of the present invention. Figure 2 As shown:

[0165] 2-bit information, 2-bit CRC, 8-bit polar code encoding, In the 16-order quadrature amplitude modulation, bit flip threshold is set to 1, 2×2 MIMO system (denoted as C2A-SFD1-JDD), there are 4 layers of trees, each layer corresponds to 2 bits, according to the information bit It can be concluded that the path extensions from the 4th layer to the 1st layer are {4, 2, 2, 1}, omitting one expansion. The partial Euclidean distance or total Euclidean distance that can be calculated for each path are as follows: Figure 2 shown.

[0166] If the Euclidean distance of a path exceeds the current search radius, the path will be cut off. If the end of a path is reached for the first time, the CRC check ( Figure 2 If the total Euclidean distance is less than the initial radius, the path will become the reference path and the search radius will be updated. If the bit flip of a path is higher than the threshold compared with the reference path, the path will be cut off. The end of the path will continue to be updated through CRC check. We assume that the initial radius is 37.6, and after the first valid path ( Figure 2 The baseline path becomes [00 01 00 01], and the search radius becomes 35.2. Paths with bit flips greater than 1 are discarded, and the output after the second round of search is [00 01 00 11].

[0167] Further, Figure 3 FIG. 1 is a schematic diagram comparing the frame error rate performance of different detection and decoding methods for the MIMO system provided by an embodiment of the present invention, such as Figure 3As shown, the embodiment of the present invention provides the performance simulation of SD-JDD, CA-SD-JDD and CA-SFD-JDD in a 4×4 MIMO system with polar code (N=64) encoding and 16-order orthogonal amplitude modulation, assuming that the channel conditions are perfectly known. In CA-SD-JDD, 4-bit and 6-bit CRC check codes are selected respectively. In CA-SFD-JDD, 2-bit and 4-bit bit flip thresholds are set under 4-bit and 6-bit CRC check codes respectively. Among them, p and t in CpA-SD-JDD and CpA-SFDt-JDD represent the CRC length and bit flip threshold respectively.

[0168] Figure 3 Part (a) gives the polar code The comparison of the Frame Error Rate (FER) performance under different conditions shows that both CA-SD-JDD and CA-SFD-JDD outperform SD-JDD. Among them, the 6-bit CRC performs better than the 4-bit one. Under the high bit rate of 57 information bits, the introduction of CRC does not lead to performance degradation. On the contrary, the performance is improved after using a longer CRC code. This proves that the distance spectrum between each path in the depth-first sphere decoding algorithm plays a decisive role in the error correction performance. It can also be noted that the application of the bidirectional pruning strategy has almost no impact on the error correction performance of the algorithm. At FER=10 -3 At this point, the performance of C6A-SD-JDD is nearly 2dB better than that of SD-JDD. Figure 3 In part (b), the performance advantage of CA-SD-JDD is more significant, with 6 CRC bits in 10 -3 At the same time, bidirectional pruning allows CA-SFD-JDD to maintain almost the same performance as CA-SD-JDD at lower bit rates.

[0169] Further, Figure 4 FIG. 1 is a schematic diagram comparing the computational complexity of different detection and decoding methods for the MIMO system provided by an embodiment of the present invention. Figure 4 As shown, this embodiment of the present invention provides a complexity simulation of SD-JDD, CA-SD-JDD, and CA-SFD-JDD in a 4×4 MIMO system with polar code (N=64) encoding and 16-order quadrature amplitude modulation. The computational complexity is measured by the number of nodes in a depth-first tree search.

[0170] The complexity of the search method based on depth-first sphere decoding depends on the node parameters of the search tree. Different input parameters result in a highly random computational complexity when searching the tree. Therefore, Monte Carlo methods can be used to analyze the mathematical expectation of the computational complexity of different detection and decoding methods. The computational complexity is defined as the number of nodes in the depth-first tree search. Statistically, this number of nodes is linearly related to the number of additions and multiplications in the real number domain.

[0171] Figure 4 As can be seen from the figure, CA-SD-JDD requires more search nodes than SD-JDD. The difference becomes more pronounced with increasing CRC bits and lower bitrates. The bidirectional pruning strategy reduces the complexity of CA-SD-JDD, especially at high bitrates and low SNRs. Furthermore, despite the increased complexity of the search space due to the CRC, CA-SD-JDD can gradually converge to SD-JDD as the SNR increases.

[0172] In summary, CA-SFD-JDD can reduce complexity in high-code rate scenarios without compromising error correction performance. For MIMO systems with short-code and long polar code encoding, ML performance can be achieved with relatively reasonable complexity.

[0173] The following describes a joint detection and decoding apparatus for a polar code MIMO system provided by the present invention. The joint detection and decoding apparatus for a polar code MIMO system described below and the joint detection and decoding method for a polar code MIMO system described above can be referenced to each other.

[0174] Figure 5 FIG. 1 is a structural diagram of a joint detection and decoding device for a polar code MIMO system provided by an embodiment of the present invention. Figure 5 As shown, the device at least includes:

[0175] A setting module 501 is configured to set an initial radius and a bit flip threshold in a multiple-input multiple-output system using polar coding and multi-ary quadrature amplitude modulation, and to search the search space in a detection order from the N / mth layer to the first layer. The initial radius is determined based on the noise variance.

[0176] A first pruning module 502 is configured to prune search paths that do not meet a first preset condition during a search process, and determine a first search path that meets the first preset condition as a reference path;

[0177] A second pruning module 503 is configured to prune the search paths that meet the second preset condition until a valid path is output as the path with the shortest Euclidean distance to the received signal, and obtain a decoding result based on the valid path;

[0178] Where N is the codeword length of the polar code, and m is the number of bits corresponding to each real number symbol;

[0179] The first preset condition includes: when searching to the i-th layer, the partial Euclidean distance of the search path is less than the initial radius, and when searching to the first layer, the total Euclidean distance of the search path is less than the initial radius; the value range of i is 1 to N / m;

[0180] The second preset condition includes: a ratio of the number of flipped bits of the search path to the number of flipped bits of the reference path is greater than a bit flip threshold.

[0181] In some embodiments, before the transmitting end in the MIMO system performs polar code encoding on the information bits, it also performs cascaded CRC encoding;

[0182] The first precondition also includes:

[0183] When searching to the first layer, the search path passes the CRC check and the total Euclidean distance is less than the initial radius;

[0184] The second precondition also includes:

[0185] The search path failed the cyclic redundancy check when searching to layer 1.

[0186] In some embodiments, the apparatus further comprises:

[0187] The adjustment module is used to adjust the initial radius according to a preset step value when a valid path cannot be found.

[0188] In some embodiments, the initial radius is the product of the noise variance and the number of real symbols.

[0189] In some embodiments, the total Euclidean distance of the search path is equal to the sum of the increments of the partial Euclidean distances corresponding to each layer.

[0190] In some embodiments, the partial Euclidean distance corresponding to the i-th level of the search path is determined by the following steps:

[0191] Determine the information bits and frozen bits corresponding to the i-th layer of the search path according to the information bit set after bit flipping and permutation;

[0192] Determine M based on the information bit and frozen bit i There are m candidate bits, where M i ∈{1,2,4,...,2 m};

[0193] Determine the M corresponding to the i-th layer i Codewords, and modulation mapping is M i A real number symbol;

[0194] Determine M i The partial Euclidean distance corresponding to the real number symbol.

[0195] It should be noted that the methods and devices provided in each embodiment of this aspect are based on the same inventive concept. Since the principles of solving problems by the methods and devices are similar, the implementation of the devices and methods can refer to each other, and the repeated parts will not be repeated.

[0196] Figure 6 FIG. 1 is a schematic diagram of the hardware structure of a receiver provided by an embodiment of the present invention, such as Figure 6 As shown, the receiver may include: a processor 610, a communication interface 620, a memory 630, and a communication bus 640. The processor 610, the communication interface 620, and the memory 630 communicate with each other via the communication bus 640. The processor 610 may call logic instructions in the memory 630 to execute a joint detection and decoding method for a polar code MIMO system, which includes:

[0197] In a multiple-input multiple-output system with polar coding and multi-ary quadrature amplitude modulation, an initial radius and a bit flip threshold are set, and a search is performed in a search space in a detection order from the N / mth layer to the first layer. The initial radius is determined based on the noise variance.

[0198] During the search process, the search paths that do not meet the first preset condition are pruned, and the first search path that meets the first preset condition is determined as the reference path;

[0199] Pruning the search paths that meet the second preset condition until a valid path is output as the path with the shortest Euclidean distance to the received signal, and obtaining a decoding result according to the valid path;

[0200] Wherein, N is the codeword length of the polar code, and m is the number of bits corresponding to each real number symbol;

[0201] The first preset condition includes: when searching to the i-th layer, the partial Euclidean distance of the search path is less than the initial radius, and when searching to the first layer, the total Euclidean distance of the search path is less than the initial radius; the value range of i is 1 to N / m;

[0202] The second preset condition includes: a ratio of the number of flipped bits of the search path to the number of flipped bits of the reference path is greater than the bit flip threshold.

[0203] In addition, the logic instructions in the above-mentioned memory 630 can be implemented in the form of a software functional unit and can be stored in a computer-readable storage medium when sold or used as an independent product. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to perform all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes: various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk or an optical disk.

[0204] In another aspect, the present invention further provides a computer program product, comprising a computer program. The computer program may be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer is capable of performing the joint detection and decoding method for a polar code MIMO system provided by each of the above methods. The method comprises:

[0205] In a multiple-input multiple-output system with polar coding and multi-ary quadrature amplitude modulation, an initial radius and a bit flip threshold are set. A search is performed in the search space in the order from the N / mth layer to the first layer. The initial radius is determined based on the noise variance.

[0206] During the search process, the search paths that do not meet the first preset condition are pruned, and the first search path that meets the first preset condition is determined as the reference path;

[0207] Pruning the search paths that meet the second preset condition until a valid path is output as the path with the shortest Euclidean distance to the received signal, and obtaining a decoding result based on the valid path;

[0208] Where N is the codeword length of the polar code, and m is the number of bits corresponding to each real number symbol;

[0209] The first preset condition includes: when searching to the i-th layer, the partial Euclidean distance of the search path is less than the initial radius, and when searching to the first layer, the total Euclidean distance of the search path is less than the initial radius; the value range of i is 1 to N / m;

[0210] The second preset condition includes: a ratio of the number of flipped bits of the search path to the number of flipped bits of the reference path is greater than a bit flip threshold.

[0211] In yet another aspect, the present invention further provides a non-transitory computer-readable storage medium having a computer program stored thereon. When executed by a processor, the computer program is implemented to perform the joint detection and decoding method for a polar code MIMO system provided by the above methods, the method comprising:

[0212] In a multiple-input multiple-output system with polar coding and multi-ary quadrature amplitude modulation, an initial radius and a bit flip threshold are set. A search is performed in the search space in the order from the N / mth layer to the first layer. The initial radius is determined based on the noise variance.

[0213] During the search process, the search paths that do not meet the first preset condition are pruned, and the first search path that meets the first preset condition is determined as the reference path;

[0214] Pruning the search paths that meet the second preset condition until a valid path is output as the path with the shortest Euclidean distance to the received signal, and obtaining a decoding result based on the valid path;

[0215] Where N is the codeword length of the polar code, and m is the number of bits corresponding to each real number symbol;

[0216] The first preset condition includes: when searching to the i-th layer, the partial Euclidean distance of the search path is less than the initial radius, and when searching to the first layer, the total Euclidean distance of the search path is less than the initial radius; the value range of i is 1 to N / m;

[0217] The second preset condition includes: a ratio of the number of flipped bits of the search path to the number of flipped bits of the reference path is greater than a bit flip threshold.

[0218] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, i.e., they may be located in one location or distributed across multiple network units. Some or all of the modules may be selected based on actual needs to achieve the objectives of the present embodiment. Persons of ordinary skill in the art will be able to understand and implement the present invention without inventive effort.

[0219] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, or of course, by hardware. Based on this understanding, the essence of the above technical solution or the part that contributes to the existing technology can be embodied in the form of a software product. The computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or certain parts of the embodiments.

[0220] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present invention.

Claims

1. A joint detection and decoding method for a polar code coded multiple-input multiple-output system, characterized in that: include: In a multiple-input multiple-output system with polar coding and multi-ary quadrature amplitude modulation, an initial radius and a bit flip threshold are set, and a search is performed in a search space in a detection order from the N / mth layer to the first layer. The initial radius is determined based on the noise variance. During the search process, the search paths that do not meet the first preset condition are pruned, and the first search path that meets the first preset condition is determined as the reference path; Pruning the search paths that meet the second preset condition until a valid path is output as the path with the shortest Euclidean distance to the received signal, and obtaining a decoding result according to the valid path; Wherein, N is the codeword length of the polar code, and m is the number of bits corresponding to each real number symbol; The first preset condition includes: when searching to the i-th layer, the partial Euclidean distance of the search path is less than the initial radius, and when searching to the first layer, the total Euclidean distance of the search path is less than the initial radius; the value range of i is 1 to N / m; The second preset condition includes: a ratio of the number of flipped bits of the search path to the number of flipped bits of the reference path is greater than the bit flip threshold.

2. The joint detection and decoding method for a polar code coded multiple-input multiple-output system according to claim 1, characterized in that: In the MIMO system, the transmitting end further performs cascaded cyclic redundancy check encoding on the information bits before performing the polar code encoding on the information bits; The first preset condition also includes: When searching to the first layer, the search path passes the cyclic redundancy check, and the total Euclidean distance is less than the initial radius; The second preset condition also includes: The search path failed the cyclic redundancy check when searching to layer 1.

3. The joint detection and decoding method for a polar code coded multiple-input multiple-output system according to claim 1 or 2, characterized in that: The method further comprises: In the case that the valid path cannot be found, the initial radius is adjusted according to a preset step value.

4. The joint detection and decoding method for a polar code coded multiple-input multiple-output system according to claim 3, wherein: The initial radius is the product of the noise variance and the number of real symbols.

5. The joint detection and decoding method for a polar code coded multiple-input multiple-output system according to claim 1, wherein: The total Euclidean distance of the search path is equal to the sum of the increments of the partial Euclidean distances corresponding to each layer.

6. The joint detection and decoding method for a polar code coded multiple-input multiple-output system according to claim 5, characterized in that: The partial Euclidean distance corresponding to the i-th level of the search path is determined by the following steps: Determine the information bits and frozen bits corresponding to the i-th layer of the search path according to the information bit set after bit flipping and permutation; Determine M based on the information bits and the frozen bits i There are m candidate bits, where M i ∈{1,2,4,...,2 m }; Determine the M corresponding to the i-th layer i Codewords, and modulation mapping is M i A real number symbol; Determine the M i The partial Euclidean distance corresponding to the real number symbol.

7. A joint detection and decoding device for a polar code coded multiple-input multiple-output system, characterized in that: include: a setting module, configured to set an initial radius and a bit flip threshold in a multiple-input multiple-output system using polar coding and multi-ary quadrature amplitude modulation, and to search in a search space in a detection order from the N / mth layer to the first layer, wherein the initial radius is determined based on the noise variance; A first pruning module is used to prune the search paths that do not meet the first preset condition during the search process, and determine the first search path that meets the first preset condition as the reference path; a second pruning module, configured to prune search paths that meet a second preset condition until a valid path is output as a path with the shortest Euclidean distance to the received signal, and obtain a decoding result according to the valid path; Wherein, N is the codeword length of the polar code, and m is the number of bits corresponding to each real number symbol; The first preset condition includes: when searching to the i-th layer, the partial Euclidean distance of the search path is less than the initial radius, and when searching to the first layer, the total Euclidean distance of the search path is less than the initial radius; the value range of i is 1 to N / m; The second preset condition includes: a ratio of the number of flipped bits of the search path to the number of flipped bits of the reference path is greater than the bit flip threshold.

8. A receiver comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the joint detection and decoding method for a polar code coded multiple-input multiple-output system according to any one of claims 1 to 6 is implemented.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the joint detection and decoding method for a polar code coded multiple-input multiple-output system according to any one of claims 1 to 6 is implemented.

10. A computer program product comprising a computer program, characterized in that When the computer program is executed by a processor, the joint detection and decoding method for a polar code coded multiple-input multiple-output system according to any one of claims 1 to 6 is implemented.

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