BP algorithm is one of the most prominent decoding algorithms based on message passing. However, it is not commonly adopted in hardware implementation for the high computational complexity. The normalized min-sum (NMS) algorithm was then proposed to solve this problem but with performance flaws. To satisfy the comprehensive requirements of complexity and accuracy in 5G systems, we introduce an approximated algorithm based on BP in log-domain and name it piecewise linear interpolation based LOG-BP (PLI-LOG-BP) algorithm. In our novel algorithm, the non-linear mapping function in the horizontal step of BP is replaced by several linear functions for simplification. Meanwhile, we also propose an MMSE-based selection algorithm of segment points that improves the approximation accuracy. To verify the validation of the proposed algorithm, we apply 5G LDPC codes in our simulation and obtain BLER performance results. According to these results, PLI-LOG-BP algorithm decoding performance is significantly better than the NMS algorithm and even almost as good as the BP algorithm.
BP algorithm is one of the most prominent decoding algorithms based on message passing. However, it is not commonly adopted in hardware implementation for the high computational complexity. The normalized min-sum (NMS) algorithm was then proposed to solve this problem but with performance flaws. To satisfy the comprehensive requirements of complexity and accuracy in 5G systems, we introduce an approximated algorithm based on BP in log-domain and name it piecewise linear interpolation based LOG-BP (PLI-LOG-BP) algorithm. In our novel algorithm, the non-linear mapping function in the horizontal step of BP is replaced by several linear functions for simplification. Meanwhile, we also propose an MMSE-based selection algorithm of segment points that improves the approximation accuracy. To verify the validation of the proposed algorithm, we apply 5G LDPC codes in our simulation and obtain BLER performance results. According to these results, PLI-LOG-BP algorithm decoding performance is significantly better than the NMS algorithm and even almost as good as the BP algorithm.
A hybrid decoding algorithm for low-density parity-check codes is presented. The proposed algorithm applies different updating schemes, such as the normalized min-sum (NMS) simplification and linear approximation, to the check-node based on its degree. Meanwhile, to eliminate the dependence on the channel variance estimation, the proposed algorithm adopts a multiplicative factor to initialize the channel input and a fixed linear functions for check-node updating. From the iterative thresholds and decoding simulations, our proposed algorithm can be shown to achieve improved performance (much closer to that of the belief propagation decoding) at the expense of a slight increase in complexity to NMS algorithm.
For recent years, deep learning has been studied and utilized among decoders in wireless and optical communication. For low density parity check (LDPC) codes, most works use neural network (NN) to implement the belief propagation (BP) decoder and unfold its iterations into layers activated by different functions. However, the whole decoder composed by neural network performs lots of non-linear operations, which are time consuming and unfriendly to hardware implementation. In this work, a neural network-aided normalized min-sum (NN-aided NMS) decoder for LDPC code is proposed, in which the normalization factors are inferred from input log likelihood ratio (LLR) by apre-trained NN, while maintaining check and variable nodes processing the same as in min-sum (MS) decoder. In order to test the proposed decoder with irregular LDPC code, a rate-7/8 one was constructed using progressive edge growth (PEG) algorithm, showing better error correction capability than the standard of consultative committee for space data systems (CCSDS) LDPC (8176,7154) code by 0.08 dB with the same rate. Simulation results show that, NN-aided NMS decoder outperforms MS decoder by 0.3 dB, and its performance approaches BP decoder with a gap of 0.02 dB, which is 50% closer than the best NMS decoder using 0.7 as the normalization factor. The proposed decoder has good performance for both regular and irregular LDPC codes, and needs much less computation complexity than BP decoder. It introduces more linear computation than NMS decoder but achieves better bit error rate (BER) performance, thus becoming a good complement between BP and NMS decoder when trading off among complexity, error correction performance and hardware implementation for wireless and satellite communication.
Low-density parity-check(LDPC) code has been selected as the channel coding method by 5G NR because of its excellent error-correcting performance. To further improve the performance of LDPC decoding, this paper proposes a neural normalized min-sum(NNMS) algorithm based on multi-edge-type(MET). Based on the LLR convergence analysis of the protograph matrix of 5G NR, the base matrix is divided into several independent regions. Each part is assigned a unique scaling factor at different iterations. To verify the effectiveness of the proposed algorithm, We use two parity-check matrixes(PCM) derived from different base graphs in simulations. The results show that the proposed algorithm performs at most 0.45dB better than BP, 0.37dB better than NMS, and 0.25dB better than OMS, respectively, when the frame error rate (FER) is at 10−5 level over additive white Gaussian noise (AWGN) channels using BPSK modulation.
The high complexity of the Belief Propagation (BP) decoding algorithm in LDPC decoding leads to greater resource consumption and increased communication link latency. This has become a critical challenge in designing efficient communication systems. The Box-Plus operation can effectively transform the nonlinear equations in check nodes into an addition operation of the minimum and the logarithmic functions, but the logarithmic function still has high complexity. In this paper, we propose an Approximate Box-Plus (ABP) decoding algorithm, which reduces decoding complexity while maintaining decoding performance. We first deduced that the logarithmic function in addition operations essentially represents the error between the BP decoding algorithm and the Min-Sum (MS). Based on this insight, a low-complexity, high-precision substitute function is designed. This function utilizes the boundary control ability and symmetry of the min and max functions to effectively express the relative size changes, thereby reducing the unreliability in check node message passing. The proposed decoding algorithm based on the above function reduces the complexity by 38.9% compared to the BP algorithm, and the mean square error of the substitute function and logarithmic function is only 0.0018. Simulation results demonstrate that the decoding performance improves by approximately 0.4 dB compared to the classical Normalized Min-Sum (NMS) and Offset Min-Sum (OMS) algorithms, and the complexity is increased by only three and two new operations per operation compared to NMS and OMS, respectively.
Low density parity check code is a kind of high-performance linear block code. It has excellent performance which is near the Shannon limit. LDPC has low decoding complexity, free structure and receives extensive attention. The typical decoding algorithm of LDPC is LLR BP algorithm, which is also called “sum-product algorithm”. LLR BP algorithm is the best algorithm at present. But it needs complex computation, which causes great difficulty in its hardware design. To solve this problem, an algorithm that gets approximation of LLR BP algorithm is put forward, which is called min-sum algorithm. Min-sum algorithm greatly reduces the computation and makes the hardware design simpler, but its accuracy has a wide gap with BP algorithm. This article analyzes the reason why min-sum algorithm has errors, and puts forward an improved algorithm called min-sum linear approximation algorithm based on min-sum algorithm.
Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.