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International Symposium on Problems of Redundancy in Information and Control Systems (REDUNDANCY)

On the Hard-Decision Multi-Threshold Decoding of Binary and Non-Binary LDPC Codes

Andrei Dzis, Pavel S. Rybin, Alexey Frolov

Published Oct 1, 2019• 0 citations
Publisher

Abstract

In this paper, we investigate the effect of single and multiple thresholds approaches applied to iterative hard-decision decoders for binary and non-binary low-density parity-check (LDPC) codes in terms of error correction and managed to optimize the performance of decoding algorithms for these codes.
DOI
10.1109/redundancy48165.2019.9003311

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Low-density parity-check codes are one of the most common forward error-correction techniques used in many existing and perspective standards including 5G wireless transmission standards and ultra-high-rate (400 Gbit/s and more) fiber-optic transmission standards. These codes should combine scalability of codelength from dozens to dozens of thousands bits and of coderate from low to very high with outstanding error-correcting performance when operating under severe practical limitations both from the point of view of decoding error and complexity issues. In many practical cases most widely used decoders suffer either from complexity out of system restrictions or from error performance penalties. In this paper the performance-complexity trade-off approach is considered, based on improved hard-decision decoders. Decoding of low-density parity-check codes with bit-flip algorithm is considered. The multi-threshold decoder based on the bit inversion algorithm is described using dynamically changed threshold during the decoding iterations, as well as the simplest empirical method is proposed for thresholds calculation. Simulation results in Gaussian channel with hard decision demodulation are given.
Non-binary low-density parity-check (LDPC) codes have some advantages over their binary counterparts, but unfortunately their decoding complexity is a significant challenge. The iterative hard- and soft-reliability based majority-logic decoding algorithms are attractive for nonbinary LDPC codes, since they involve only finite field additions and multiplications as well as integer operations and, hence, have significantly lower complexity than other algorithms. In this paper, we propose two improvements to the majority-logic decoding algorithms. Instead of the accumulation of reliability information in the existing majority-logic decoding algorithms, our first improvement is a new reliability information update. The new update not only results in better error performance and fewer iterations on average, but also further reduces computational complexity. Since existing majority-logic decoding algorithms tend to have a high error floor for codes whose parity check matrices have low column weights, our second improvement is a reselection scheme, which leads to much lower error floors, at the expense of more finite field operations and integer operations, by identifying periodic points, reselecting intermediate hard decisions, and changing reliability information.
In this paper, a low complexity algorithm for binary linear block codes is applied to low-density parity-check (LDPC) codes and improvements are described, namely an extension to soft-decision decoding and a loop detection mechanism. For soft decoding, only one real-valued addition per code symbol is needed, while the remaining operations are only binary as in the hard decision case. The decoding performance is considerably increased by the loop detection. Simulation results are used to compare the performance with other known decoding strategies for LDPC codes, with the result that the presented algorithms offer excellent performance at smaller complexity.
The bit-flipping (BF) algorithm for decoding of low-density parity-check (LDPC) codes requires less complex hardware than other decoding algorithms, but its error correcting performance needs to be improved. In this letter, a threshold adaptation scheme is applied to BF algorithm based decoding of LDPC codes. Our experiments show that the optimal threshold value for BF depends on the error conditions, and threshold adjustment during decoding helps to prevent meaningless no-flipping iterations. Based on these statistical observations, the adaptive threshold technique is proposed to pursue both the maximum error correcting capability and the fastest decoding convergence.
Non-binary low density parity check codes can achieve better err-correcting performance than binary LDPC codes when the code length is moderate at the cost of higher decoding complexity. Min-Max decoding algorithm is one of the low-complexity quasi-optimal iterative algorithms. However, a problem of the Min-Max decoding algorithm is iteration inefficient in the case of low SNR. In this paper, an adaptive method is proposed based on the Min-Max decoding algorithm. By comparing the correlation among each iteration output, setting an appropriate threshold to determine whether ahead of the end of iteration, which makes the adaptive Min-Max decoding algorithm very attractive for practical purposes
This letter proposes two methods to improve the iterative hard-reliability based majority-logic decoding algorithm for non-binary low-density parity-check (NB-LDPC) codes. The first method improves the error-correcting performance by modifying the initialization process, which is based on the fact that Gray coded modulation is used in general. In addition, a storage reduction method is proposed to make the proposed decoding hardware-friendly, which reduces the memory size considerably while sustaining the error-correcting performance achieved by the modified initialization. For an NB-LDPC code over Galois field of 32 elements, the memory size is reduced by about 75% compared with that of the conventional decoding algorithm.