Two efficient and low-complexity iterative reliability-based majority-logic decoding algorithms for LDPC codes (original) (raw)
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Analytical Performance of One-Step Majority Logic Decoding of Regular LDPC Codes
2007 IEEE International Symposium on Information Theory, 2007
In this paper, we present a combinatorial algorithm to calculate the exact bit error rate performance of regular low-density parity check codes under one-step majority logic decoding. Majority logic decoders have regained importance in nano-scale memories due to their resilience to both memory and logic gate failures. This result is an extension of the work of Rudolph on error correction capability of majority-logic decoders.
A New Reliability Ratio Weighted Bit Flipping Algorithm for Decoding LDPC Codes
Wirel. Commun. Mob. Comput., 2021
In this study, we propose a “New Reliability Ratio Weighted Bit Flipping” (NRRWBF) algorithm for Low-Density Parity-Check (LDPC) codes. This algorithm improves the “Reliability Ratio Weighted Bit Flipping” (RRWBF) algorithm by modifying the reliability ratio. It surpasses the RRWBF in performance, reaching a 0.6 dB coding gain at a Binary Error Rate (BER) of 10 over the Additive White Gaussian Noise (AWGN) channel, and presents a significant reduction in the decoding complexity. Furthermore, we improved NRRWBF using the sum of the syndromes as a criterion to avoid the infinite loop. This will enable the decoder to attain a more efficient and effective decoding performance.
The main challenge for hardware implementation of non-binary LDPC decoding is the high computational complexity and large memory requirement. To address this challenge, five new low complexity LDPC decoding algorithms are proposed in this paper. The proposed algorithms are developed specifically towards the low complexity, yet effective, decoding of the NB LDPC codes. The proposed decoding algorithms update, iteratively, the hard decision received vector to search for the valid codeword in the vector space of Galois field (GF). The selection criterion for least reliable symbol positions is based on the information from the failed checks and the reliability information from the Galois field structure as well as from the received channel soft information. To choose the correct value for the candidate symbol, two methods are used. The first method is based on the prediction of the error symbol from the set of Galois field symbols which maximize an objective function. In the second method, individual bits are flipped based on the reliability information obtained from the channel. Algorithms 1 and 2 flip a single symbol per iteration whilst the other three algorithms 3,4 and 5 flip multiple symbols in each iteration. The proposed voting based Algorithms 1,2 and 5 first short list the unreliable positions using a majority voting scheme and then choose the candidate symbol value from the set of the symbols in GF(q) while not violating the field order q. These methods simplify the decoding complexity in terms of computation and memory. Results and analysis of these algorithms show an appealing tradeoff between computational complexity and bit error rate performance for NB LDPC codes. INDEX TERMS Multiple vote, non-binary LDPC, iterative reliability decoding, symbol flipping, sum product algorithm, low complexity decoding.
Coset Probability Based Majority-logic Decoding for Non-binary LDPC Codes
2019
This paper presents a majority-logic decoding (MLgD) algorithm for non-binary LDPC codes based on a novel expansion of the Tanner graph. The expansion introduced converts the Q-ary graph into a binary one, which makes the new MLgD algorithm more attractive for hardware implementations. Proposed algorithm performs significantly better than the existing MLgD algorithms in the waterfall region, and it shows a much lower error-floor as well. Algorithm only requires integer additions, comparisons, finite field operations and some binary operations. Thus, it offers an effective trade-off between performance and complexity in decoding non-binary LDPC codes.
Reliability Ratio Weighted Bit Flipping– Sum Product Algorithm for Regular LDPC Codes
E3S Web of Conferences
In this work, we introduce a novel decoding algorithm named “Reliability Ratio Weighted Bit Flipping–Sum Product” (RRWBFSP) is proposed for regular LDPC codes. “Sum Product” [4] and “Reliability Ratio Weighted Bit Flipping” [6] are two separate methods that are combined in the new algorithm. The simulations show novel algorithm to exceed Sum-Product decoding algorithms by 0.34 dB. In addition, when compared to the Sum-Product, the RRWBFSP approach has about the same computational complexity. Thus, LDPC codes, of which the “Double-Orthogonal Convolutional Recursive” (RCDO) subfamily is envisioned for use in electronic hard disks and mobile terminals, can be easily iteratively decoded. This would have the impact of prolonging the life of the batteries and consequently reducing the ecological footprint of the discarded batteries.
Improved Decoding Algorithms of LDPC Codes Based on Reliability Metrics of Variable Nodes
IEEE Access, 2019
The informed dynamic scheduling (IDS) strategies for decoding of low-density parity-check codes obtained superior performance in error correction performance and convergence speed. However, there are still two problems existing in the current IDS algorithms. The first is that the current IDS algorithms only preferentially update the selected unreliable messages, but they do not guarantee the updating is performed with reliable information. In the paper, a two-step message selecting strategy is introduced. On the basis of the two reliability metrics and two types of variable node residuals, the residual BP decoding algorithm, short for TRM-TVRBP, is proposed. With the algorithm, the reliability of the updating-messages can be improved. The second is the greediness problem, prevalently existed in the IDSlike algorithms. The problem arises mainly from the fact that the major computing resources are allocated to or concentrated on some nodes and edges. To overcome the problem, the reliability metric-based RBP algorithm (RM-RBP) is proposed, which can force every variable node to contribute its intrinsic information to the iterative decoding. At the same time, the algorithm can force the related variable nodes to be updated, and make every edge have an equal opportunity of being updated. Simulation results show that both the TRM-TVRBP and the RM-RBP have appealing convergence rate and error-correcting performance compared to the previous IDS decoders over the white Gaussian noise (AWGN) channel. INDEX TERMS Low-density parity-check (LDPC) codes, dynamic selection strategies, dynamic updating strategies, residuals of variable nodes.
On the error-correcting capability of LDPC codes
Problems of Information Transmission, 2008
We consider the ensemble of low-density parity-check (LDPC) codes introduced by Gallager [1]. The Zyablov-Pinsker majority-logic iterative algorithm [2] for decoding LDPC codes is analyzed on the binary symmetric channel. An analytical lower bound on the errorcorrecting capability τ max that grows linearly in the code block length is obtained.
IEEE Access
This paper addresses the problem of decoding non-binary low density parity check codes(LDPC) over finite field GF(q) using symbol flipping approach. To achieve low complexity reliable communication, three new algorithms for improving the bit error rate performance of the non-binary LDPC decoder are presented. The first type is the symbol flipping decoding algorithm using a flipping function based on the channel reliability to identify the least reliable symbol position. In this algorithm, if the predicted symbol value satisfies the check sum, then the value is declared as correct otherwise the value is adjusted and sent back to the QAM detector. Algorithms 2 in this paper is an improvement to iterative joint detection-decoding algorithm by using the method of iterative hard decision based majority logic to select the new candidate symbol value. The feedback value to the QAM detector is adjusted by using Euclidean distance between the current symbol and the newly selected symbol value. Algorithm 3 is a low complexity version of Algorithm 2 which is derived by applying a majority voting scheme. In the majority voting scheme, symbols are short listed first by voting and all the computation are carried out only for the short listed least reliable symbols which significantly lowers the processing complexity. Numerical results and complexity analysis show that the proposed methods have good bit error rate versus complexity trade-off for various applications when compared with some existing algorithms.
Bootstrapped Iterative Decoding Algorithms for Low Density Parity Check (LDPC) Codes
2010
Reliability ratio based weighted bit-flipping algorithm is one of the best hard decision decoding algorithms in performance. Recently several modifications are done to this technique either to improve performance or to lower the complexity. The implementation efficient reliability ratio based weighted bit-flipping is developed targeting decreasing processing time of the decoding process. In this paper we are targeting improving performance of recent developed algorithm named low complex implementation efficient reliability ratio based weighted bit-flipping by adding a bootstrap step to the decoding technique which leads to increase in reliability of received bits then number of decoded bits will be increased leading to improve in performance. Also a modification done to bootstrap step for further increase the performance.
Two-Bit Bit Flipping Decoding of LDPC Codes
In this paper, we propose a new class of bit flipping algorithms for low-density parity-check (LDPC) codes over the binary symmetric channel (BSC). Compared to the regular (parallel or serial) bit flipping algorithms, the proposed algorithms employ one additional bit at a variable node to represent its "strength." The introduction of this additional bit increases the guaranteed error correction capability by a factor of at least 2. An additional bit can also be employed at a check node to capture information which is beneficial to decoding. A framework for failure analysis of the proposed algorithms is described. These algorithms outperform the Gallager A/B algorithm and the minsum algorithm at much lower complexity. Concatenation of twobit bit flipping algorithms show a potential to approach the performance of belief propagation (BP) decoding in the error floor region, also at lower complexity.