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Telecommunication Engineering

An Adaptive Decoding Algorithm for Majority-Logic Decodable LDPC Codes

Zhang Ka

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

Majority- logic decodable low- density parity check( LDPC) codes have large column weight.For these special LDPC codes,a low complexity adaptive decoding algorithm based on the integer reliabilities is proposed. In the process of decoding,different adaptive scaling factor is introduced for each check node to modify the extrinsic information. Simulation results show that the performance of the adaptive decoding algorithm is almost the same as that of the sum- product algorithm( SPA) and there is only 0. 1 d B difference between two decoding algorithms when the bit error rate( BER) is about 10- 5. Featured by low complexity,parallel computation and integer information,the proposed adaptive decoding algorithm is very easy to be realized in practice.

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Majority- logic decodable low- density parity check( LDPC) codes have large column weight.For these special LDPC codes,a low complexity adaptive decoding algorithm based on the integer reliabilities is proposed. In the process of decoding,different adaptive scaling factor is introduced for each check node to modify the extrinsic information. Simulation results show that the performance of the adaptive decoding algorithm is almost the same as that of the sum- product algorithm( SPA) and there is only 0. 1 d B difference between two decoding algorithms when the bit error rate( BER) is about 10- 5. Featured by low complexity,parallel computation and integer information,the proposed adaptive decoding algorithm is very easy to be realized in practice.
In this paper, an adaptive decoding algorithm for majority-logic decodable LDPC codes is present based on a recent work by Chen et al. Different from the RBI-MSD algorithm, the presented adaptive reliability-based iteration min-sum decoding algorithm does not need to predesignate the scaling factor, which is optimized by discretized density evolution. In the adaptive RBIMSD algorithm, an adaptive scaling factor is induced for each check node to modify the extrinsic message. The adaptive scaling factor is computed by the ratio of the second minimum and the maximum value among the message, which is received by the check nodes. Simulation results show that, the performance of the adaptive RBI-MSD algorithm is almost as well as that of the original RBI-MSD algorithm but with a little (or negligible) computation increase.
This paper presents a low complexity Min-Sum algorithm for decoding irregular Low-Density Parity-Check (LDPC) codes. In the proposed algorithm, the significant improvement in the error correcting performance without enhancing the hardware complexity is achieved by employing adaptive and optimized normalization factors for both the extrinsic information and log-likelihood ratio data bits respectively. The experimental results demonstrate that the proposed algorithm with 6-bit non-uniform quantization achieves reasonable decoding performance in terms of Frame Error Rate (FER) and Bit Error Rate (BER) without increasing the hardware complexity by avoiding finite word length effects of soft information.
In this paper, we present a reliability-based iterative proportionality-logic decoding algorithm for two classes of structured low-density parity-check (LDPC) codes. The main contributions of this paper include: 1) Syndrome messages instead of extrinsic messages are processed and exchanged between variable nodes and check nodes, which can reduce the decoding complexity; 2) a more flexible decision mechanism is developed in which the decision threshold can be self-adjusted during the iterative process. Such decision mechanism is particularly effective for decoding the majority-logic decodable codes; 3) only part of the variable nodes satisfying the pre-designed criterion are involved for the presented algorithm, which is in the proportionality-logic sense and can further reduce the computational complexity. Simulation results show that, when combined with factor correction techniques and appropriate proportionality parameter, the presented algorithm performs well and can achieve fast decoding convergence rate while maintaining relative low decoding complexity, especially for small quantized levels (3-4 bits). The presented algorithm provides a candidate for those application scenarios where the memory load and the energy consumption are extremely constrained.
A reliability-based iterative majority-logic decoding algorithm for regular low-density parity-check (LDPC) codes was recently proposed by Huang et al. In this paper we present an improved version of that algorithm by introducing a different reliability measure for each check-sum of the parity-check matrix, and taking it into account in the computation of the extrinsic information that is used to update the reliability measure of each received bit in each iteration. Some simulations results are given, which show that the new algorithm, while requiring very little additional computational complexity, not only achieves a considerable error performance gain over the standard one, but also, importantly, outperforms the iterative decoding based on belief propagation (IDBP), especially for short and medium block length finite-geometry (FG) LDPC codes.
Based on decoding performance, complexity and latency of finite-geometry low-density parity-check (LDPC) codes, an efficient decoding algorithm is proposed. The algorithm is a hybrid bit-flipping (BF)/majority-logic (MLG) algorithm. In the algorithm, there are two stages. At the first stage, a code is decoded with bit-flipping (BF) with a small fixed number of iterations. Then the output from bit-flipping (BF) decoder is decoded by majority-logic (MLG) decoding. And in bit-flipping (BF) decoding, a new method is used to find the least reliable position. In the hybrid algorithm, there aren't real operations. Simulation results show that the algorithm provides 0.3dB coding gain over weight bit-flipping (WBF) decoding, and within 1 dB away from sum-product algorithm (SPA) decoding.
An attenuated iterative reliability-based majority-logic (AIML) decoding algorithm for low-density parity-check (LDPC) codes is proposed. This novel algorithm is devised based on the orthogonal check-sums of the one-step majority-logic decoding algorithm in conjunction with certain of reliability measures of the received symbols. The computation of reliability measure of the syndrome sum is refined by introducing an attenuation factor. Simulation results show that in binary input-additive white Gaussian noise channel, the AIML algorithm outperforms other popular iterative reliability-based majority-logic decoding algorithms with a slight increase in computational complexity. With maximum iterations five and fifty, the AIML algorithm can achieve almost identical error performance for LDPC codes. No error floor effect can be observed for AIML algorithm down to the bit error rate (BER) of 10−8, while error floor appears for sum product algorithm (SPA) around the BER of 10−7even with maximum iteration 100. The inherent feature of parallel decoding for AIML algorithm enforces the decoding speed in contrast to those serial decoding schemes, such as weighted bit-flipping algorithm.