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International Conference on Computing, Communication and Networking Technologies (ICCCNT)

Adaptive reliability-based iteration min-sum decoding algorithm for majority-logic decodable LDPC codes

Hongwei Zhao, Kai Zhang, Mengmeng Shi

Published Jul 1, 2015• 2 citations
Publisher

Abstract

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.

DOI
10.1109/icccnt.2015.7395208

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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.
A modified reliability-based iterative majority-logic decoding (MRBI-MLGD) algorithm for two classes of structured LDPC codes is presented based on a recent work by Huang et al. Compared with the original one, the modified algorithm has better performance with slightly increased complexity. Then a reliability-based iterative min-sum decoding (RBI-MSD) algorithm is presented. For the presented RBI-MSD algorithm, reliability-based integer messages are processed and exchanged between variable nodes and check nodes. The main computations include only binary logical operations and integer additions. Different from the conventional min-sum algorithm, the variable nodes pass full messages rather than extrinsic messages to check nodes. This can reduce the memory loads and the computational complexity but with a little (or negligible) performance degradation. Simulation results show that, compared with the (M)RBI-MLGD algorithms, the presented RBI-MSD algorithm achieves better error performance, faster decoding convergence rate and fewer quantization bits with moderate increased computational complexity. Furthermore, the RBI-MSD algorithm is also applicable to decoding random LDPC codes, a distinct difference from the (M)RBI-MLGD algorithms. Finally, we point out that the scaling factors employed in the MRBI-MLGD algorithm and the RBI-MSD algorithm can be optimized using discretized density evolution.
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.
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.
In this letter, a new reliability-based iterative majority-logic decoding (RBI-MLGD) algorithm that computes the extrinsic information of previous iterations of the variable node is proposed. This decoding algorithm is called historical-extrinsic reliability-based iterative decoder (HE-RBID) and improves the bit-error-rate performance of the previous RBI-MLGD. HE-RBID is particularly interesting for codes with a low degree of variable node, where traditional RBI-MLGD algorithms do not provide a good behavior. HE-RBID ensures a good performance without searching for the minimum at the check node and only by exchanging 1-bit messages between variable and check nodes.
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 modified bit-reliability based decoding algorithm is presented based on a recent work by Huang et al. For the presented algorithm, only one Galois field element is passed and exchanged along the edges of the Tanner graph. At variable nodes, full messages rather than extrinsic messages are processed to further reduce the computational complexity. At check nodes, only hard reliability is considered and the main operation is to compute the check-sum and send one extrinsic symbol back to variable nodes. Simulation results show that, even with lower complexity and less memory consumption, the presented algorithm still can perform very closely to the original wBRB algorithm with low quantization bits (3 ~ 4 bits) when decoding the majority-logic decodable nonbinary LDPC codes. For codes constructed in high order fields, the presented algorithm can even outperform the original wBRB algorithm.