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IET Communications

Decoding of non‐binary low‐density parity‐check codes based on the genetic algorithm and applications over mobile fading channels

Xingcheng Liu, Chulong Liang, Yuanbin Zhang, Lin Zhang

Published Oct 8, 2015• 0 citations
Publisher

Abstract

In this study, an efficient decoding algorithm is proposed to decode non‐binary low‐density parity‐check (LDPC) codes. The algorithm is derived from the belief‐propagation (BP) decoding with genetic algorithm of binary LDPC codes. For the proposed algorithm, two decoding constraints are introduced to determine variable nodes which are considered highly reliable. The messages from these highly reliable variable nodes are then magnified with an appropriate parameter γ . This process can make the messages propagate in the Tanner graph more efficiently. Simulation results show that, compared with the fast Fourier transform‐based BP algorithm, the proposed algorithm can have an equal or better performance in low bit‐error‐rate region over both the additive white Gaussian noise channels and the mobile fading channels.

DOI
10.1049/iet-com.2015.0085

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In this study, an efficient decoding algorithm is proposed to decode non‐binary low‐density parity‐check (LDPC) codes. The algorithm is derived from the belief‐propagation (BP) decoding with genetic algorithm of binary LDPC codes. For the proposed algorithm, two decoding constraints are introduced to determine variable nodes which are considered highly reliable. The messages from these highly reliable variable nodes are then magnified with an appropriate parameter γ . This process can make the messages propagate in the Tanner graph more efficiently. Simulation results show that, compared with the fast Fourier transform‐based BP algorithm, the proposed algorithm can have an equal or better performance in low bit‐error‐rate region over both the additive white Gaussian noise channels and the mobile fading channels.
Summary The simplicity of decoding is one of the most important characteristics of the low density parity check (LDPC) codes. Belief propagation (BP) decoding algorithm is a well‐known decoding algorithm for LDPC codes. Most LDPC codes with long lengths have short cycles in their Tanner graphs, which reduce the performance of the BP algorithm. In this paper, we present 2 methods to improve the BP decoding algorithm for LDPC codes. In these methods, the calculation of the variable nodes is controlled by using “multiplicative correction factor” and “additive correction factor.” These factors are obtained for 2 separate channels, namely additive white Gaussian noise (AWGN) and binary symmetric channel (BSC), as 2 functions of code and channel parameters. Moreover, we use the BP‐based method in the calculation of the check nodes, which reduces the required resources. Simulation results show the proposed algorithm has better performance and lower decoding error as compared to BP and similar methods like normalized‐BP and offset‐BP algorithms.
The Layered Belief Propagation L-BP algorithm is is a modified Belief Propagation BP algorithm, where the check nodes are divided in subgroups called layers and each iteration is broken into multiple sub-iterations. In this paper, we consider layered belief propagation decoding and propose an efficient variable node layering for decoding LDPC codes that performs well. We compare the performance of the first introduced LDPC decoding algorithm BP and Layered BP using check node layering with Layered BP using variable node layering in terms of bit error rate (BER). We show that the convergence for decoding LDPC codes is increasing by using a simple and efficient layering strategy.
In communication systems, the transmitted data is corrupted by channel perturbations, such as noise and fading, which affect the reliability of the received data. Error correction codes are employed to mitigate channel perturbations. However, design and implementation of good and efficient error correction codes remains an open problem. In this paper, Low Density Parity Check (LDPC) codes are considered as they provide a reasonable trade-off between computational complexity and reliability. Good LDPC codes should ideally provide low complexity, close to capacity acheivable transmission rate, high coding threshold, and high decoding stability. In this paper, we investigate a joint LDPC code optimization algorithm using Genetic Algorithm (GA) and Linear Programming (LP) to determine the variable nodes and check nodes degrees distributions. EXIT chart analysis and Frame Error Rate (FER) performance are used to validate the proposed method.
This paper proposes a more efficient resource‐constrained decoding algorithm for Adaptive Offset Min‐Sum (A‐OMS) low‐density parity check (LDPC) optimized decoder parameters in fifth‐generation New Radio (5G‐NR) Base Graph 2 codes (BG2). To curb the challenge of observing the all‐time finest offset to use the irregular BG2 structure, a genetic algorithm (GA) is utilized to enhance the respective offset aspect in the updating of check nodes to achieve the required objective of creating a near‐optimal solution offset aspect. Depending on the GA, the bit error rate (BER) can achieve optimal performance over a wide range of signal‐to‐noise ratios (SNRs), which is a metaheuristic optimizer. These results of the simulation indicate that this proposed optimized decoder outperforms the conventional fixed‐offset OMS by 0.2–0.5 dB in terms of belief propagation (BP) decoding performance, coding gains, and a BER that are 0.3–0.6 dB and a BER of 4.6, respectively. The proposed method achieves BP at about 35 percent decoding computation. In the case of 5G‐NR next‐generation receivers, the suggested approach will provide a fair trade‐off between the implementation efficiency and performance.
Since irregular low‐density parity‐check (LDPC) codes are known to perform better than regular ones, and to exhibit, like them, the so‐called ‘threshold phenomenon’, this Letter investigates a low‐complexity upper bound on belief‐propagation decoding thresholds for this class of codes on memoryless binary input additive white Gaussian noise channels, with sum‐product decoding. A simplified analysis of the belief‐propagation decoding algorithm is used, i.e. consider a Gaussian approximation for message densities under density evolution, and a simple algorithmic method, defined recently, to estimate the decoding thresholds for regular and irregular LDPC codes.