Minimum Distance Optimization with Chord Edge Growth for High Girth Non-Binary LDPC Codes

Changcai Han,Hui Li,Weigang Chen

doi:10.3390/electronics9122161

Abstract

Short or moderate-length non-binary low-density parity-check (NB-LDPC) codes have the potential applications in future low latency and high-reliability communication thanks to the strong error correction capability and parallel decoding. Because of the existence of the error floor, the NB-LDPC codes usually cannot satisfy very low bit error rate (BER) requirements. In this paper, a low-complexity method is proposed for optimizing the minimum distance of the NB-LDPC code in a progressive chord edge growth manner. Specifically, each chord edge connecting two non-adjacent vertices is added to the Hamiltonian cycle one-by-one. For each newly added chord edge, the configuration of non-zero entries corresponding to the chord edge is determined according to the so-called full rank condition (FRC) of all cycles that are related to the chord edge in the obtained subgraph. With minor modifications to the designed method, it can be used to construct the NB-LDPC codes with an efficient encoding structure. The analysis results show that the method for designing NB-LDPC codes while using progressive chord edge growth has lower complexity than traditional methods. The simulation results show that the proposed method can effectively improve the performance of the NB-LDPC code in the high signal-to-noise ratio (SNR) region. While using the proposed scheme, an NB-LDPC code with a quite low BER can be constructed with extremely low complexity.

Highlights

The design of efficient short codes has attracted widespread interest due to the emergence of applications requiring high reliability and low latency data transmission [1,2]
This paper aims to design a method for configuring non-zero entries that are based on the full rank condition (FRC) of a cycle, optimizing the global minimum distance of the non-binary low-density parity-check (NB-low-density parity check (LDPC)) codes
A low-complexity method that is based on progressive chord edge growth is developed for the configuration of non-zero entries, which can construct NB-LDPC codes with a low error floor

Summary

Introduction

The design of efficient short codes has attracted widespread interest due to the emergence of applications requiring high reliability and low latency data transmission [1,2]. The low-density parity check (LDPC) codes, which were first proposed by Gallager et al [3] and rediscovered by MacKay and Neal [4,5], have performance close to the Shannon limit as the code length approaches infinity [6]. For short or moderate code lengths, non-binary low-density parity-check (NB-LDPC) codes exhibit better error-correction capabilities than binary LDPC codes in certain cases [7,8]. The construction of NB-LDPC codes can adopt algebraic or graph theory methods. The algebraic methods for constructing non-binary quasi-cyclic LDPC codes that are based on finite Euclidean geometric planes and array masks were studied by Zhou et al [9], Huang et al [10] and Peng et al [11].

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