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IEEE International Symposium on Information Theory (ISIT)

Reed-solomon based nonbinary globally coupled LDPC codes: Correction of random errors and bursts of erasures

Juane Li, Keke Liu, Shu Lin, Khaled Abdel-Ghaffar

Published Jun 1, 2017• 20 citations
Publisher

Abstract

This paper presents a special type of nonbinary LDPC codes which are constructed based on Reed-Solomon codes. For a code of this type, its Tanner graph is composed of a set of disjoint and identical Tanner graphs, which are coupled together by a group of global check-nodes. Such a code is called a globally coupled LDPC code. This type of codes are capable of correcting random symbol errors, multiple phased bursts of erasures, and a single long burst of erasures.

DOI
10.1109/isit.2017.8006554

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This paper presents a special type of nonbinary LDPC codes which are constructed based on Reed-Solomon codes. For a code of this type, its Tanner graph is composed of a set of disjoint and identical Tanner graphs, which are coupled together by a group of global check-nodes. Such a code is called a globally coupled LDPC code. This type of codes are capable of correcting random symbol errors, multiple phased bursts of erasures, and a single long burst of erasures.
This paper presents a special type of LDPC codes constructed based on the conventional parity-check matrices of Reed-Solomon (RS) codes. LDPC codes of this type are referred to as globally coupled RS-LDPC codes. These codes are designed for correcting random errors, random short phased bursts of erasures and long bursts of erasures. The Tanner graph of a globally coupled RS-LDPC is composed of a number of disjoint copies of the Tanner graph of a local RS-LDPC code which are connected together by a group of overall check-nodes (CNs), called global CNs. A globally coupled RS-LDPC code can be decoded with a two-phase local/global iterative scheme which allows correction of local random errors and phased bursts of erasures in the local phase and global random errors and a single long burst of erasures in the global phase.
This paper presents a special type of LDPC codes with a structure related to but different from that of the spatially coupled LDPC codes. For an LDPC code of this type, its Tanner graph is composed of a set of small disjoint Tanner graphs which are connected together by a group of overall check-nodes, called global check-nodes. Codes of this type are called globally coupled LDPC codes and they perform well over both the additive Gaussian white noise and the binary-erasure channels. Furthermore, they are very effective at correcting erasures clustered in bursts. Two algebraic methods are presented for constructing these codes. A two-phase local/global iterative scheme for decoding these codes is presented. This decoding scheme allows correction of local random and global errors and/or erasures in two phases.
This paper presents designs and constructions of two classes of binary quasi-cyclic LDPC codes for correcting multiple random phased-bursts of erasures over the binary erasure channel. The erasure correction of codes in both classes is characterized by the cycle and adjacency structure of their Tanner graphs. Erasure correction of these codes is a very simple process which requires only modulo-2 additions. The codes in the second class are capable of correcting locally and globally distributed phased-bursts of erasures with a two-phase iterative erasure-correction process.
This paper presents a construction of a class of partial geometries based on RS codes of prime lengths and shows that LDPC codes constructed based on Reed-Solomon codes of prime lengths are finite geometry LDPC codes. Furthermore, a new method for design and construction of nonbinary quasi-cyclic LDPC codes based on the conventional parity-check matrices of Reed-Solomon codes is presented. Simulation results show that the constructed nonbinary LDPC codes perform well over the additive white Gaussian channel.