CTH08-1: Construction of High Performance and Efficiently Encodable Nonbinary Quasi-Cyclic LDPC Codes (original) (raw)

Construction of High Performance and Efficiently Encodable Nonbinary Quasi-Cyclic LDPC Codes

2006

This paper presents a general and three specific algebraic methods for constructing efficiently encodable nonbinary quasi-cyclic LDPC codes. Three classes of quasi-cyclic LDPC codes over nonbinary finite fields are constructed. Codes constructed perform very well over the AWGN channel with iterative decoding and achieve large coding gains over the Reed-Solomon codes of the same parameters. Nonbinary LDPC codes may be used to replace Reed-Solomon codes in some communication environments or storage systems for combating mixed types of noises and interferences.

Efficient encoding for a family of quasi-cyclic LDPC codes

2003

In general, encoding for LDPC codes can be difficult to realize efficiently. The paper presents techniques and architectures for LDPC encoding that are efficient and practical for a particular class of codes. These codes are the irregular partitioned permutation LDPC codes recently introduced by the author (Hocevar, D.E., Proc. IEEE Int. Conf. on Commun., p.2708-12, 2003). Since these codes are quasi-cyclic, it is known that a simpler encoding process does exist. The paper goes beyond that basic method by exploiting other structural properties to allow for a simpler and faster encoding process, in both software and hardware. Solutions for some rank deficient codes are also given.

Decoding of quasi-cyclic LDPC codes with section-wise cyclic structure

2014 Information Theory and Applications Workshop (ITA), 2014

Presented in this paper is a reduced-complexity iterative decoding scheme for quasi-cyclic (QC) LDPC codes. This decoding scheme is devised based on the section-wise cyclic structure of the parity-check matrix of a QC-LDPC code. Using this decoding scheme, the hardware implementation complexity of a QC-LDPC decoder can be significantly reduced without performance degradation. A high-rate QC-LDPC code that can achieve a very low error-rate without a visible error-floor is used to demonstrate the effectiveness of the proposed decoding scheme. Also presented in this paper are two other high-rate QC-LDPC codes and a method for constructing rate-1 2 QC-LDPC codes whose Tanner graphs have girth 8. All the codes constructed perform well with low error-floor using the proposed decoding scheme.