IEEE Transactions on Communications

Algebraic Quasi-Cyclic LDPC Codes: Construction, Low Error-Floor, Large Girth and a Reduced-Complexity Decoding Scheme

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

Published Jul 15, 2014• 141 citations

Abstract

This paper presents a simple and very flexible method for constructing quasi-cyclic (QC) low density paritycheck (LDPC) codes based on finite fields. The code construction is based on two arbitrary subsets of elements from a given field. Some well known constructions of QC-LDPC codes based on finite fields and combinatorial designs are special cases of the proposed construction. The proposed construction in conjunction with a technique, known as masking, results in codes whose Tanner graphs have girth 8 or larger. Experimental results show that codes constructed using the proposed construction perform well and have low error-floors. Also presented in the paper is a reduced-complexity iterative decoding scheme for QC-LDPC codes based on the section-wise cyclic structure of their parity-check matrices. The proposed decoding scheme is an improvement of an earlier proposed reduced-complexity iterative decoding scheme.

DOI: 10.1109/tcomm.2014.2339329

Related papers

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

Juane Li, Keke Liu, Shu Lin +1 more

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.

Information Theory and Applications Workshop (ITA)Feb 1, 201425 citations

Construction of Regular and Irregular QC-LDPC Codes: a Finite Field Approach and Masking

Xiaopeng Chen, Lin Zhou, Rui Zhao +1 more

Quasi-Cyclic Low-Density Parity-Check (QC-LDPC) codes require less hardware resources due to the quasi-cyclic structure of parity-check matrices.In this paper, two improved methods for constructing QC-LDPC codes are proposed.Firstly, in order to make sure the masked LDPC codes have flexible code rate and code length, an improved construction of masking matrix is presented.The proposed regular masking matrix of QC-LDPC codes have the girth at least 6.Then, the irregular codes are constructed by using improved finite field approach and PEG algorithm, which result in large girth and less short cycles.Simulations demonstrate that the proposed QC-LDPC codes have both lower error floor and good waterfall performance.

International Symposium on Advances in Electrical, Electronics and Computer Engineering (ISAEECE)Jan 1, 20161 citation

Quasi-cyclic LDPC codes on two arbitrary sets of a finite field

Juane Li, Keke Liu, Shu Lin +1 more

This paper presents a simple and flexible method for constructing QC-LDPC codes based on two arbitrary sets of a finite field. Based on this method, a high-rate, high-performance and very low error-floor QC-LDPC code is first constructed and then a class of rate-1/2 QC-LDPC codes whose Tanner graphs have girth 8 or larger is presented. Also presented is a reduced-complexity iterative decoding algorithm for QC-LDPC codes.

IEEE International Symposium on Information Theory (ISIT)Jun 1, 20149 citations

Construction of Finite Field Based QC-LDPC Codes from Isomorphism Perspective

Huaan Li, Hengzhou Xu, Baoming Bai +2 more

There are many algebraic tools, e.g., finite fields and combinatorial designs, for constructing good quasi-cyclic LDPC (QC-LDPC) codes. In particular, QC-LDPC codes designed based on two arbitrary subsets of a given finite field perform very well and some well-known algebraic constructions of QC-LDPC codes have been verified as special cases of this method. How to choose these two subsets to further improve the performance of finite field based QC-LDPC codes is of interest. In this paper, we study such codes and analyze their structural properties from isomorphism perspective, and generalize some rules to efficiently determine the non-isomorphic finite field based codes. By comparing the cycle distributions of non-isomorphic codes, we can easily construct the finite field based QC-LDPC codes with larger girth and fewer short cycles. These codes generally perform very well and can be used as the ingredients of some further processings, e.g., masking. Numerical results show that the constructed codes have better performance with the iterative decoding algorithms.

International Conference on Wireless Communications and Signal Processing (WCSP)Oct 1, 20191 citation

A reduced-complexity iterative scheme for decoding quasi-cyclic low-density parity-check codes

Shu Lin, Keke Liu, Juane Li +1 more

This paper presents a reduced-complexity iterative decoding scheme for quasi-cyclic (QC) low-density parity-check (LDPC) codes which is devised based on the section-wise cyclic structure of their parity-check matrices. The decoding scheme significantly reduces the hardware implementation complexity of a QC-LDPC code decoder in terms of the number of message processing units and the number of wires required to connect the message processing units. A long high-rate high-performance QC-LDPC code is used to demonstrate the effectiveness of the proposed decoding scheme. Using this long code as the mother code, descendant QC-LDPC codes of various lengths and rates can be constructed by puncturing and masking the columns and rows of the parity-check matrix of the mother code. These descendant codes can be decoded by deactivating specific sets of message processing units of the mother decoder.

Asilomar Conference on Signals, Systems and Computers (ACSSC)Nov 1, 20146 citations

Construction of Quasi-Cyclic LDPC Codes for AWGN and Binary Erasure Channels: A Finite Field Approach

Lan Lan, Lingqi Zeng, Y.Y. Tai +3 more

In the late 1950s and early 1960s, finite fields were successfully used to construct linear block codes, especially cyclic codes, with large minimum distances for hard-decision algebraic decoding, such as Bose-Chaudhuri-Hocquenghem (BCH) and Reed-Solomon (RS) codes. This paper shows that finite fields can also be successfully used to construct algebraic low-density parity-check (LDPC) codes for iterative soft-decision decoding. Methods of construction are presented. LDPC codes constructed by these methods are quasi-cyclic (QC) and they perform very well over the additive white Gaussian noise (AWGN), binary random, and burst erasure channels with iterative decoding in terms of bit-error probability, block-error probability, error-floor, and rate of decoding convergence, collectively. Particularly, they have low error floors. Since the codes are QC, they can be encoded using simple shift registers with linear complexity.

IEEE Transactions on Information TheoryJun 28, 2007263 citations