New Families of LDPC Block Codes Formed by Terminating Irregular Protograph-Based LDPC Convolutional Codes

TL;DR

This paper introduces a new method for constructing LDPC block codes by terminating irregular protograph-based LDPC convolutional codes, resulting in ensembles with near-capacity thresholds and linear minimum distance growth.

Contribution

It presents a novel construction technique for LDPC codes from convolutional codes using protographs, demonstrating good thresholds and asymptotic goodness.

Findings

Ensembles have thresholds close to channel capacity.

Minimum distance grows linearly with block length.

Flexible design allows varying code rates.

Abstract

In this paper, we present a method of constructing new families of LDPC block code ensembles formed by terminating irregular protograph-based LDPC convolutional codes. Using the accumulate-repeat-by-4-jagged-accumulate (AR4JA) protograph as an example, a density evolution analysis for the binary erasure channel shows that this flexible design technique gives rise to a large selection of LDPC block code ensembles with varying code rates and thresholds close to capacity. Further, by means of an asymptotic weight enumerator analysis, we show that all the ensembles in this family also have minimum distance that grows linearly with block length, i.e., they are asymptotically good.