Progressive Differences Convolutional Low-Density Parity-Check Codes

TL;DR

This paper introduces a new class of LDPC convolutional codes designed with progressive differences, offering fixed minimum distance and cycle-free Tanner graphs, suitable for high-rate, bandwidth-efficient applications.

Contribution

It proposes a novel design method for LDPC convolutional codes using ordered progressive differences, ensuring desirable properties regardless of code rate.

Findings

Codes have fixed minimum distance.

Tanner graphs lack short cycles.

Applicable to high-rate bandwidth-saving scenarios.

Abstract

We present a new family of low-density parity-check (LDPC) convolutional codes that can be designed using ordered sets of progressive differences. We study their properties and define a subset of codes in this class that have some desirable features, such as fixed minimum distance and Tanner graphs without short cycles. The design approach we propose ensures that these properties are guaranteed independently of the code rate. This makes these codes of interest in many practical applications, particularly when high rate codes are needed for saving bandwidth. We provide some examples of coded transmission schemes exploiting this new class of codes.