Constructing Linear Codes with Good Joint Spectra

TL;DR

This paper develops methods to construct linear codes with excellent joint spectra for joint source-channel coding, using LDPC and LDGM codes, to improve coding performance.

Contribution

It introduces a new explicit construction of linear codes with good joint spectra based on LDPC and LDGM codes, advancing code design for JSCC.

Findings

Developed a spectrum calculation method for codes.

Presented principles for constructing good linear codes.

Proposed explicit LDPC/LDGM-based code construction.

Abstract

The problem of finding good linear codes for joint source-channel coding (JSCC) is investigated in this paper. By the code-spectrum approach, it has been proved in the authors' previous paper that a good linear code for the authors' JSCC scheme is a code with a good joint spectrum, so the main task in this paper is to construct linear codes with good joint spectra. First, the code-spectrum approach is developed further to facilitate the calculation of spectra. Second, some general principles for constructing good linear codes are presented. Finally, we propose an explicit construction of linear codes with good joint spectra based on low density parity check (LDPC) codes and low density generator matrix (LDGM) codes.