Punctured Binary Simplex Codes as LDPC codes

TL;DR

This paper introduces a class of rate-adaptive LDPC codes derived from punctured simplex codes, enabling efficient decoding and a wide range of code rates with minimal impact on minimum distance.

Contribution

The paper proposes a novel method to create rate-adaptive LDPC codes from punctured simplex codes, maintaining decoding efficiency and code performance.

Findings

Codes achieve higher rates than original simplex codes

Puncturing does not violate the row-column constraint

Trade-offs between code rate and minimum distance are favorable

Abstract

Digital data transfer can be protected by means of suitable error correcting codes. Among the families of state-of-the-art codes, LDPC (Low Density Parity-Check) codes have received a great deal of attention recently, because of their performance and flexibility of operation, in wireless and mobile radio channels, as well as in cable transmission systems. In this paper, we present a class of rate-adaptive LDPC codes, obtained as properly punctured simplex codes. These codes allow for the use of an efficient soft-decision decoding algorithm, provided that a condition called row-column constraint is satisfied. This condition is tested on small-length codes, and then extended to medium-length codes. The puncturing operations we apply do not influence the satisfaction of the row-column constraint, assuring that a wide range of code rates can be obtained. We can reach code rates remarkably higher than those obtainable by the original simplex code, and the price in terms of minimum distance turns out to be relatively small, leading to interesting trade-offs in the resulting asymptotic coding gain.