Rate-Adaptive LDPC Codes Obtained from Simplex Codes

In this paper we show that, when a binary primitive polynomial can be associated to a sparse Golomb ruler, the simplex code obtained by taking it as the code parity-check polynomial exhibits good distance properties and performance. We define some conditions under which the obtained codes are also Low-Density Parity-Check (LDPC) codes, and can hence be decoded through efficient iterative algorithms. We perform code puncturing, leading to a family of rate-adaptive codes, and we predict some of their structural properties in terms of minimum distance and weight distribution. We show that, in addition to having some useful properties, these codes achieve good performance in terms of error rate under LDPC decoding.