Minimum Distance and Convergence Analysis of Hamming-Accumulate-Acccumulate Codes

TL;DR

This paper analyzes a serial concatenation of Hamming and accumulate codes, demonstrating they are asymptotically good with high minimum distances and suitable for high-rate, low-error applications.

Contribution

It introduces a new ensemble of concatenated codes with proven linear minimum distance growth and good iterative decoding convergence properties.

Findings

Most codes in the ensemble have minimum distance growing linearly with block length.

Codes achieve about half or more of the minimum distance of random linear codes.

The codes exhibit good iterative convergence thresholds.

Abstract

In this letter we consider the ensemble of codes formed by the serial concatenation of a Hamming code and two accumulate codes. We show that this ensemble is asymptotically good, in the sense that most codes in the ensemble have minimum distance growing linearly with the block length. Thus, the resulting codes achieve high minimum distances with high probability, about half or more of the minimum distance of a typical random linear code of the same rate and length in our examples. The proposed codes also show reasonably good iterative convergence thresholds, which makes them attractive for applications requiring high code rates and low error rates, such as optical communications and magnetic recording.