Asymptotically Good Convolutional Codes

TL;DR

This paper introduces new sequences of asymptotically good convolutional codes derived from special block codes, using various code construction techniques, and demonstrates their effectiveness in approaching theoretical bounds.

Contribution

The paper presents novel methods for constructing asymptotically good convolutional codes from sequences of special block codes, expanding the toolkit for coding theory.

Findings

Constructed new sequences of asymptotically good convolutional codes.

Applied multiple code construction techniques to enhance code properties.

Proved the generality of the construction method for all sequences of good block codes.

Abstract

In this paper, we construct new sequences of asymptotically good convolutional codes. These sequences are obtained from sequences of transitive, self-orthogonal and self-dual block codes that attain the Tsfasman-Vladut-Zink bound. Furthermore, by applying the techniques of expanding, extending, puncturing, direct sum, the |u|u+v| construction and the product code construction to these block codes, we construct more new sequences of asymptotically good convolutional codes. Additionally, we show that the proposed construction method presented here also works when applied for all sequences of good block codes where lim kj/nj and lim dj/nj exist.