A Sugiyama-like decoding algorithm for convolutional codes

TL;DR

This paper introduces a Sugiyama-like decoding algorithm tailored for skew BCH convolutional codes, leveraging their cyclic structure and algebraic properties to improve error correction capabilities.

Contribution

It presents a novel decoding algorithm specifically designed for skew BCH convolutional codes, utilizing their algebraic structure and division algorithms.

Findings

The algorithm effectively decodes skew BCH convolutional codes.

It extends Sugiyama's procedure to a new class of convolutional codes.

The method exploits the cyclic structure and algebraic properties of the codes.

Abstract

We propose a decoding algorithm for a class of convolutional codes called skew BCH convolutional codes. These are convolutional codes of designed Hamming distance endowed with a cyclic structure yielding a left ideal of a non-commutative ring (a quotient of a skew polynomial ring). In this setting, right and left division algorithms exist, so our algorithm follows the guidelines of the Sugiyama's procedure for finding the error locator and error evaluator polynomials for BCH block codes.