Algebraic Decoding for Doubly Cyclic Convolutional Codes

TL;DR

This paper introduces an algebraic iterative decoding algorithm tailored for doubly cyclic convolutional codes, leveraging their algebraic structure for efficient decoding and providing bounds on correctable error configurations.

Contribution

It presents a novel algebraic decoding method specifically designed for doubly cyclic convolutional codes, utilizing Reed-Solomon decoding for improved efficiency.

Findings

Decoding algorithm successfully applied to doubly cyclic convolutional codes.

Bound established for correctable error configurations.

Comparison shows advantages over existing algorithms.

Abstract

An iterative decoding algorithm for convolutional codes is presented. It successively processes $N$ consecutive blocks of the received word in order to decode the first block. A bound is presented showing which error configurations can be corrected. The algorithm can be efficiently used on a particular class of convolutional codes, known as doubly cyclic convolutional codes. Due to their highly algebraic structure those codes are well suited for the algorithm and the main step of the procedure can be carried out using Reed-Solomon decoding. Examples illustrate the decoding and a comparison with existing algorithms is being made.