On doubly-cyclic convolutional codes

TL;DR

This paper introduces doubly-cyclic convolutional codes, explores their properties, and demonstrates that Reed-Solomon and BCH codes within this class can be optimal or near optimal in distance and performance.

Contribution

The paper defines doubly-cyclic convolutional codes and analyzes their properties, including the construction of Reed-Solomon and BCH codes within this class.

Findings

Some Reed-Solomon convolutional codes are optimal or near optimal in distance.

Basic properties of doubly-cyclic codes are established.

Distance and performance of these codes are analyzed.

Abstract

Cyclicity of a convolutional code (CC) is relying on a nontrivial automorphism of the algebra F[x]/(x^n-1), where F is a finite field. If this automorphism itself has certain specific cyclicity properties one is lead to the class of doubly-cyclic CC's. Within this large class Reed-Solomon and BCH convolutional codes can be defined. After constructing doubly-cyclic CC's, basic properties are derived on the basis of which distance properties of Reed-Solomon convolutional codes are investigated.This shows that some of them are optimal or near optimal with respect to distance and performance.