Line codes generated by finite Coxeter groups

TL;DR

This paper introduces a new class of line codes for parallel data transmission, leveraging Coxeter group theory to achieve simple encoding and decoding, with some designs being novel or improved.

Contribution

It applies Coxeter group theory to design line codes that enable efficient encoding and decoding for parallel transmission, including novel code designs.

Findings

Codes have simple encoding and decoding algorithms.

Some codes are novel or improve existing ones.

Performance characteristics are described.

Abstract

Using an algebraic approach based on the theory of Coxeter groups, we design, and describe the performance of, a class of line codes for parallel transmission of $b$ bits over $b+1$ wires that admit especially simple encoding and decoding algorithms. A number of designs are exhibited, some of them being novel or improving on previously obtained codes.