Optimal Constant-Weight and Mixed-Weight Conflict-Avoiding Codes

TL;DR

This paper introduces new optimal conflict-avoiding codes (CACs), including mixed-weight variants, using combinatorial mathematics to improve asynchronous multiple access communication efficiency.

Contribution

It generalizes existing constant-weight CAC constructions and introduces the first study of mixed-weight CACs to enhance throughput and reduce delay.

Findings

Derived classes of optimal constant-weight CACs using Kneser's Theorem.

First study of mixed-weight CACs for prioritized user access.

Improved throughput and reduced access delay in communication systems.

Abstract

A conflict-avoiding code (CAC) is a deterministic transmission scheme for asynchronous multiple access without feedback. When the number of simultaneously active users is less than or equal to $w$, a CAC of length $L$ with weight $w$ can provide a hard guarantee that each active user has at least one successful transmission within every consecutive $L$ slots. In this paper, we generalize some previously known constructions of constant-weight CACs, and then derive several classes of optimal CACs by the help of Kneser's Theorem and some techniques in Additive Combinatorics. Another spotlight of this paper is to relax the identical-weight constraint in prior studies to study mixed-weight CACs for the first time, for the purpose of increasing the throughput and reducing the access delay of some potential users with higher priority. As applications of those obtained optimal CACs, we derive some classes of optimal mixed-weight CACs.