Multichannel Conflict-Avoiding Codes for Expanded Scenarios

TL;DR

This paper introduces and constructs optimal multichannel conflict-avoiding codes for scenarios where the number of channels is less than the code weight, using additive combinatorics techniques.

Contribution

It extends the theory of MC-CACs to cases with fewer channels than code weight, introducing exceptional codewords and deriving optimal codes.

Findings

Derived a series of optimal MC-CACs for M < w

Generalized known optimal CAC results to multichannel scenarios

Extended results to AM-OPPTS and mixed-weight MC-CACs

Abstract

A conflict-avoiding code (CAC) of length L and weight w is used for deterministic multiple-access without feedback. When the number of simultaneous active users is less than or equal to w, such a code is able to provide a hard guarantee that each active user has a successful transmission within every consecutive L time slots. Recently, CACs were extended to multichannel CAcs (MC-CACs) over M orthogonal channels with the aim of increasing the number of potential users that can be supported. While most existing results on MC-CAC are derived under the assumption that M is not less than w, this paper focuses on the case that M is less than w, which is more relevant to practical application scenarios. In this paper, we first introduce the concept of exceptional codewords in MC-CACs. By employing some techniques from additive combinatorics, we derive a series of optimal MC-CACs. Along the way, several previously known optimal CAC results are generalized. Finally, our results extend naturally to AM-OPPTS MC-CACs and mixed-weight MC-CACs, two classes of relevant codes.