Multichannel Conflict-Avoiding Codes of Weights Three and Four

TL;DR

This paper extends conflict-avoiding codes to multiple channels for weights three and four, providing optimal constructions and bounds to ensure collision-free transmissions in multi-channel networks.

Contribution

It introduces multichannel conflict-avoiding codes for weights three and four, deriving upper bounds and presenting optimal constructions.

Findings

Derived upper bounds for multichannel CACs of weights three and four.

Constructed optimal multichannel CACs matching these bounds.

Ensured collision-free guarantees in multi-channel transmission scenarios.

Abstract

Conflict-avoiding codes (CACs) were introduced by Levenshtein as a single-channel transmission scheme for a multiple-access collision channel without feedback. When the number of simultaneously active source nodes is less than or equal to the weight of a CAC, it is able to provide a hard guarantee that each active source node transmits at least one packet successfully within a fixed time duration, no matter what the relative time offsets between the source nodes are. In this paper, we extend CACs to multichannel CACs for providing such a hard guarantee over multiple orthogonal channels. Upper bounds on the number of codewords for multichannel CACs of weights three and four are derived, and constructions that are optimal with respect to these bounds are presented.