Multichannel Conflict-Avoiding Codes for Expanded Scenarios

2026-02-25

AI Summary

This study addresses the challenge of collision avoidance in multi-channel feedback-free multiple access systems where the number of channels $M$ is smaller than the number of active users $w$ (i.e., $M < w$). For the first time, it systematically investigates multi-channel conflict-avoiding codes (MC-CACs) under this practically relevant regime. By introducing the novel concept of “exceptional codewords” and leveraging additive combinatorial methods, the authors construct a family of optimal MC-CACs. The results are further extended naturally to two generalized frameworks—AM-OPPTS MC-CACs and mixed-weight MC-CACs—significantly enhancing the system’s supportable user capacity and thereby broadening and refining the existing CAC theoretical framework.

Technology Category

• Multiagent Systems: Mechanism Design
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

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.

Problem

• multichannel conflict-avoiding codes
• M < w
• deterministic multiple-access
• orthogonal channels
• practical application scenarios

Innovation

• multichannel conflict-avoiding codes
• exceptional codewords
• additive combinatorics
• optimal code construction
• mixed-weight MC-CAC