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.

翻译：避撞码（CAC）是一种长度为L、重量为w的码，用于无反馈的确定性多址接入。当同时活跃用户数不超过w时，此类码能够严格保证每个活跃用户在任意连续L个时隙内至少有一次成功传输。近年来，CAC被推广至具有M个正交信道的多信道CAC（MC-CAC），旨在提升可支持的最大潜在用户数。现有关于MC-CAC的研究大多基于M ≥ w的假设，本文则聚焦于M < w的情形，该情形在实际应用场景中更具相关性。本文首先引入MC-CAC中例外码字的概念，借助加性组合学中的若干技术，推导出一系列最优MC-CAC构造。在此过程中，若干已知的最优CAC结果被推广至多信道场景。最后，本文结果可自然扩展至AM-OPPTS MC-CAC与混合重量MC-CAC这两类相关码型。