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：冲突避免码（CAC）是一种长度为L、重量为w的码字，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，该类码能够严格保证每个活跃用户在每连续L个时隙内成功完成一次传输。近年来，为增加可支持潜在用户数量，CAC被扩展至M个正交信道上的多信道冲突避免码（MC-CAC）。现有MC-CAC结果大多基于M不小于w的假设，而本文聚焦于M小于w这一更贴近实际应用场景的情形。首先引入MC-CAC中异常码字的概念，通过运用加性组合学中的若干技术，推导出一系列最优MC-CAC。在此过程中，部分已知最优CAC结果得以推广。最后，本文结果自然延伸至两类相关码：AM-OPPTS MC-CAC与混合重量MC-CAC。