最优常重量和混合重量冲突避免码
Optimal Constant-Weight and Mixed-Weight Conflict-Avoiding Codes
AI总结：
本文推广常重量冲突避免码的构造，并首次引入混合重量冲突避免码，利用Kneser定理等工具得到多类最优码，以提高吞吐量并减少高优先级用户的接入延迟。
摘要：
冲突避免码（CAC）是一种用于无反馈异步多址接入的确定性传输方案。当同时活跃用户数小于或等于$w$时，长度为$L$、重量为$w$的CAC能够硬性保证每个活跃用户在每连续的$L$个时隙内至少有一次成功传输。本文推广了先前已知的常重量CAC的一些构造，并借助Kneser定理及加性组合学中的一些技术，推导出几类最优CAC。本文的另一个亮点是首次放宽先前研究中的等重量约束，研究混合重量CAC，目的是提高吞吐量并减少一些具有较高优先级的潜在用户的接入延迟。作为所得最优CAC的应用，我们推导出几类最优混合重量CAC。
英文摘要：
A conflict-avoiding code (CAC) is a deterministic transmission scheme for asynchronous multiple access without feedback. When the number of simultaneously active users is less than or equal to $w$, a CAC of length $L$ with weight $w$ can provide a hard guarantee that each active user has at least one successful transmission within every consecutive $L$ slots. In this paper, we generalize some previously known constructions of constant-weight CACs, and then derive several classes of optimal CACs by the help of Kneser's Theorem and some techniques in Additive Combinatorics. Another spotlight of this paper is to relax the identical-weight constraint in prior studies to study mixed-weight CACs for the first time, for the purpose of increasing the throughput and reducing the access delay of some potential users with higher priority. As applications of those obtained optimal CACs, we derive some classes of optimal mixed-weight CACs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
