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A tight asymptotic bound on the size of constant-weight conflict-avoiding codes

机译：恒定权重避免冲突代码的大小的紧渐近边界

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摘要

In the study of multiple-access in the collision channel, conflict-avoiding code is used to guarantee that each transmitting user can send at least one packet successfully in the worst case within a fixed period of time, provided that at most k users out of M potential users are active simultaneously. The number of codewords in a conflict-avoiding code determines the number of potential users that can be supported in a system. Previously, upper bound on the size of conflict-avoiding code is known only for Hamming weights three, four and five. The asymptotic upper in this paper extends the known results to all Hamming weights, and is proved to be tight by exhibiting infinite sequences of conflict-avoiding codes which meet this bound asymptotically for all Hamming weights.
机译：在冲突信道中的多路访问研究中，避免冲突的代码用于确保每个发送用户在固定的时间段内在最坏的情况下至少可以成功发送至少一个数据包，前提是最多不超过k个用户M个潜在用户同时处于活动状态。避免冲突代码中的代码字数量决定了系统中可以支持的潜在用户数量。以前，仅对于汉明权重3、4和5，才知道避免冲突的代码大小的上限。本文的渐近上半部将已知结果扩展到所有汉明权重，并且通过展示无冲突序列的无穷序列而证明是紧的，这些序列在所有汉明权重上都渐近地满足此约束。

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