Construction of Short Protocol Sequences with Worst-Case Throughput Guarantee

Protocol sequences are used in channel access for the multiple-access collision channel without feedback. A new construction of protocol sequences with a guarantee of worst-case system throughput is proposed. The construction is based on Chinese remainder theorem. The Hamming crosscorrelation is proved to be concentrated around the mean. The sequence period is much shorter than existing protocol sequences with the same throughput performance. The new construction reduces the complexity in implementation and also shortens the waiting time until a packet can be sent successfully.

💡 Research Summary

The paper addresses the long‑standing problem of designing protocol sequences for a multiple‑access collision channel that provides no feedback to the users. In such environments, users transmit according to pre‑assigned binary sequences; a “1” indicates a transmission slot and a “0” a silent slot. The main performance metric is the worst‑case system throughput, i.e., the minimum fraction of successful transmissions over all possible relative shifts of the users’ sequences. Existing constructions (e.g., shift‑invariant or prime‑based sequences) achieve good average throughput but can suffer severe degradation in the worst case because the Hamming cross‑correlation between some user pairs can become large.

The authors propose a novel construction based on the Chinese Remainder Theorem (CRT). For each user i they select two relatively prime integers (p_i) and (q_i) (typically small primes) and define the sequence length (N_i = p_i q_i). A transmission occurs at time t if and only if
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