Construction and Applications of CRT Sequences

TL;DR

This paper introduces a method for constructing protocol sequences using the Chinese Remainder Theorem to optimize channel access in collision channels without feedback, aiming for stable throughput despite delays.

Contribution

It presents a novel construction of protocol sequences based on CRT, providing a systematic way to minimize throughput fluctuation in collision channels.

Findings

Constructed protocol sequences with near-constant cross-correlation

Derived a lower bound on system throughput in collision channels

Demonstrated improved stability in channel access

Abstract

Protocol sequences are used for channel access in the collision channel without feedback. Each user accesses the channel according to a deterministic zero-one pattern, called the protocol sequence. In order to minimize fluctuation of throughput due to delay offsets, we want to construct protocol sequences whose pairwise Hamming cross-correlation is as close to a constant as possible. In this paper, we present a construction of protocol sequences which is based on the bijective mapping between one-dimensional sequence and two-dimensional array by the Chinese Remainder Theorem (CRT). In the application to the collision channel without feedback, a worst-case lower bound on system throughput is derived.