168 research outputs found
Construction and Applications of CRT Sequences
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.Comment: 16 pages, 5 figures. Some typos in Section V are correcte
A General Upper Bound on the Size of Constant-Weight Conflict-Avoiding Codes
Conflict-avoiding codes are used in the multiple-access collision channel
without feedback. The number of codewords in a conflict-avoiding code is the
number of potential users that can be supported in the system. In this paper, a
new upper bound on the size of conflict-avoiding codes is proved. This upper
bound is general in the sense that it is applicable to all code lengths and all
Hamming weights. Several existing constructions for conflict-avoiding codes,
which are known to be optimal for Hamming weights equal to four and five, are
shown to be optimal for all Hamming weights in general.Comment: 10 pages, 1 figur
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