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

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

Applications of additive sequence of permutations

AbstractLet X1 be the m-vector (−r,−r+1,…,−1,0,1,…,r−1,r), m=2r+1, and X2,…,Xn be permutations of X1. Then X1,X2,…,Xn is said to be an additive sequence of permutations (ASP) of order m and length n if the vector sum of every subsequence of consecutive permutations is again a permutation of X1. ASPs had been extensively studied and used to construct perfect difference families. In this paper, ASPs are used to construct perfect difference families and properly centered permutation matrices (which are related to radar arrays). More existence results on perfect difference families and properly centered permutation matrices are obtained