We study the size of a collection $\{ \mathcal{P}_1 , \ldots ,\mathcal{P}_T \}$ whose members $\mathcal{P}_i ,i = 1, \ldots ,T$, are disjoint sets of integral vectors such that $\sum _{i = 1}^T \bar x_i $ are all distinct and each n-tuple $\bar x_i $ comes from a different set $\mathcal{P}_i $. In particular, if $\mathcal{P}_i = \{ \bar 0_n ,\bar x_i \}$, we have a well-known problem on maximum cardinality of sum-distinct sets of integral vectors. We state bounds on $n^{ - 1} \sum _{i = 1}^T \log _2 | \mathcal{P}_i |$ and give a construction that meets the lower bound.

Disjoint uniquely decodable codebooks for noiseless synchronized multiple-access adder channels are studied. Codebooks are applicable to multiple access systems in which the number of transmitting users varies over the life of the system. Several designs of codebooks, based on certain integer sets from (0,1,2,3,. . .,2/sup n/-1), are presented. They are restricted to codebooks which have the rate sum above one and simple and efficient decoding algorithms.>

A geometric approach in the design of codebooks for OR frequency-hopping multiple-access (FHMA) channels is developed by treating a signal matrix as a finite set of distinct points. The relationship among the parameters of an interference-free j-distinguishable-point codebook, j>or=1, is established by using coordinate-free arguments. Geometry induced by such a codebook is characterized, and the design of a well-structured j-distinguishable-point codebook is related to a block design problem. It is shown that a well-structured 1-distinguishable-point codebook implies the axiom system of a finite affine plane.>

Basic notions pertinent to code-division multiple-user communication signals are defined in set-theoretic terms. A general treatment of composition codes by identifying a time-frequency spectrogram with a set of points in a finite plane is provided. It is shown that a finite affine plane is a powerful generator of frequency-hopping codes for multiple-access channels and that it provides optimum performance codes in a noiseless environment.>