SUPERIMPOSED CODES FOR THE MULTIACCESS BINARY ADDER CHANNEL

Superimposed codes for multiple-access communication in a binary adder channel are analyzed. The superposition mechanism used in this corres pondence is ordinary addition. Each user is assigned a codeword from a superimposed code. It is proved that every constant-weight code C of weight ru and maximal correlation c corresponds to a subclass of a dis junctive code D of order m < w/c. Therefore, any m or less codewords i n C which are used at the same time yield a uniquely decodable code co mbination at the output of the adder channel. In the noisy case, for e ach subset A subset of or equal to C of size \A\ less than or equal to m much less than T the receiver is able to determine the number of ac tive users and to distinguish between the active users if the weight o f the error pattern e satisfies Wt(e) < min{w - c\A\, w/2}. Decoding a lgorithms for both the noiseless and the noisy cases are proposed.