SUPERIMPOSED CODES IN THE HAMMING SPACE

We consider the problem of simultaneous identification and transmissio n of information by means of superimposed codes. It is assumed that a total population of T users share a common channel. At each time at mo st m of the T users are active. The output from the channel is the mod ulo-2 sum of the binary codewords transmitted by the active users, pos sibly disturbed by errors. A superimposed code is actually a set of co des-one for each user-designed in such a way that both the (at most) m active users and their messages can be identified, even in the presen ce of a permissible number of errors in the channel. We give several e xplicit constructions for superimposed codes and analyze in detail the ir performance. In several of the cases under study we offer codes tha t are proved to be best possible.