Nearly optimal multiuser codes for the binary adder channel

Coding schemes for the T-user binary adder channel are investigated. Recursive constructions are given for two families of mixed-rate, multiuser codes. It is shown that these basic codes can be combined by time-sharing to yield codes approaching most rates in the T-user capacity region. In particular, the best codes constructed herein achieve a sum-rate, R₁+...+R_T, which is higher than all previously reported codes for almost every T and is within 0.547-bit-per-channel use of the information-theoretic limit. Extensions to a T-user, Q-frequency adder channel are also discussed