Optimal Multiuser Codes for the Real Adder Channel

A new family of uniquely decodable binary codes is presented for the T-user real adder channel. The codes consist of T individual codebooks, each containing only two codewords, one of which is the all-zero sequence. These codes achieve a sum rate that is equal, asymptotically in T, to the sum capacity. An iterative decoding algorithm is also presented. Applications are discussed to codes for T active users out of M potential users, and to superimposed codes.