A multiuser k-ary code for the noisy multiple-access adder channel

Multiuser k-ary coding is proposed for a noisy multiple-access adder channel. It is shown that when a T-user δ-decodable k-ary code C is given a priori, a qT-user λδ-decodable k-ary code C^* is obtained by using a matrix, such as a Hadamard matrix or a conference matrix of order q, where λ is a positive integer depending on the matrix. More noteworthy is that the code C is an arbitrary δ-decodable k-ary code, and that the coding scheme preserves the total rate, i.e., the total rate of C^* is equal to that of C