Code construction for the T-user noiseless adder channel

A general method for constructing codes for the T-user noiseless adder channel is proposed which achieves the largest sum rate known. The authors consider a multiple-access communication system. In this system, T statistically independent sources which use binary block codes C₁ ,...,C_T of equal length n, simultaneously transmit information via one common channel, maintaining synchronization with respect to words and bits. The output of the adder channel is the (T+l)-ary vector which is the component-wise arithmetic sum of the transmitted binary vectors. The task of the decoder is to uniquely determine the messages of all users