A Family of -Ary Signature Codes for Noisy Multiple-Access Adder Channel

A coding scheme of (k+1) -ary error-correcting signature codes for a noisy multiple-access adder channel is proposed. Given a signature matrix A and a difference matrix D=D⁺ - D^- a priori, a larger signature matrix is obtained by replacing each element in the Hadamard matrix with A , or D⁺ , or D^- depending on the values of the elements and their locations in the Hadamard matrix. The set of rows in the proposed matrix gives an error-correcting signature code. Introducing a difference matrix makes it possible to construct an error-correcting signature code whose sum rate is increased with an increase in the order of the Hadamard matrix. Either binary or non-binary signature codes are constructed when the pairs of matrices A and D are given.