A Family of $(k+1)$ -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.