Generalized construction of signature code for multiple-access adder channel

We propose a generalized construction scheme of error-correcting signature code. We form a signature matrix whose rows become the non-zero codewords of the signature code. In the coding scheme, a signature matrix is obtained from a Hadamard matrix by replacing every element by an initial signature matrix or its associated matrix depending on the element´s binary value. The proposed code has longer length, higher decodability, and larger cardinality. In this coding scheme, the initial signature matrix is in a general form and can be a signature matrix of any initial signature code. Different initial matrices provide different error-correcting signature codes, including conventional codes. This general form makes it possible to obtain error-correcting signature codes with a higher sum rate than conventional codes.