Irregular repeat accumulate codes with few iterations for the binary adder channel

Iterative interference cancellation is a powerful technique for design of multiuser decoders. Careful encoder and decoder design is essential for reducing implementation complexity. When used in conjunction with iteratively-decodeable sparse graph codes, there is a choice to be made between the number of multiuser interference cancellation stages and the number of iterations used for decoding each user´s code. Too few decoder iterations may increase the number of interference cancellation steps, whereas too many may superfluous, or even inhibit the convergence behaviour of the cancellation loop. In this paper we design non-systematic irregular repeat-accumulate codes for multiple-access channels where the number of cancellation stages and number of decoder iterations at each stage are fixed. The design goal is minimal bit error rate. Our formulation is based on extrinsic information transfer, and introduces the number of iterations directly into the curve fitting problem. For clear development of concepts, we restrict attention to the binary adder channel, where our approach is exact. Generalisation to other sparse graph codes and other multiple-access channels is straightforward, subject to the usual approximations.