Rate optimization for repeat-accumulate interleave-division system by fixed-point analysis

A K-user repeat-accumulate interleave-division (RAID) system is considered for a Gaussian multiple access channel (GMAC) with binary inputs, equal-power, and symbol synchronization. In this system, a regular repeat accumulate (RA) code serially concatenated with spreading, where the rate of RA code and spreading length both can be changed, is employed for each user. K users are divided into M groups equally. The mth group contains K/M users with rate R_m (1 ≤ m ≤ M). At the receiver, multiuser message-passing decoding is performed on a single factor graph. A fixed point analysis is developed to obtain all achievable rate profiles for an arbitrary small decoding error rate over the GMAC. It shows that the sum rate of our optimal rate profile is superior to that of conventional multiuser RAID scheme with equal rate.