Iterative multiuser joint decoding: unified framework and asymptotic analysis

The synchronous chip-rate discrete-time CDMA channel with channel coding is analysed and the corresponding factor graph is presented. Iterative joint decoding can be derived in a simple and direct way by applying the sum-product algorithm to the factor graph. Since variables have degree 2, no computation takes place at the variable nodes. Computation at the code nodes is just soft-in soft-out (SISO) decoding, whose output is the extrinsic PMF of the coded symbols. Computation at the channel transition nodes is equivalent to MAP symbol-by-symbol multiuser detection, whose complexity is generally exponential in K. We show that several previously proposed low-complexity algorithms based on interference cancellation (IC) can be derived in a simple direct way by approximating the extrinsic PMF output by the SISO decoders either as a single mass-point PMF (hard decision) or as a Gaussian PDF with the same mean and variance (moment matching). Differently from all previously presented methods (derived from heuristic reasoning), we see clearly that extrinsic rather than a posteriori PMF should be fed back. This yields important advantages in terms of limiting achievable throughput.