Joint decoding of multiple non-binary LDPC codewords

We develop a belief-propagation (BP) decoder for the joint decoding of multiple codewords which belong to the same non-binary LDPC code. Decoding is based on soft information in form of joint channel-posterior probabilities of all codeword symbols. We extend the BP algorithm for q-ary LDPC codes such that the FFT-based check node processing is preserved and the complexity remains manageable. This joint decoding is useful in settings in which multiple codewords are transmitted in a non-orthogonal way over the same channel, including multiple-access with packet collisions, physical-layer network coding and multi-resolution broadcasting. We show in an example that joint decoding can be far superior to separate decoding.