A novel soft information algorithm for closest point search in lattices with Tanner graph representations

An efficient, low-complexity, soft-information detector for multiple input multiple output channels and lattice constellations was devised, based on Tanner graph representations of lattices. Due to the coding gain associated with a lattice, structural relations exist between certain lattice points, which can be associated via an equivalence relation for detection purposes. The algorithm can generate both total and extrinsic a posteriori probability at detector’s output. The step-back artifact (of traditional sphere decoders) is eliminated. The algorithm applies to general lattices and enables iterative receivers; it was tested in the case of uncoded transmission for a superorthogonal constellation in two scenarios. In quasistatic (block) fading it was found to achieve maximum likelihood performance even with one ‘surviving’ label (out of six); in independent fading with coordinate (component) interleaving and iterations between equalization and detection, it performs close to interference-free transmission. The coordinate interleaved scenario outperforms former despite absence of forward error correction coding. Index Terms Belief propagation on a lattice, sphere decoder, soft information lattice detection, closest point search in lattices, Tanner graph, MIMO, iterations detector-decoder.