SISO APP Searches in Lattices with Tanner Graphs

TL;DR

This paper introduces a low-complexity, soft-output lattice detector using Tanner graph belief propagation, enabling efficient maximum likelihood detection and iterative decoding in MIMO systems with lattice constellations.

Contribution

It presents a novel belief propagation-based lattice detection algorithm that requires no backtracking and provides soft information for iterative schemes, outperforming traditional sphere decoding in complexity.

Findings

Achieves maximum likelihood performance in quasistatic fading.

Performs close to interference-free transmission in independent fading.

Outperforms traditional sphere decoding in computational complexity.

Abstract

An efficient, low-complexity, soft-output detector for general lattices is presented, based on their Tanner graph (TG) representations. Closest-point searches in lattices can be performed as non-binary belief propagation on associated TGs; soft-information output is naturally generated in the process; the algorithm requires no backtrack (cf. classic sphere decoding), and extracts extrinsic information. A lattice's coding gain enables equivalence relations between lattice points, which can be thereby partitioned in cosets. Total and extrinsic a posteriori probabilities at the detector's output further enable the use of soft detection information in iterative schemes. The algorithm is illustrated via two scenarios that transmit a 32-point, uncoded super-orthogonal (SO) constellation for multiple-input multiple-output (MIMO) channels, carved from an 8-dimensional non-orthogonal lattice (a direct sum of two 4-dimensional checkerboard lattice): it achieves maximum likelihood performance in quasistatic fading; and, performs close to interference-free transmission, and identically to list sphere decoding, in independent fading with coordinate interleaving and iterative equalization and detection. Latter scenario outperforms former despite the absence of forward error correction coding---because the inherent lattice coding gain allows for the refining of extrinsic information. The lattice constellation is the same as the one employed in the SO space-time trellis codes first introduced for 2-by-2 MIMO by Ionescu et al., then independently by Jafarkhani and Seshadri. Complexity is log-linear in lattice dimensionality, vs. cubic in sphere decoders.