On the Separability of Ergodic Fading MIMO Channels: A Lattice Coding Approach

TL;DR

This paper introduces a lattice coding scheme for ergodic fading MIMO channels that achieves capacity without separable coding, reducing memory requirements and providing universal codebooks for various fading distributions.

Contribution

It proposes a universal lattice coding scheme that attains ergodic capacity without separable coding, applicable to both finite and continuous fading distributions, and extends to MIMO systems.

Findings

Achieves ergodic capacity with lattice coding without separable coding.

Universal codebooks work across different fading realizations.

Small constant-gap to capacity for MIMO channels with CSIR only.

Abstract

This paper addresses point-to-point communication over block-fading channels with independent fading blocks. When both channel state information at the transmitter (CSIT) and receiver (CSIR) are available, most achievable schemes use separable coding, i.e., coding independently and in parallel over different fading states. Unfortunately, separable coding has drawbacks including large memory requirements at both communication ends. In this paper a lattice coding and decoding scheme is proposed that achieves the ergodic capacity without separable coding, with lattice codebooks and decoding decision regions that are universal across channel realizations. We first demonstrate this result for fading distributions with discrete, finite support whose sequences are robustly typical. Results are then extended to continuous fading distributions, as well as multiple-input multiple-output (MIMO) systems. In addition, a variant of the proposed scheme is presented for the MIMO ergodic fading channel with CSIR only, where we prove the existence of a universal codebook that achieves rates within a constant gap to capacity for finite-support fading distributions. The gap is small compared with other schemes in the literature. Extension to continuous-valued fading is also provided.