# Lattice Coding and Decoding for Multiple-Antenna Ergodic Fading Channels

## TL;DR

This paper introduces a lattice coding and decoding strategy for ergodic fading channels, achieving near-capacity performance with fixed decision regions, applicable to SISO, MIMO, and MAC scenarios with limited channel state information.

## Contribution

It proposes a novel lattice coding and decoding method with fixed decision regions that approach capacity in fading channels, reducing dependence on channel realizations.

## Key findings

- Gap to capacity is bounded for SISO channels across various fading distributions.
- Achieves near-capacity rates in MIMO channels with Rayleigh fading, improving with more receive antennas.
- Extends results to multi-user MAC, maintaining small gaps to capacity.

## Abstract

For ergodic fading, a lattice coding and decoding strategy is proposed and its performance is analyzed for the single-input single-output (SISO) and multiple-input multiple-output (MIMO) point-to-point channel as well as the multiple-access channel (MAC), with channel state information available only at the receiver (CSIR). At the decoder a novel strategy is proposed consisting of a time-varying equalization matrix followed by decision regions that depend only on channel statistics, not individual realizations. Our encoder has a similar structure to that of Erez and Zamir. For the SISO channel, the gap to capacity is bounded by a constant under a wide range of fading distributions. For the MIMO channel under Rayleigh fading, the rate achieved is within a gap to capacity that does not depend on the signal-to-noise ratio (SNR), and diminishes with the number of receive antennas. The analysis is extended to the K-user MAC where similar results hold. Achieving a small gap to capacity while limiting the use of CSIR to the equalizer highlights the scope for efficient decoder implementations, since decision regions are fixed, i.e., independent of channel realizations.