DMT Optimality of LR-Aided Linear Decoders for a General Class of Channels, Lattice Designs, and System Models

TL;DR

This paper proves that LR-aided linear decoders can achieve the optimal diversity-multiplexing tradeoff in various MIMO and related channels, offering a computationally efficient alternative to ML decoding.

Contribution

It establishes the DMT optimality of lattice-reduction aided linear decoders for a broad class of channels and codes, reducing decoding complexity while maintaining optimality.

Findings

LR-aided linear decoders are DMT optimal across all channel types and dimensions.

LLL-based LR-aided MMSE-GDFE decoders enable linear complexity DMT optimal decoding.

Results apply to diverse scenarios like MIMO, OFDM, ISI, and cooperative relaying.

Abstract

The work identifies the first general, explicit, and non-random MIMO encoder-decoder structures that guarantee optimality with respect to the diversity-multiplexing tradeoff (DMT), without employing a computationally expensive maximum-likelihood (ML) receiver. Specifically, the work establishes the DMT optimality of a class of regularized lattice decoders, and more importantly the DMT optimality of their lattice-reduction (LR)-aided linear counterparts. The results hold for all channel statistics, for all channel dimensions, and most interestingly, irrespective of the particular lattice-code applied. As a special case, it is established that the LLL-based LR-aided linear implementation of the MMSE-GDFE lattice decoder facilitates DMT optimal decoding of any lattice code at a worst-case complexity that grows at most linearly in the data rate. This represents a fundamental reduction in the decoding complexity when compared to ML decoding whose complexity is generally exponential in rate. The results' generality lends them applicable to a plethora of pertinent communication scenarios such as quasi-static MIMO, MIMO-OFDM, ISI, cooperative-relaying, and MIMO-ARQ channels, in all of which the DMT optimality of the LR-aided linear decoder is guaranteed. The adopted approach yields insight, and motivates further study, into joint transceiver designs with an improved SNR gap to ML decoding.