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

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.Comment: 16 pages, 1 figure (3 subfigures), submitted to the IEEE Transactions on Information Theor

Multi-user lattice coding for the multiple-access relay channel

This paper considers the multi-antenna multiple access relay channel (MARC), in which multiple users transmit messages to a common destination with the assistance of a relay. In a variety of MARC settings, the dynamic decode and forward (DDF) protocol is very useful due to its outstanding rate performance. However, the lack of good structured codebooks so far hinders practical applications of DDF for MARC. In this work, two classes of structured MARC codes are proposed: 1) one-to-one relay-mapper aided multiuser lattice coding (O-MLC), and 2) modulo-sum relay-mapper aided multiuser lattice coding (MS-MLC). The former enjoys better rate performance, while the latter provides more flexibility to tradeoff between the complexity of the relay mapper and the rate performance. It is shown that, in order to approach the rate performance achievable by an unstructured codebook with maximum-likelihood decoding, it is crucial to use a new K-stage coset decoder for structured O-MLC, instead of the one-stage decoder proposed in previous works. However, if O-MLC is decoded with the one-stage decoder only, it can still achieve the optimal DDF diversity-multiplexing gain tradeoff in the high signal-to-noise ratio regime. As for MS-MLC, its rate performance can approach that of the O-MLC by increasing the complexity of the modulo-sum relay-mapper. Finally, for practical implementations of both O-MLC and MS-MLC, practical short length lattice codes with linear mappers are designed, which facilitate efficient lattice decoding. Simulation results show that the proposed coding schemes outperform existing schemes in terms of outage probabilities in a variety of channel settings.Comment: 32 pages, 5 figure