Lattice coding and decoding achieve the optimal diversity-multiplexing tradeoff of MIMO channels

• Published in: IEEE transactions on information theory Vol. 50; no. 6; pp. 968 - 985
• Main Authors: El Gamal, H., Caire, G., Damen, M.O.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2004; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: AWGN; Channels; Codes; Coding; Construction costs; Decision feedback equalizers; Decoding; Delay; Euclidean distance; Gaussian; Information theory; Lattice theory; Lattices; Mean square errors; MIMO; Optimization; Signal design; Signal to noise ratio; Space time codes
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/TIT.2004.828067

This paper considers communication over coherent multiple-input multiple-output (MIMO) flat-fading channels where the channel is only known at the receiver. For this setting, we introduce the class of LAttice Space-Time (LAST) codes. We show that these codes achieve the optimal diversity-multiplexing tradeoff defined by Zheng and Tse under generalized minimum Euclidean distance lattice decoding. Our scheme is based on a generalization of Erez and Zamir mod-Lambda scheme to the MIMO case. In our construction the scalar "scaling" of Erez-Zamir and Costa Gaussian "dirty-paper" schemes is replaced by the minimum mean-square error generalized decision-feedback equalizer (MMSE-GDFE). This result settles the open problem posed by Zheng and Tse on the construction of explicit coding and decoding schemes that achieve the optimal diversity-multiplexing tradeoff. Moreover, our results shed more light on the structure of optimal coding/decoding techniques in delay-limited MIMO channels, and hence, open the door for novel approaches for space-time code constructions. In particular, 1) we show that MMSE-GDFE plays a fundamental role in approaching the limits of delay-limited MIMO channels in the high signal-to-noise ratio (SNR) regime, unlike the additive white Gaussian noise (AWGN) channel case and 2) our random coding arguments represent a major departure from traditional space-time code designs based on the rank and/or mutual information design criteria.