Lattice Coding and Decoding Achieve the Optimal Diversity–Multiplexing Tradeoff of MIMO Channels (original) (raw)
Related papers
Lattice coding and decoding achieve the optimal diversity-multiplexing tradeoff of MIMO channels
IEEE Transactions on Information Theory, 2004
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-vs-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-Λ 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-vs-multiplexing tradeoff. Moreover, our results shed more light on the structure of optimal coding/decoding techniques in delay limited MIMO channels, and hence, opens 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 SNR regime, unlike the 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.
Lattice code decoder for space-time codes
IEEE Communications Letters, 2000
We explore the lattice sphere packing representation of a multi-antenna system and the algebraic space-time (ST) codes. We apply the sphere decoding (SD) algorithm to the resulted lattice code. For the uncoded system, SD yields, with small increase in complexity, a huge improvement over the well-known V-BLAST detection algorithm. SD of algebraic ST codes exploits the full diversity of the coded multi-antenna system, and makes the proposed scheme very appealing to take advantage of the richness of the multi-antenna environment. The fact that the SD does not depend on the constellation size, gives rise to systems with very high spectral efficiency, maximum-likelihood performance, and low decoding complexity.
2011
In this paper, the asymptotic performance of the lattice sequential decoder for LAttice Space-Time (LAST) coded MIMO channel is analyzed. We determine the rates achievable by lattice coding and sequential decoding applied to such a channel. The diversity-multiplexing tradeoff (DMT) under lattice sequential decoding is derived as a function of its parameter-the bias term, which is critical for controlling the amount of computations required at the decoding stage. Achieving low decoding complexity requires increasing the value of the bias term. However, this is done at the expense of losing the optimal tradeoff of the channel. In this work, we derive the tail distribution of the decoder's computational complexity in the high signal-to-noise ratio regime. Our analysis reveals that the tail distribution of such a low complexity decoder is dominated by the outage probability of the channel for the underlying coding scheme. Also, the tail exponent of the complexity distribution is shown to be equivalent to the DMT achieved by lattice coding and lattice sequential decoding schemes. We derive the asymptotic average complexity of the sequential decoder as a function of the system parameters. In particular, we show that there exists a cut-off multiplexing gain for which the average computational complexity of the decoder remains bounded.
Efficient Lattice Decoders for the Linear Gaussian Vector Channel: Performance & Complexity Analysis
2011
The theory of lattices -a mathematical approach for representing infinite discrete points in Euclidean space, has become a powerful tool to analyze many point-to-point digital and wireless communication systems, particularly, communication systems that can be well-described by the linear Gaussian vector channel model. This is mainly due to the three facts about channel codes constructed using lattices: they have simple structure, their ability to achieve the fundamental limits (the capacity) of the channel, and most importantly, they can be decoded using efficient decoders called lattice decoders.
Space-time codes from structured lattices
2008
Abstract: We present constructions of Space-Time (ST) codes based on lattice coset coding. First, we focus on ST code constructions for the short block-length case, ie, when the block-length is equal to or slightly larger than the number of transmit antennas. We present constructions based on dense lattice packings and nested lattice (Voronoi) shaping.
On the Computational Complexity of Sphere Decoder for Lattice Space-Time Coded MIMO Channel
Computing Research Repository - CORR, 2011
The exact complexity analysis of the basic sphere decoder for general space-time codes applied to multiple-input multiple-output (MIMO) wireless channel is known to be difficult. In this work, we shed the light on the computational complexity of sphere decoding for the quasi-static, LAttice Space-Time (LAST) coded MIMO channel. Specifically, we drive an upper bound of the tail distribution of the decoder's computational complexity. We show that, when the computational complexity exceeds a certain limit, this upper bound becomes dominated by the outage probability achieved by LAST coding and sphere decoding schemes. We then calculate the minimum (average) computational complexity that is required by the decoder to achieve near optimal performance in terms of the system parameters. Moreover, we show analytically how the minimum-mean square-error decision feed-back equalization can significantly improve the tail exponent and as a consequence reduces (average) computational complex...
Space–Time Codes From Structured Lattices
IEEE Transactions on Information Theory, 2009
We present constructions of Space-Time (ST) codes based on lattice coset coding. First, we focus on ST code constructions for the short block-length case, i.e., when the block-length is equal to or slightly larger than the number of transmit antennas. We present constructions based on dense lattice packings and nested lattice (Voronoi) shaping. Our codes achieve the optimal diversity-multiplexing tradeoff of quasi-static MIMO fading channels for any fading statistics, and perform very well also at practical, moderate values of signal to noise ratios (SNR). Then, we extend the construction to the case of large block lengths, by using trellis coset coding. We provide constructions of trellis coded modulation (TCM) schemes that are endowed with good packing and shaping properties. Both short-block and trellis constructions allow for a reduced complexity decoding algorithm based on minimum mean squared error generalized decision feedback equalizer (MMSE-GDFE) lattice decoding and a combination of this with a Viterbi TCM decoder for the TCM case. Beyond the interesting algebraic structure, we exhibit codes whose performance is among the state-of-the art considering codes with similar encoding/decoding complexity.
Explicit Space-Time Codes Achieving The Diversity-Multiplexing Gain Tradeoff
IEEE Transactions on Information Theory, 2006
A recent result of Zheng and Tse states that over a quasi-static channel, there exists a fundamental tradeoff, referred to as the diversity-multiplexing gain (D-MG) tradeoff, between the spatial multiplexing gain and the diversity gain that can be simultaneously achieved by a space-time (ST) code. This tradeoff is precisely known in the case of independent and identically distributed (i.i.d.) Rayleigh fading, for T nt + nr 0 1 where T is the number of time slots over which coding takes place and nt ; nr are the number of transmit and receive antennas, respectively. For T < nt + nr 0 1, only upper and lower bounds on the D-MG tradeoff are available.
A new lattice decoding for space time block codes with low complexity
2002
We present an algorithm based on the closest point search (CPS) in lattices for decoding of space-time block codes (STBC). The modified CPS algorithm based on the Schnorr-Euchner variation of the Pohst (1981) method is used to perform the decoding of STBC. This method is shown to be substantially faster than other known sphere decoding methods. Also we exploit a fast method for decoding of orthogonal STBC with low complexity. We show that our proposed method gives the same decoding performance as the maximum-likelihood (ML) ratio decoding while it shows much lower complexity.
Filter and Nested Lattice Code Design for MIMO Fading Channels with Side-Information
IEEE Transactions on Communications, 2000
Linear-assignment Gel'fand-Pinsker coding (LA-GPC) is a coding technique for channels with interference known only at the transmitter, where the known interference is treated as side-information (SI). As a special case of LA-GPC, dirty paper coding has been shown to be able to achieve the optimal interference-free rate for interference channels with perfect channel state information at the transmitter (CSIT). In the cases where only the channel distribution information at the transmitter (CDIT) is available, LA-GPC also has good (sometimes optimal) performance in a variety of fast and slow fading SI channels. In this paper, we design the filters in nested-lattice based coding to make it achieve the same rate performance as LA-GPC in multiple-input multiple-output (MIMO) channels. Compared with the random Gaussian codebooks used in previous works, our resultant coding schemes have an algebraic structure and can be implemented in practical systems. A simulation in a slow-fading channel is also provided, and near interference-free error performance is obtained. The proposed coding schemes can serve as the fundamental building blocks to achieve the promised rate performance of MIMO Gaussian broadcast channels with CDIT or perfect CSIT.