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.

/pdf/lattice-coding-and-decoding-achieve-the-optimal-diversity-3ozg8xf9iw.pdf

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

Multi-input multi-output (MIMO) systems equipped with multiple antennas have well documented merits in combating fading and enhancing data rates. MIMO V-BLAST transmission is a widely adopted method to achieve high spectral efficiency and low-complexity implementation. When the maximum likelihood (ML) or near-ML detector is employed, receive diversity is collected for MIMO V-BLAST systems to enhance the performance. However, because of its exponential complexity, ML detector may be infeasible for practical systems when the number of antennas and/or the constellation size is large. On the other hand, linear equalizers have much lower complexity but come with inferior performance. In this paper, we analytically quantify the diversity order of linear detectors for MIMO V-BLAST systems. Then, we adopt low-complexity complex lattice-reduction (LR) aided linear equalizers for V-BLAST systems to improve the performance and prove that LR-aided linear equalizers collect the same diversity order as that exploited by the ML detector but with much lower complexity. Relative to the existing real LR-aided equalizers, we illustrate that the complex LR further reduces the complexity while keeping the same performance. Simulation results corroborate our theoretical claims.

Performance analysis for MIMO systems with lattice-reduction aided linear equalization

In Borodin-von zur Gathen-Hopcroft[82] the following program is laid out: obtain a “theory package for parallel algebraic computations”, i.e. fast parallel computations for the widely used problems of symbolic manipulation in an algebraic context. In that paper, two basic problems were considered: solving systems of linear equations and computing the gcd of two polynomials, both over arbitrary ground fields. The present paper continues this program, and fast parallel solutions to the following algebraic problems are given: computing all entries of the Extended Euclidean Scheme of two polynomials over an arbitrary field, gcd and lcm of many polynomials, factoring polynomials over finite fields, and the squarefree decomposition of polynomials over fields of characteristic zero and over finite fields.

Parallel algorithms for algebraic problems

The McEliece public-key cryptosystem relies on the NP-hard decoding problem, and therefore, is regarded as a solution for postquantum cryptography. Though early known, this cryptosystem was not employed so far because of efficiency questions regarding performance and communication overhead. This paper presents a novel processor architecture as a high-performance platform to execute key generation, encryption, and decryption according to this cryptosystem. A prototype of this processor is realized on a reconfigurable device and tested via a dedicated software interface. A comparison with a similar software solution highlights the performance advantage of the proposed hardware solution.

A Novel Cryptoprocessor Architecture for the McEliece Public-Key Cryptosystem

Approximate vector perturbation techniques assisted by LLL lattice reduction (LR) can exploit all the diversity that is available in multi-user multi-antenna broadcast systems. However, the required computational complexity of LLL-LR can be quite large. In this paper, we propose a much simpler and much more efficient LR algorithm than LLL. This LR technique is based on Brun's algorithm for finding approximate integer relations (IRs). The link between LR and IRs is established by considering poorly conditioned channels with a single small singular value. Simulation results show that our scheme can achieve large (but bot full) diversity at a fraction of the complexity required for LLL-assisted vector perturbation.

/pdf/efficient-vector-perturbation-in-multi-antenna-multi-user-gaocnjessk.pdf

Efficient vector perturbation in multi-antenna multi-user systems based on approximate integer relations

Factoring polynomials with rational coefficients : (preprint)

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Factoring polynomials with rational coefficients : (preprint)