Mahmoud Taherzadeh

LLL Reduction Achieves the Receive Diversity in MIMO Decoding

Diversity order is an important measure for the performance of communication systems over multiple-input-multiple-output (MIMO) fading channels. In this correspondence, we prove that in MIMO multiple- access systems (or MIMO point-to-point systems with V-BLAST transmission), lattice-reduction-aided decoding achieves the maximum receive diversity (which is equal to the number of receive antennas). Also, we prove that the naive lattice decoding (which discards the out-of-region decoded points) achieves the maximum diversity.

Communication Over MIMO Broadcast Channels Using Lattice-Basis Reduction

A new viewpoint for adopting the lattice reduction in communication over multiple-input multiple-output (MIMO) broadcast channels is introduced. Lattice basis reduction helps us to reduce the average transmitted energy by modifying the region which includes the constellation points. The new viewpoint helps us to generalize the idea of lattice-reduction-aided (LRA) preceding for the case of unequal-rate transmission, and obtain analytic results for the asymptotic behavior (signal-to-noise ratio (SNR) rarr infin) of the symbol error rate for the LRA precoding and the perturbation technique. Also, the outage probability for both cases of fixed-rate users and fixed sum rate is analyzed. It is shown that the LRA method, using the Lenstra-Lenstra-Lovasz (LLL) algorithm, achieves the optimum asymptotic slope of symbol error rate (called the precoding diversity).

A Near-Maximum-Likelihood Decoding Algorithm for MIMO Systems Based on Semi-Definite Programming

In multiple-input multiple-output (MIMO) systems, maximum-likelihood (ML) decoding is equivalent to finding the closest lattice point in an N-dimensional complex space. In general, this problem is known to be NP-hard. In this paper, a quasi-ML algorithm based on semi-definite programming (SDP) is proposed. We introduce several SDP relaxation models for MIMO systems, with increasing complexity. We use interior-point methods for solving the models and obtain a near-ML performance with polynomial computational complexity. Lattice basis reduction is applied to further reduce the computational complexity of solving these models. The proposed relaxation models are also used for soft output decoding in MIMO systems.

LLLl lattice-basis reduction achieves the maximum diversity in MIMO systems

Diversity order is an important measure for the performance of different communication systems over MIMO fading channels. In this paper, we define the preceding diversity for the fixed-rate MIMO broadcast systems and we prove that in these systems, lattice-reduction-aided preceding achieves the preceding diversity. Also, we prove that lattice-reduction-aided decoding achieves the receive diversity in MIMO point-to-point and multiple-access systems

On the Limitations of the Naive Lattice Decoding

In this paper, the inherent drawbacks of the naive lattice decoding (NLD) for MIMO fading systems is investigated. We show that using the NLD for MIMO systems has considerable deficiencies in terms of the diversity-multiplexing tradeoff. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the nonvanishing determinant property cannot achieve the optimal diversity-multiplexing tradeoff. Indeed, we show that in the case of NLD, when we fix the underlying lattice, all the codes based on full-rate lattices have the same diversity-multiplexing tradeoff as V-BLAST. Also, we derive a lower bound on the symbol error probability of the NLD for the fixed-rate MIMO systems (with equal numbers of receive and transmit antennas). This bound shows that asymptotically, the NLD has an unbounded loss in terms of the required SNR, compared to the maximum likelihood decoding.

A near maximum likelihood decoding algorithm for MIMO systems based on semi-definite programming

In multi-input multi-output (MIMO) systems, maximum-likelihood (ML) decoding is equivalent to finding the closest lattice point in an N-dimensional complex space. In general, this problem is known to be NP hard. In this paper, we propose a quasi-maximum likelihood algorithm based on semi-definite programming (SDP). We introduce several SDP relaxation models for MIMO systems, with increasing complexity. We use interior-point methods for solving the models and obtain a near-ML performance with polynomial computational complexity. Lattice basis reduction is applied to further reduce the computational complexity of solving these models

Robust Joint Source-Channel Coding for Delay-Limited Applications

In this paper, we consider the problem of robust joint source-channel coding over an additive white Gaussian noise channel. We propose a new scheme which achieves the optimal slope for the signal-to-distortion (SDR) curve (unlike the previous known coding schemes). We also drive some theoretical bounds on the asymptotic performance of delay-limited hybrid digital-analog (HDA) coding schemes. We show that, unlike the delay-unlimited case, for any family of HDA codes, the asymptotic performance loss is unbounded (in terms of dB).

On The Limitations of The Naive Lattice Decoding

In this paper, the inherent drawbacks of the naive lattice decoding (NLD) for MIMO fading systems is investigated. We show that using the NLD for MIMO systems has considerable deficiencies in terms of the diversity-multiplexing tradeoff. Unlike the case of maximum-likelihood decoding, in this case, even the perfect lattice space-time codes which have the nonvanishing determinant property cannot achieve the optimal diversity-multiplexing tradeoff. Indeed, we show that in the case of NLD, when we fix the underlying lattice, all the codes based on full-rate lattices have the same diversity-multiplexing tradeoff as V-BLAST. Also, we derive a lower bound on the symbol error probability of the NLD for the fixed-rate MIMO systems (with equal numbers of receive and transmit antennas). This bound shows that asymptotically, the NLD has an unbounded loss in terms of the required SNR, compared to the maximum likelihood decoding.

Single-Sample Robust Joint Source–Channel Coding: Achieving Asymptotically Optimum Scaling of SDR Versus SNR

In this paper, we consider the problem of zero-delay (encoding a single-source sample) robust joint source-channel coding over an additive white Gaussian noise channel. We propose a new scheme that, unlike previously known coding schemes, achieves the optimal scaling of the source signal-to-distortion ratio (SDR) versus channel signal-to-noise ratio (SNR). Also, we propose a family of robust codes, which together maintain a bounded gap with the optimum SDR curve (in terms of decibel). To show the importance of this result, we derive some theoretical bounds on the asymptotic performance of a widely used class of delay-limited hybrid digital-analog (HDA) coding schemes based on superposition of analog and digital components. We show that, unlike the delay-unlimited case, for this class of delay-limited HDA codes, the asymptotic performance loss is unbounded (in terms of decibels). Although the main focus of this paper is on uniform sources, it is also shown that the results are also valid for a more general class of well-behaved distributions.

Analog Coding for Delay-Limited Applications

In this paper, we consider the problem of sending an analog source over an additive white Gaussian noise channel. The traditional analog coding schemes suffer from the threshold effect We introduce two robust schemes for analog conding. Unlike the previous methods, the new methods asymptotically achieve the optimal scaling of the signal-to-distortion-ratio (SDR) without being affected by the threshold effect. Also, we show that approximated versions of these techniques perform well for the practical applications, with a low complexity in encoding/decoding.