Very Low-Rate Variable-Length Channel Quantization for Minimum Outage Probability

We identify a practical vector quantizer design problem where any fixed-length quantizer (FLQ) yields non-zero distortion at any finite rate, while there is a variable-length quantizer (VLQ) that can achieve zero distortion with arbitrarily low rate. The problem arises in a $t \times 1$ multiple-antenna fading channel where we would like to minimize the channel outage probability by employing beamforming via quantized channel state information at the transmitter (CSIT). It is well-known that in such a scenario, finite-rate FLQs cannot achieve the full-CSIT (zero distortion) outage performance. We construct VLQs that can achieve the full-CSIT performance with finite rate. In particular, with $P$ denoting the power constraint of the transmitter, we show that the necessary and sufficient VLQ rate that guarantees the full-CSIT performance is $\Theta(1/P)$. We also discuss several extensions (e.g. to precoding) of this result

Outage Probability and Outage-Based Robust Beamforming for MIMO Interference Channels with Imperfect Channel State Information

In this paper, the outage probability and outage-based beam design for multiple-input multiple-output (MIMO) interference channels are considered. First, closed-form expressions for the outage probability in MIMO interference channels are derived under the assumption of Gaussian-distributed channel state information (CSI) error, and the asymptotic behavior of the outage probability as a function of several system parameters is examined by using the Chernoff bound. It is shown that the outage probability decreases exponentially with respect to the quality of CSI measured by the inverse of the mean square error of CSI. Second, based on the derived outage probability expressions, an iterative beam design algorithm for maximizing the sum outage rate is proposed. Numerical results show that the proposed beam design algorithm yields better sum outage rate performance than conventional algorithms such as interference alignment developed under the assumption of perfect CSI.Comment: 41 pages, 14 figures. accepted to IEEE Transactions on Wireless Communication

Distortion Exponent in MIMO Fading Channels with Time-Varying Source Side Information

Transmission of a Gaussian source over a time-varying multiple-input multiple-output (MIMO) channel is studied under strict delay constraints. Availability of a correlated side information at the receiver is assumed, whose quality, i.e., correlation with the source signal, also varies over time. A block-fading model is considered for the states of the time-varying channel and the time-varying side information; and perfect state information at the receiver is assumed, while the transmitter knows only the statistics. The high SNR performance, characterized by the \textit{distortion exponent}, is studied for this joint source-channel coding problem. An upper bound is derived and compared with lowers based on list decoding, hybrid digital-analog transmission, as well as multi-layer schemes which transmit successive refinements of the source, relying on progressive and superposed transmission with list decoding. The optimal distortion exponent is characterized for the single-input multiple-output (SIMO) and multiple-input single-output (MISO) scenarios by showing that the distortion exponent achieved by multi-layer superpositon encoding with joint decoding meets the proposed upper bound. In the MIMO scenario, the optimal distortion exponent is characterized in the low bandwidth ratio regime, and it is shown that the multi-layer superposition encoding performs very close to the upper bound in the high bandwidth expansion regime.Comment: Submitted to IEEE Transactions on Information Theor

Principles of Physical Layer Security in Multiuser Wireless Networks: A Survey

This paper provides a comprehensive review of the domain of physical layer security in multiuser wireless networks. The essential premise of physical-layer security is to enable the exchange of confidential messages over a wireless medium in the presence of unauthorized eavesdroppers without relying on higher-layer encryption. This can be achieved primarily in two ways: without the need for a secret key by intelligently designing transmit coding strategies, or by exploiting the wireless communication medium to develop secret keys over public channels. The survey begins with an overview of the foundations dating back to the pioneering work of Shannon and Wyner on information-theoretic security. We then describe the evolution of secure transmission strategies from point-to-point channels to multiple-antenna systems, followed by generalizations to multiuser broadcast, multiple-access, interference, and relay networks. Secret-key generation and establishment protocols based on physical layer mechanisms are subsequently covered. Approaches for secrecy based on channel coding design are then examined, along with a description of inter-disciplinary approaches based on game theory and stochastic geometry. The associated problem of physical-layer message authentication is also introduced briefly. The survey concludes with observations on potential research directions in this area.Comment: 23 pages, 10 figures, 303 refs. arXiv admin note: text overlap with arXiv:1303.1609 by other authors. IEEE Communications Surveys and Tutorials, 201