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

Distributed Channel Quantization for Two-User Interference Networks

We introduce conferencing-based distributed channel quantizers for two-user interference networks where interference signals are treated as noise. Compared with the conventional distributed quantizers where each receiver quantizes its own channel independently, the proposed quantizers allow multiple rounds of feedback communication in the form of conferencing between receivers. We take the network outage probabilities of sum rate and minimum rate as performance measures and consider quantizer design in the transmission strategies of time sharing and interference transmission. First, we propose distributed quantizers that achieve the optimal network outage probability of sum rate for both time sharing and interference transmission strategies with an average feedback rate of only two bits per channel state. Then, for the time sharing strategy, we propose a distributed quantizer that achieves the optimal network outage probability of minimum rate with finite average feedback rate; conventional quantizers require infinite rate to achieve the same performance. For the interference transmission strategy, a distributed quantizer that can approach the optimal network outage probability of minimum rate closely is also proposed. Numerical simulations confirm that our distributed quantizers based on conferencing outperform the conventional ones.Comment: 30 pages, 4 figure

On the Benefits of Partial Channel State Information for Repetition Protocols in Block Fading Channels

This paper studies the throughput performance of HARQ (hybrid automatic repeat request) protocols over block fading Gaussian channels. It proposes new protocols that use the available feedback bit(s) not only to request a retransmission, but also to inform the transmitter about the instantaneous channel quality. An explicit protocol construction is given for any number of retransmissions and any number of feedback bits. The novel protocol is shown to simultaneously realize the gains of HARQ and of power control with partial CSI (channel state information). Remarkable throughput improvements are shown, especially at low and moderate SNR (signal to noise ratio), with respect to protocols that use the feedback bits for retransmission request only. In particular, for the case of a single retransmission and a single feedback bit, it is shown that the repetition is not needed at low \snr where the throughput improvement is due to power control only. On the other hand, at high SNR, the repetition is useful and the performance gain comes form a combination of power control and ability of make up for deep fades.Comment: Accepted for publication on IEEE Transactions on Information Theory; Presented in parts at ITW 2007 and ICC 200

Joint Source-Channel Coding with Time-Varying Channel and Side-Information

Transmission of a Gaussian source over a time-varying Gaussian channel is studied in the presence of time-varying correlated side information at the receiver. A block fading model is considered for both the channel and the side information, whose states are assumed to be known only at the receiver. The optimality of separate source and channel coding in terms of average end-to-end distortion is shown when the channel is static while the side information state follows a discrete or a continuous and quasiconcave distribution. When both the channel and side information states are time-varying, separate source and channel coding is suboptimal in general. A partially informed encoder lower bound is studied by providing the channel state information to the encoder. Several achievable transmission schemes are proposed based on uncoded transmission, separate source and channel coding, joint decoding as well as hybrid digital-analog transmission. Uncoded transmission is shown to be optimal for a class of continuous and quasiconcave side information state distributions, while the channel gain may have an arbitrary distribution. To the best of our knowledge, this is the first example in which the uncoded transmission achieves the optimal performance thanks to the time-varying nature of the states, while it is suboptimal in the static version of the same problem. Then, the optimal \emph{distortion exponent}, that quantifies the exponential decay rate of the expected distortion in the high SNR regime, is characterized for Nakagami distributed channel and side information states, and it is shown to be achieved by hybrid digital-analog and joint decoding schemes in certain cases, illustrating the suboptimality of pure digital or analog transmission in general.Comment: Submitted to IEEE Transactions on Information Theor