Degrees of Freedom of Time Correlated MISO Broadcast Channel with Delayed CSIT

We consider the time correlated multiple-input single-output (MISO) broadcast channel where the transmitter has imperfect knowledge on the current channel state, in addition to delayed channel state information. By representing the quality of the current channel state information as P^-{\alpha} for the signal-to-noise ratio P and some constant {\alpha} \geq 0, we characterize the optimal degree of freedom region for this more general two-user MISO broadcast correlated channel. The essential ingredients of the proposed scheme lie in the quantization and multicasting of the overheard interferences, while broadcasting new private messages. Our proposed scheme smoothly bridges between the scheme recently proposed by Maddah-Ali and Tse with no current state information and a simple zero-forcing beamforming with perfect current state information.Comment: revised and final version, to appear in IEEE transactions on Information Theor

Distortion Exponent in MIMO Channels with Feedback

The transmission of a Gaussian source over a block-fading multiple antenna channel in the presence of a feedback link is considered. The feedback link is assumed to be an error and delay free link of capacity 1 bit per channel use. Under the short-term power constraint, the optimal exponential behavior of the end-to-end average distortion is characterized for all source-channel bandwidth ratios. It is shown that the optimal transmission strategy is successive refinement source coding followed by progressive transmission over the channel, in which the channel block is allocated dynamically among the layers based on the channel state using the feedback link as an instantaneous automatic repeat request (ARQ) signal.Comment: Presented at the IEEE Information Theory Workshop (ITW), Taormina, Italy, Oct. 200

Distortion Minimization in Gaussian Layered Broadcast Coding with Successive Refinement

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the source layers. For two source layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For convex distortion cost functions with convex constraints, the minimization is formulated as a convex optimization problem. In the limit of a continuum of infinite layers, the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. As the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.Comment: Accepted for publication in IEEE Transactions on Information Theor

Downlink SDMA with Limited Feedback in Interference-Limited Wireless Networks

The tremendous capacity gains promised by space division multiple access (SDMA) depend critically on the accuracy of the transmit channel state information. In the broadcast channel, even without any network interference, it is known that such gains collapse due to interstream interference if the feedback is delayed or low rate. In this paper, we investigate SDMA in the presence of interference from many other simultaneously active transmitters distributed randomly over the network. In particular we consider zero-forcing beamforming in a decentralized (ad hoc) network where each receiver provides feedback to its respective transmitter. We derive closed-form expressions for the outage probability, network throughput, transmission capacity, and average achievable rate and go on to quantify the degradation in network performance due to residual self-interference as a function of key system parameters. One particular finding is that as in the classical broadcast channel, the per-user feedback rate must increase linearly with the number of transmit antennas and SINR (in dB) for the full multiplexing gains to be preserved with limited feedback. We derive the throughput-maximizing number of streams, establishing that single-stream transmission is optimal in most practically relevant settings. In short, SDMA does not appear to be a prudent design choice for interference-limited wireless networks.Comment: Submitted to IEEE Transactions on Wireless Communication

Interference Channel with Intermittent Feedback

We investigate how to exploit intermittent feedback for interference management. Focusing on the two-user linear deterministic interference channel, we completely characterize the capacity region. We find that the characterization only depends on the forward channel parameters and the marginal probability distribution of each feedback link. The scheme we propose makes use of block Markov encoding and quantize-map-and-forward at the transmitters, and backward decoding at the receivers. Matching outer bounds are derived based on novel genie-aided techniques. As a consequence, the perfect-feedback capacity can be achieved once the two feedback links are active with large enough probabilities.Comment: Extended version of the same-titled paper that appears in IEEE International Symposium on Information Theory (ISIT) 201

The Multi-way Relay Channel

The multiuser communication channel, in which multiple users exchange information with the help of a relay terminal, termed the multi-way relay channel (mRC), is introduced. In this model, multiple interfering clusters of users communicate simultaneously, where the users within the same cluster wish to exchange messages among themselves. It is assumed that the users cannot receive each other's signals directly, and hence the relay terminal in this model is the enabler of communication. In particular, restricted encoders, which ignore the received channel output and use only the corresponding messages for generating the channel input, are considered. Achievable rate regions and an outer bound are characterized for the Gaussian mRC, and their comparison is presented in terms of exchange rates in a symmetric Gaussian network scenario. It is shown that the compress-and-forward (CF) protocol achieves exchange rates within a constant bit offset of the exchange capacity independent of the power constraints of the terminals in the network. A finite bit gap between the exchange rates achieved by the CF and the amplify-and-forward (AF) protocols is also shown. The two special cases of the mRC, the full data exchange model, in which every user wants to receive messages of all other users, and the pairwise data exchange model which consists of multiple two-way relay channels, are investigated in detail. In particular for the pairwise data exchange model, in addition to the proposed random coding based achievable schemes, a nested lattice coding based scheme is also presented and is shown to achieve exchange rates within a constant bit gap of the exchange capacity.Comment: Revised version of our submission to the Transactions on Information Theor

Joint Unitary Triangularization for MIMO Networks

This work considers communication networks where individual links can be described as MIMO channels. Unlike orthogonal modulation methods (such as the singular-value decomposition), we allow interference between sub-channels, which can be removed by the receivers via successive cancellation. The degrees of freedom earned by this relaxation are used for obtaining a basis which is simultaneously good for more than one link. Specifically, we derive necessary and sufficient conditions for shaping the ratio vector of sub-channel gains of two broadcast-channel receivers. We then apply this to two scenarios: First, in digital multicasting we present a practical capacity-achieving scheme which only uses scalar codes and linear processing. Then, we consider the joint source-channel problem of transmitting a Gaussian source over a two-user MIMO channel, where we show the existence of non-trivial cases, where the optimal distortion pair (which for high signal-to-noise ratios equals the optimal point-to-point distortions of the individual users) may be achieved by employing a hybrid digital-analog scheme over the induced equivalent channel. These scenarios demonstrate the advantage of choosing a modulation basis based upon multiple links in the network, thus we coin the approach "network modulation".Comment: Submitted to IEEE Tran. Signal Processing. Revised versio

Rate Splitting for MIMO Wireless Networks: A Promising PHY-Layer Strategy for LTE Evolution

MIMO processing plays a central part towards the recent increase in spectral and energy efficiencies of wireless networks. MIMO has grown beyond the original point-to-point channel and nowadays refers to a diverse range of centralized and distributed deployments. The fundamental bottleneck towards enormous spectral and energy efficiency benefits in multiuser MIMO networks lies in a huge demand for accurate channel state information at the transmitter (CSIT). This has become increasingly difficult to satisfy due to the increasing number of antennas and access points in next generation wireless networks relying on dense heterogeneous networks and transmitters equipped with a large number of antennas. CSIT inaccuracy results in a multi-user interference problem that is the primary bottleneck of MIMO wireless networks. Looking backward, the problem has been to strive to apply techniques designed for perfect CSIT to scenarios with imperfect CSIT. In this paper, we depart from this conventional approach and introduce the readers to a promising strategy based on rate-splitting. Rate-splitting relies on the transmission of common and private messages and is shown to provide significant benefits in terms of spectral and energy efficiencies, reliability and CSI feedback overhead reduction over conventional strategies used in LTE-A and exclusively relying on private message transmissions. Open problems, impact on standard specifications and operational challenges are also discussed.Comment: accepted to IEEE Communication Magazine, special issue on LTE Evolutio

An Achievable Rate Region for the Broadcast Channel with Feedback

A single-letter achievable rate region is proposed for the two-receiver discrete memoryless broadcast channel with generalized feedback. The coding strategy involves block-Markov superposition coding, using Marton's coding scheme for the broadcast channel without feedback as the starting point. If the message rates in the Marton scheme are too high to be decoded at the end of a block, each receiver is left with a list of messages compatible with its output. Resolution information is sent in the following block to enable each receiver to resolve its list. The key observation is that the resolution information of the first receiver is correlated with that of the second. This correlated information is efficiently transmitted via joint source-channel coding, using ideas similar to the Han-Costa coding scheme. Using the result, we obtain an achievable rate region for the stochastically degraded AWGN broadcast channel with noisy feedback from only one receiver. It is shown that this region is strictly larger than the no-feedback capacity region.Comment: To appear in IEEE Transactions on Information Theory. Contains example of AWGN Broadcast Channel with noisy feedbac