For compressive sensing, we derive achievable performance guarantees for recovering partial support sets of sparse vectors. The guarantees are determined in terms of the fraction of signal power to be detected and the measurement rate, defined as a relation between the dimensions of the measurement matrix. Based on this result we derive a tradeoff between the measurement rate and the mean square error, and illustrate it by a numerical example.

In this paper we consider the coexistence of a single-input single-output (SISO) primary link with a multiple-input single-output (MISO) secondary user pair that has non-causal knowledge of the primary message. We study an achievable rate region that exploits this knowledge by combining selfless relaying to maintain the rate supported by the primary link with dirty paper coding to pre-cancel the interference at the secondary receiver. We find the optimal choice of power allocation between these operating modes at the secondary transmitter as well as the optimal beamforming vectors. Moreover, we address the robustness of the solution to uncertainties in the channel knowledge. Finally, we show by numerical evaluation the gains obtained due to the additional knowledge of the primary message.

We consider the symmetric discrete memoryless relay channel with orthogonal receiver components and show that polar codes are suitable for decode-and-forward and compress-and-forward relaying. In the first case we prove that polar codes are capacity achieving for the physically degraded relay channel; for stochastically degraded relay channels our construction provides an achievable rate. In the second case we construct sequences of polar codes that achieve the compress-and-forward rate by nesting polar codes for source compression into polar codes for channel coding. In both cases our constructions inherit most of the properties of polar codes. In particular, the encoding and decoding algorithms and the bound on the block error probability O(2-Nβ) which holds for any 0<;β<;1/2.

We propose a new code design for compress-and-forward relaying over bandlimited relay-to-destination channels. The main contribution of this paper is a code design based on joint (source-channel) coding and modulation that uses the correlation between the observations at the relay and the destination as protection against channel errors. This allows for relay nodes with reduced complexity, shifting most of the processing requirements to the destination node. Moreover, by using scalar quantizers with an entropy constraint our system provides remarkable performance in channel conditions where neither amplify-and-forward nor compress-and-forward efficiently exploit the presence of a relay node. Simulation results confirm the benefits of our proposed system.

We propose a new compress-and-forward implementation for the relay channel based on joint source-channel coding techniques. The relay performs scalar quantization of its observation in combination with a redundant index mapping. Our system utilizes the correlation between the quantized signal and the direct-link observation of the transmitted symbols as redundancy for error protection on the relay-to-destination link. In order to fully exploit this correlation the destination requires iterative decoding to recover the quantized observation sent by the relay. Once regenerated, this quantized signal is optimally combined with the direct-link observation to decode the message conveyed by the source. By quantizing the observed signal itself rather than a measure on the reliability of the information bits (e.g. a posteriori probabilities from a decoder), and by using digital communication methods on the relay- to-destination link our system yields superior performance to that of amplify-and-forward, decode- and-forward and previous implementations of compress-and-forward based on soft decoding.