This paper is motivated by the challenge of high fidelity processing of images using a relatively small set of projection measurements. This is a problem of great interest in many sensing applications, for example where high photodetector counts are precluded by a combination of available power, form factor and expense. The emerging methods of dictionary learning and compressive sensing offer great potential for addressing this challenge. Combining these methods requires that the signals of interest be representable as a sparse combination of elements of some dictionary. This paper develops a method that aligns the discriminative power of such a dictionary with the physical limitations of the imaging system. Alignment is accomplished by designing a projection matrix that exposes and then aligns the modes of the noise with those of the dictionary. The design algorithm is obtained by modifying an algorithm for designing the pre-filter to maximize the rate and reliability of a Multiple Input Multiple Output (MIMO) communications channel. The difference is that in the communications problem a source is being matched to a channel, whereas in the imaging problem a channel, or equivalently the noise covariance, is being matched to a source. Our results shown that using the proposed communications design framework we can reduce reconstruction error between 20%, after only 20 projections of a 28 × 28 image, and 10% after 100 projections. Furthermore, we noticeably see the superior quality of the reconstructed images.

We consider the recovery of an underlying signal $\mathbf{x}\in\mathbb{C}^m$ based on projection measurements of the form $\mathbf{y}=\mathbf{M}\mathbf{x}+\mathbf{w}$, where $\mathbf{y}\in\mathbb{C}^\ell$ and $\mathbf{w}$ is measurement noise; we are interested in the case $\ell\ll m$. It is assumed that the signal model $p(\mathbf{x})$ is known and that $\mathbf{w}\sim\mathcal{CN}(\mathbf{w};\boldsymbol{0},\bf \Sigma_w)$ for known $\bf \Sigma_w$. The objective is to design a projection matrix $\mathbf{M}\in\mathbb{C}^{\ell\times m}$ to maximize key information-theoretic quantities with operational significance, including the mutual information between the signal and the projections $\mathcal{I}(\mathbf{x};\mathbf{y})$ or the Rényi entropy of the projections $\mbox{h}_\alpha \left( \mathbf{y} \right)$ (Shannon entropy is a special case). By capitalizing on explicit characterizations of the gradients of the information measures with respect to the projection matrix, where we also partially extend the well-known results of Palomar and Verdú from the mutual information to the Rényi entropy domain, we reveal the key operations carried out by the optimal projection designs: mode exposure and mode alignment. Experiments are considered for the case of compressive sensing (CS) applied to imagery. In this context, we provide a demonstration of the performance improvement possible through the application of the novel projection designs in relation to conventional ones, as well as justification for a fast online projection design method with which state-of-the-art adaptive CS signal recovery is achieved.

This paper introduces a divide and conquer approach to the design of transmit and receive filters for communication over a Multiple Input Multiple Output (MIMO) Gaussian channel subject to an average power constraint. It involves conversion to a set of parallel scalar channels, possibly with very different gains, followed by coding per sub-channel (i.e. over time) rather than coding across sub-channels (i.e. over time and space). The loss in performance is negligible at high signal-to-noise ratio (SNR) and not significant at medium SNR. The advantages are reduction in signal processing complexity and greater insight into the SNR thresholds at which a channel is first allocated power. This insight is a consequence of formulating the optimal power allocation in terms of an upper bound on error rate that is determined by parameters of the input lattice such as the minimum distance and kissing number. The resulting thresholds are given explicitly in terms of these lattice parameters. By contrast, when the optimization problem is phrased in terms of maximizing mutual information, the solution is mercury waterfilling, and the thresholds are implicit.

This paper introduces a less is more approach to the modelling of iterative decoding for bit-interleaved coded modulation (BICM). It considers modelling the iterative exchange of soft a priori information between the demapper and decoder with a binary erasure channel model. This simplification, unlike the usual additive white Gaussian noise (AWGN) channel model, allows us to express the extrinsic information transfer (EXIT) chart curves for the demapper with polynomials whose order makes explicit the degrees of freedom available for design. The accuracy of our expressions simplifies the design process enabling us to compare in a more manageable manner the key performance parameters: the BER performance and the convergence threshold. This enabled us to find the pairing of memory-two recursive systematic convolutional (RSC) codes and mappers that achieve the earliest convergence threshold for a target BER floor at convergence: for 8-PSK semi-set partitioning (SSP) was optimal and converged at a signal-to-noise ratio (SNR)= 3.0 dB for a BER target of at least 10-5; two new mappings were the optimal pairings for 16-QAM, where the L4b2 mapping converged at 2.9 dB for a BER floor ≤ 3.46 × 10-4and the H2b2 mapping converged at 3.1 dB for a BER floor ≤ 2.44 × 10-5.

In this paper, we put forth a model to generate closed-form expressions for EXIT chart curves for BICM-ID systems. This model is based on the representation of the a-priori AWGN channels by BEC channels. We present various applications of the model in the estimation of key performance metrics in BICM-ID systems. This also includes the selection of suitable mapper-encoder pairings for quasi-static fading channels that exhibit the best known performance.

In this paper, we investigate in detail the performance of iterative demapping and decoding techniques over quasi-static fading channels both with and without antenna diversity. In particular, we consider the effect on the system performance of various mapping schemes, different coding schemes, the inter- leaver size as well as space diversity. Results demonstrate that over quasi-static fading channels characterized by significant antenna diversity, mappings traditionally optimized for iterative receivers (e.g., Boronka mapping) outperform mappings more appropriate for non-iterative receivers (e.g., Gray mapping). In contrast, over quasi-static fading channels characterized by limited antenna diversity, Gray mapping always outperform Boronka mapping for all Eb/N0and all iterations. Strikingly, this situation is in sharp contrast to that in the AWGN case. We note that we can further improve the performance of non-iterative systems (e.g., Gray mapping) having limited antenna diversity by increasing the memory size and removing the interleaving.