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Recently, Gallager's bounding techniques have been used to derive tight performance bounds for coded systems in fading channels. Most works in this field have thus far dealt with coherent decoding. This paper develops Gallager bounds for noncoherent systems in fading channels. Unlike coherent decoding, the exact error probability of a noncoherent decoder/detector conditioned on the fading coefficients does not admit a closed-form expression. This difficulty is overcome in this paper by employing the Chernoff technique. Although it weakens the bounds to some extent, the Chernoff technique enables the derivations of the limit-before-average (LBA) bound and Gallager bounds in closed form for noncoherent fading channels. Numerical examples show that the proposed bounds are convergent and are tighter than the conventional union bound. [ABSTRACT FROM AUTHOR]

Compressed sensing (CS) decoding algorithms can efficiently recover an N-dimensional real-valued vector x to within a factor of its best k-term approximation by taking m = O(k log N/k) measurements y = Φx. If the sparsity or approximate sparsity level of x were known, then this theoretical guarantee would imply quality assurance of the resulting estimate. However, because the underlying sparsity of the signal x is unknown, the quality of a CS estimate ... using m measurements is not assured. It is nevertheless shown in this paper that sharp bounds on the error ||x - ...||𝓁N2 can be achieved with no effort. More precisely, suppose that a maximum number measurements m is preimposed. One can reserve 10 log p of these m measurements and compute a sequence of possible estimates (...j)pj=1 to x from the m - 10 log p remaining measurements; errors ||x - ...j||𝓁N2 for j = 1,..., p can then be bounded high probability. As a consequence, numerical upper and lower bounds on the error between x and the best k-term approximation to x can be estimated for p values of k with almost no cost. observation has applications outside CS as well. [ABSTRACT FROM AUTHOR]

In this paper, we consider a graph-based framework for transmission of correlated sources over multiple-access channels. It is well known that the separation approach is not optimal for this multiuser communication. Our objective in this work is to reintroduce modularity in this problem using a graph-based discrete interface and to minimize the performance loss as compared to the optimal joint source-channel coding scheme. The proposed framework envisages a transmission systems with two modules: a source-coding module and a channel-coding module. In the former module, the correlated sources are encoded distributively into correlated messages whose correlation structure can be associated with a bipartite graph. These correlated messages are then encoded by using correlated codewords and are reliably transmitted over the multiple-access channel -in the latter module. This leads to performance gains in terms of enlarging the class of correlated sources that can be reliably transmitted over a multiple-access channel as compared to the conventional separation approach. We provide an information-theoretic characterization of 1) the rate of exponential growth (as a function of the number of channel uses) of the size of the bipartite graphs whose edges can be reliably transmitted over a multiuser channel and 2) the rate of exponential growth (as a function of the number of source samples) of the size of the bipartite graphs which can reliably represent a pair of correlated sources to be transmitted over a multiuser channel. [ABSTRACT FROM AUTHOR]