Information Theory (cs.IT)

Abstract: In this work, we consider the problem of distributed computing of functions of structured sources, focusing on the classical setting of two correlated sources and one user that seeks the outcome of the function while benefiting from low-rate side information provided by a helper node. Focusing on the case where the sources are jointly distributed according to a very general mixture model, we here provide an achievable coding scheme that manages to substantially reduce the communication cost of distributed computing by exploiting the nature of the joint distribution of the sources, the side information, as well as the symmetry enjoyed by the desired functions. Our scheme -- which can readily apply in a variety of real-life scenarios including learning, combinatorics, and graph neural network applications -- is here shown to provide substantial reductions in the communication costs, while simultaneously providing computational savings by reducing the exponential complexity of joint decoding techniques to a complexity that is merely linear.

Abstract: In this paper, we consider intelligent reflecting surface (IRS) in a non-orthogonal multiple access (NOMA)-aided Integrated Sensing and Multicast-Unicast Communication (ISMUC) system, where the multicast signal is used for sensing and communications while the unicast signal is used only for communications. Our goal is to depict whether the IRS improves the performance of NOMA-ISMUC system or not under the imperfect/perfect successive interference cancellation (SIC) scenario. Towards this end, we formulate a non-convex problem to maximize the unicast rate while ensuring the minimum target illumination power and multicast rate. To settle this problem, we employ the Dinkelbach method to transform this original problem into an equivalent one, which is then solved via alternating optimization algorithm and semidefinite relaxation (SDR) with Sequential Rank-One Constraint Relaxation (SROCR). Based on this, an iterative algorithm is devised to obtain a near-optimal solution. Computer simulations verify the quick convergence of the devised iterative algorithm, and provide insightful results. Compared to NOMA-ISMUC without IRS, IRS-aided NOMA-ISMUC achieves a higher rate with perfect SIC but keeps the almost same rate in the case of imperfect SIC.

Abstract: Relay-enabled backscatter communication (BC) is an intriguing paradigm to alleviate energy shortage and improve throughput of Internet-of-Things (IoT) devices. Most of the existing works focus on the resource allocation that considered the unequal and continuous time allocation for both source-relay and relay-destination links. However, the continuous time allocation may be infeasible since in practice, the time allocation shall be carried out in integral multiple of the subframe duration unit. In this article, we study a discrete time scheme from the perspective of frame structure, where one transmission block is divided into two phases and the linear mapping is employed as a re-encoding method to determine the number of subframes for both phases and the power allocation for each subframe in a relay-enabled BC system. Based on this, we derive an accurate system-throughput expression and formulate a mixed-integral non-convex optimization problem to maximize the system throughput by jointly optimizing the power reflection coefficient (PRC) of the IoT node, the power allocation of the hybrid access point (HAP) and the linear mapping matrix, and solve it via a three-step approach. Accordingly, we propose a low complexity iterative algorithm to obtain the throughput maximization-based resource allocation solution. Numerical results analyze the performance of our proposed algorithm, verify the superiority of our proposed scheme, and evaluate the impacts of network parameters on the system throughput.

Abstract: Sequences with low aperiodic autocorrelation are used in communications and remote sensing for synchronization and ranging. The autocorrelation demerit factor of a sequence is the sum of the squared magnitudes of its autocorrelation values at every nonzero shift when we normalize the sequence to have unit Euclidean length. The merit factor, introduced by Golay, is the reciprocal of the demerit factor. We consider the uniform probability measure on the $2^\ell$ binary sequences of length $\ell$ and investigate the distribution of the demerit factors of these sequences. Previous researchers have calculated the mean and variance of this distribution. We develop new combinatorial techniques to calculate the $p$th central moment of the demerit factor for binary sequences of length $\ell$. These techniques prove that for $p\geq 2$ and $\ell \geq 4$, all the central moments are strictly positive. For any given $p$, one may use the technique to obtain an exact formula for the $p$th central moment of the demerit factor as a function of the length $\ell$. The previously obtained formula for variance is confirmed by our technique with a short calculation, and we demonstrate that our techniques go beyond this by also deriving an exact formula for the skewness.

Abstract: We introduce and study the cumulative information generating function, which provides a unifying mathematical tool suitable to deal with classical and fractional entropies based on the cumulative distribution function and on the survival function. Specifically, after establishing its main properties and some bounds, we show that it is a variability measure itself that extends the Gini mean semi-difference. We also provide (i) an extension of such a measure, based on distortion functions, and (ii) a weighted version based on a mixture distribution. Furthermore, we explore some connections with the reliability of $k$-out-of-$n$ systems and with stress-strength models for multi-component systems. Also, we address the problem of extending the cumulative information generating function to higher dimensions.

Abstract: We contribute to the knowledge of linear codes from special polynomials and functions, which have been studied intensively in the past few years. Such codes have several applications in secret sharing, authentication codes, association schemes and strongly regular graphs. This is the first work in which we study the dual codes in the framework of the two generic constructions; in particular, we propose a Gram-Schmidt (complexity of $\mathcal{O}(n^3)$) process to compute them explicitly. The originality of this contribution is in the study of the existence or not of defining sets $D'$, which can be used as ingredients to construct the dual code $\mathcal{C}'$ for a given code $\mathcal{C}$ in the context of the second generic construction. We also determine a necessary condition expressed by employing the Walsh transform for a codeword of $\mathcal{C}$ to belong in the dual. This achievement was done in general and when the involved functions are weakly regularly bent. We shall give a novel description of the Hull code in the framework of the two generic constructions. Our primary interest is constructing linear codes of fixed Hull dimension and determining the (Hamming) weight of the codewords in their duals.