A communication link aided by a Reconfigurable Intelligent Surface (RIS) is studied, in which the transmitter can control the state of the RIS via a finite-rate control link. Prior work mostly assumed a fixed RIS configuration irrespective of the transmitted information. In contrast, this work derives information-theoretic limits, and demonstrates that the capacity is achieved by a scheme that jointly encodes information in the transmitted signal as well as in the RIS configuration. In addition, a novel signaling strategy based on layered encoding is proposed that enables practical successive cancellation-type decoding at the receiver. Numerical experiments demonstrate that the standard max-SNR scheme that fixes the configuration of the RIS as to maximize the Signal-to-Noise Ratio (SNR) at the receiver is strictly suboptimal, and is outperformed by the proposed strategies at all practical SNR levels.

Reliable transmission over a discrete-time memory-less channel with a decoding metric that is not necessarily matched to the channel (mismatched decoding) is considered. It is assumed that the encoder knows both the true channel and the decoding metric. The lower bound on the highest achievable rate found by Csiszar and Komer and by Hui for DMC's, hereafter denoted C,,, is shown to bear some interesting information -theoretic meanings. The bound C,<, turns out to be the highest achievable rate in the random coding sense, namely, the random coding capacity for mismatched decoding. It is also demonstrated that the €-capacity associated with mismatched decoding cannot exceed C,,. New bounds and some properties of C,., are established and used to find relations to the generalized mutual information and to the generalized cutoff rate. The expression for C,, is extended to a certain class of memoryless channels with continuous input and output alphabets, and is used to calculate C,, explicitly for several examples of theoretical and practical interest. Finally, it is demonstrated that in contrast to the classical matched decoding case, here, under the mismatched decoding regime, the highest achievable rate depends on whether the performance criterion is the bit error rate or the message error probability and whether the coding strategy is deterministic or randomized. Zndex Terms-Channel capacity, mismatched decoding, generalized cutoff rate, generalized mutual information, random coding , exponential families, sphere packing.

Consider a channel Y = X + N where X is an n-dimensional random vector, and N is a multivariate Gaussian vector with a full-rank covariance matrix KN. The object under consideration in this paper is the conditional mean of X given Y = y, that is y → E[X|Y = y]. Several identities in the literature connect E[X|Y = y] to other quantities such as the conditional variance, score functions, and higher-order conditional moments. The objective of this paper is to provide a unifying view of these identities.In the first part of the paper, a general derivative identity for the conditional mean estimator is derived. Specifically, for the Markov chain U ↔ X ↔ Y, it is shown that the Jacobian matrix of E[U|Y = y] is given by K −1 N Cov(X, U|Y = y) where Cov(X, U|Y = y) is the conditional covariance.In the second part of the paper, via various choices of the random vector U, the new identity is used to recover and generalize many of the known identities and derive some new identities. First, a simple proof of the Hatsel and Nolte identity for the conditional variance is shown. Second, a simple proof of the recursive identity due to Jaffer is provided. The Jaffer identity is then further explored, and several equivalent stamens are derived, such as an identity for the higher-order conditional expectation (i.e., E[X k |Y]) in terms of the derivatives of the conditional expectation. Third, a new fundamental connection between the conditional cumulants and the conditional expectation is demonstrated. In particular, in the univariate case, it is shown that the k-th derivative of the conditional expectation is proportional to the (k +1)-th conditional cumulant. A similar expression is derived in the multivariate case.The third part of the paper considers various applications of the derived identities (mostly in the scalar case). In a first application, using the new identity for higher-order derivatives of the conditional expectation, a power series representation of the conditional expectation is derived. The power series representation, together with the Lagrange inversion theorem, is then used to find an expression for the compositional inverse of y → E[X|Y = y]. In a second application, the conditional expectation is viewed as a random variable and the probability distribution of E[X|Y ] and probability distribution of the estimator error (X − E[X|Y ]) are derived. In the third application, the new identities are used to show that the higher-order conditional expectations and the conditional cumulants depended on the joint distribution only through the marginal of Y . This observation is then used to construct consistent estimators (known as the empirical Bayes estimators) of the higher-order conditional expectations and the conditional cumulants from an independent and identically distributed sequence Y1, . . . , Yn.

Over-the-air computation (AirComp) is an efficient solution to enable federated learning on wireless channels. Air-Comp assumes that the wireless channels from different devices can be controlled, e.g., via transmitter-side phase compensation, in order to ensure coherent on-air combining. Intelligent reflecting surfaces (IRSs) can provide an alternative, or additional, means of controlling channel propagation conditions. This work studies the advantages of deploying IRSs for AirComp systems in a large-scale cloud radio access network (C-RAN). In this system, worker devices upload locally updated models to a parameter server (PS) through distributed access points (APs) that communicate with the PS on finite-capacity fronthaul links. The problem of jointly optimizing the IRSs' reflecting phases and a linear detector at the PS is tackled with the goal of minimizing the mean squared error (MSE) of a parameter estimated at the PS. Numerical results validate the advantages of deploying IRSs with optimized phases for AirComp in C-RAN systems.

In this correspondence, we present new results on the reconstruction of two-dimensional signals from zero crossing or threshold crossing information. Specifically, we develop new theoretical results which state conditions under which two-dimensional bandlimited signals are uniquely specified to within a scale factor with this information. Unlike previous results in this area, our new results do not constrain the signals to be periodic or bandpass. 'Globally irreducible, in the terminology of [11]-[13] and others.