We study the vector Gaussian CEO problem under logarithmic loss distortion measure. Specifically, @math agents observe independent noisy versions of a remote vector Gaussian source, and communicate independently with a decoder over rate-constrained noise-free links. The CEO also has its own Gaussian noisy observation of the source and wants to reconstruct the remote source to within some prescribed distortion level where the incurred distortion is measured under the logarithmic loss penalty criterion. We find an explicit characterization of the rate-distortion region of this model. For the proof of this result, we first extend Courtade-Weissman's result on the rate-distortion region of the DM @math -encoder CEO problem to the case in which the CEO has access to a correlated side information stream which is such that the agents' observations are independent conditionally given the side information and remote source. Next, we obtain an outer bound on the region of the vector Gaussian CEO problem by evaluating the outer bound of the DM model by means of a technique that relies on the de Bruijn identity and the properties of Fisher information. The approach is similar to Ekrem-Ulukus outer bounding technique for the vector Gaussian CEO problem under quadratic distortion measure, for which it was there found generally non-tight; but it is shown here to yield a complete characterization of the region for the case of logarithmic loss measure. Also, we show that Gaussian test channels with time-sharing exhaust the Berger-Tung inner bound, which is optimal. Furthermore, application of our results allows us to find the complete solutions of three related problems: the vector Gaussian distributed hypothesis testing against conditional independence problem, a quadratic vector Gaussian CEO problem with determinant constraint, and the vector Gaussian distributed Information Bottleneck problem.
We investigate two closely related successive refinement (SR) coding problems: 1) In the hypothesis testing (HT) problem, bivariate hypothesis H0:PXY against H1: PXPY, i.e., test against independence is considered. One remote sensor collects data stream X and sends summary information, constrained by SR coding rates, to a decision center which observes data stream Y directly. 2) In the one-helper (OH) problem, X and Y are encoded separately and the receiver seeks to reconstruct Y losslessly. Multiple levels of coding rates are allowed at the two sensors, and the transmissions are performed in an SR manner. We show that the SR-HT rate-error-exponent region and the SR-OH rate region can be reduced to essentially the same entropy characterization form. Single-letter solutions are thus provided in a unified fashion, and the connection between them is discussed. These problems are also related to the information bottleneck (IB) problem, and through this connection we provide a straightforward operational meaning for the IB method. Connection to the pattern recognition problem, the notion of successive refinability, and two specific sources are also discussed. A strong converse for the SR-HT problem is proved by generalizing the image size characterization method, which shows the optimal type-two error exponents under constant type-one error constraints are independent of the exact values of those constants. We study the transmission over a network in which users send information to a remote destination through relay nodes that are connected to the destination via finite-capacity error-free links, i.e., a cloud radio access network. The relays are constrained to operate without knowledge of the users' codebooks, i.e., they perform oblivious processing. The destination, or central processor, however, is informed about the users' codebooks. We establish a single-letter characterization of the capacity region of this model for a class of discrete memoryless channels in which the outputs at the relay nodes are independent given the users' inputs. We show that both relaying a-la Cover-El Gamal, i.e., compress-and-forward with joint decompression and decoding, and "noisy network coding", are optimal. The proof of the converse part establishes, and utilizes, connections with the Chief Executive Officer (CEO) source coding problem under logarithmic loss distortion measure. Extensions to general discrete memoryless channels are also investigated. In this case, we establish inner and outer bounds on the capacity region. For memoryless Gaussian channels within the studied class of channels, we characterize the capacity region when the users are constrained to time-share among Gaussian codebooks. Furthermore, we also discuss the suboptimality of separate decompression-decoding and the role of time-sharing.  We consider secure multi-terminal source coding problems in the presence of a public helper. Two main scenarios are studied: 1) source coding with a helper where the coded side information from the helper is eavesdropped by an external eavesdropper and 2) triangular source coding with a helper where the helper is considered as a public terminal. We are interested in how the helper can support the source transmission subject to a constraint on the amount of information leaked due to its public nature. We characterize the tradeoff among transmission rate, incurred distortion, and information leakage rate at the helper eavesdropper in the form of the rate-distortion-leakage region for various classes of problems. The problem of a nomadic terminal sending information to a remote destination via agents with lossless connections to the destination is investigated. Such a setting suits, e.g., access points of a wireless network where each access point is connected by a wire to a wireline-based network. The Gaussian codebook capacity for the case where the agents do not have any decoding ability is characterized for the Gaussian channel. This restriction is demonstrated to be severe, and allowing the nomadic transmitter to use other signaling improves the rate. For both general and degraded discrete memoryless channels, lower and upper bounds on the capacity are derived. An achievable rate with unrestricted agents, which are capable of decoding, is also given and then used to characterize the capacity for the deterministic channel. A standard assumption in network information theory is that all nodes are informed at all times of the operations carried out (e.g., of the codebooks used) by any other terminal in the network. In this paper, information theoretic limits are sought under the assumption that, instead, some nodes are not informed about the codebooks used by other terminals. Specifically, capacity results are derived for a relay channel in which the relay is oblivious to the codebook used by the source (oblivious relaying), and an interference relay channel with oblivious relaying and in which each destination is possibly unaware of the codebook used by the interfering source (interference-oblivious decoding). Extensions are also discussed for a related scenario with standard codebook-aware relaying but interference-oblivious decoding. The class of channels under study is limited to out-of-band (or “primitive”) relaying: Relay-to-destinations links use orthogonal resources with respect to the transmission from the source encoders. Conclusions are obtained under a rigorous definition of oblivious processing that is related to the idea of randomized encoding. The framework and results discussed in this paper suggest that imperfect codebook information can be included as a source of uncertainty in network design along with, e.g., imperfect channel and topology information. This paper investigates the compress-and-forward scheme for an uplink cloud radio access network (C-RAN) model, where multi-antenna base stations (BSs) are connected to a cloud-computing-based central processor (CP) via capacity-limited fronthaul links. The BSs compress the received signals with Wyner-Ziv coding and send the representation bits to the CP; the CP performs the decoding of all the users’ messages. Under this setup, this paper makes progress toward the optimal structure of the fronthaul compression and CP decoding strategies for the compress-and-forward scheme in the C-RAN. On the CP decoding strategy design, this paper shows that under a sum fronthaul capacity constraint, a generalized successive decoding strategy of the quantization and user message codewords that allows arbitrary interleaved order at the CP achieves the same rate region as the optimal joint decoding. Furthermore, it is shown that a practical strategy of successively decoding the quantization codewords first, then the user messages, achieves the same maximum sum rate as joint decoding under individual fronthaul constraints. On the joint optimization of user transmission and BS quantization strategies, this paper shows that if the input distributions are assumed to be Gaussian, then under joint decoding, the optimal quantization scheme for maximizing the achievable rate region is Gaussian. Moreover, Gaussian input and Gaussian quantization with joint decoding achieve to within a constant gap of the capacity region of the Gaussian multiple-input multiple-output (MIMO) uplink C-RAN model. Finally, this paper addresses the computational aspect of optimizing uplink MIMO C-RAN by showing that under fixed Gaussian input, the sum rate maximization problem over the Gaussian quantization noise covariance matrices can be formulated as convex optimization problems, thereby facilitating its efficient solution. A new class of statistical problems is introduced, involving the presence of communication constraints on remotely collected data. Bivariate hypothesis testing, H_ 0 : P_ XY against H_ 1 : P_ = XY , is considered when the statistician has direct access to Y data but can be informed about X data only at a preseribed finite rate R . For any fixed R the smallest achievable probability of an error of type 2 with the probability of an error of type 1 being at most is shown to go to zero with an exponential rate not depending on as the sample size goes to infinity. A single-letter formula for the exponent is given when P_ = XY = P_ X P_ Y (test against independence), and partial results are obtained for general P_ = XY . An application to a search problem of Chernoff is also given. The multiterminal hypothesis testing H: XY against H: XY is considered where X^ n (X^ n ) and Y^ n (Y^ n ) are separately encoded at rates R_ 1 and R_ 2 , respectively. The problem is to determine the minimum n of the second kind of error probability, under the condition that the first kind of error probability n for a prescribed 0 . A good lower bound L (R_ 1 , R_ 2 ) on the power exponent (R_ 1 , R_ 2 , )= n (-1 n n ) is given and several interesting properties are revealed. The lower bound is tighter than that of Ahlswede and Csiszar. Furthermore, in the special case of testing against independence, this bound turns out to coincide with that given by them. The main arguments are devoted to the special case with R_ 2 = corresponding to full side information for Y^ n (Y^ n ) . In particular, the compact solution is established to the complete data compression cases, which are useful in statistics from the practical point of view. We study a hypothesis testing problem in which data are compressed distributively and sent to a detector that seeks to decide between two possible distributions for the data. The aim is to characterize all achievable encoding rates and exponents of the type 2 error probability when the type 1 error probability is at most a fixed value. For related problems in distributed source coding, schemes based on random binning perform well and are often optimal. For distributed hypothesis testing, however, the use of binning is hindered by the fact that the overall error probability may be dominated by errors in the binning process. We show that despite this complication, binning is optimal for a class of problems in which the goal is to “test against conditional independence.” We then use this optimality result to give an outer bound for a more general class of instances of the problem. Let X , Y , Z be zero-mean, jointly Gaussian random vectors of dimensions nx, ny, and nz, respectively. Let P be the set of random variables W such that W harr Y harr (X, Z) is a Markov string. We consider the following optimization problem: WisinP min I(Y; Z) subject to one of the following two possible constraints: 1) I(X; W|Z) ges RI, and 2) the mean squared error between X and Xcirc = E(X|W, Z) is less than d . The problem under the first kind of constraint is motivated by multiple-input multiple-output (MIMO) relay channels with an oblivious transmitter and a relay connected to the receiver through a dedicated link, while for the second case, it is motivated by source coding with decoder side information where the sensor observation is noisy. In both cases, we show that jointly Gaussian solutions are optimal. Moreover, explicit water filling interpretations are given for both cases, which suggest transform coding approaches performed in different transform domains, and that the optimal solution for one problem is, in general, suboptimal for the other. 