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We characterize the asymptotic performance of nonparametric one- and two-sample testing. The exponential decay rate or error exponent of the type-II error probability is used as the asymptotic performance metric, and an optimal test achieves the maximum rate subject to a constant level constraint on the type-I error probability. With Sanov's theorem, we derive a sufficient condition for one-sample tests to achieve the optimal error exponent in the universal setting, i.e., for any distribution defining the alternative hypothesis. We then show that two classes of Maximum Mean Discrepancy (MMD) based tests attain the optimal type-II error exponent on $\mathbb R^d$, while the quadratic-time Kernel Stein Discrepancy (KSD) based tests achieve this optimality with an asymptotic level constraint. For general two-sample testing, however, Sanov's theorem is insufficient to obtain a similar sufficient condition. We proceed to establish an extended version of Sanov's theorem and derive an exact error exponent for the quadratic-time MMD based two-sample tests. The obtained error exponent is further shown to be optimal among all two-sample tests satisfying a given level constraint. Our work hence provides an achievability result for optimal nonparametric one- and two-sample testing in the universal setting. Application to off-line change detection and related issues are also discussed., Accepted to IEEE Transactions on Information Theory. This version may be further modified

This paper studies the impact of interactive fusion on detection performance in tandem fusion networks with conditionally independent observations. Within the Neyman-Pearson framework, two distinct regimes are considered: the fixed sample size test and the large sample test. For the former, it is established that interactive distributed detection may strictly outperform the one-way tandem fusion structure. However, for the large sample regime, it is shown that interactive fusion has no improvement on the asymptotic performance characterized by the Kullback-Leibler (KL) distance compared with the simple one-way tandem fusion. The results are then extended to interactive fusion systems where the fusion center and the sensor may undergo multiple steps of memoryless interactions or that involve multiple peripheral sensors, as well as to interactive fusion with soft sensor outputs., 32 pages, 7 figures, Final version, Published in IEEE Transactions on Information Theory

This paper studies the problem of secure communication over a noiseless network from an information-theoretic perspective. A single-source single-sink acyclic planar network is considered, and the communication between the source and the sink is subject to noncooperative eavesdropping on each link. Using equivocation to measure the confidentiality of messages, we establish sufficient conditions, in terms of communication rates and network parameters, for provably secure communication. A constructive proof, which combines Shannon's key encryption and the Ford-Fulkerson algorithm, is provided and constitutes a readily implementable secure coding scheme. The derived achievable rate equivocation region is tight when specializing to several special cases. In particular, when the communication network decouples into nonoverlapping parallel paths, the proposed encoding scheme is optimal, i.e., it achieves the secure communication capacity for such networks.

For a multi-user interference channel with multi-antenna transmitters and single-antenna receivers, by restricting each transmitter to Gaussian input and each receiver to a single-user detector, computing the largest achievable rate region amounts to solving a family of non-convex optimization problems. Recognizing the intrinsic connection between the signal power at the intended receiver and the interference power at the unintended receiver, the original family of non-convex optimization problems is converted into a new family of convex optimization problems. It is shown that, for such interference channels with each receiver implementing single-user detection, transmitter beamforming can achieve all boundary points of the achievable rate region., Comment: 41 pages, 7 figures, submitted to IEEE trans. on Information Theory in Apr. 2009

A new outer bound on the capacity region of Gaussian interference channels is developed. The bound combines and improves existing genie-aided methods and is shown to give the sum-rate capacity for noisy interference as defined in this paper. Specifically, it is shown that if the channel coefficients and power constraints satisfy a simple condition then single-user detection at each receiver is sum-rate optimal, i.e., treating the interference as noise incurs no loss in performance. This is the first concrete (finite signal-to-noise ratio) capacity result for the Gaussian interference channel with weak to moderate interference. Furthermore, for certain mixed (weak and strong) interference scenarios, the new outer bounds give a corner point of the capacity region., 20 pages, 8 figures, submitted to IEEE Trans. Inform. Theory

In this paper, we consider the design of local decision rules for distributed detection systems where decisions from peripheral detectors are transmitted over dependent nonideal channels. Under the conditional independence assumption among multiple sensor observations, we show that the optimal detection performance can be achieved by employing likelihood-ratio quantizers (LRQ) as local decision rules under both the Bayesian criterion and Neyman-Pearson (NP) criterion even for the cases where the channels between the fusion center and local sensors are dependent and noisy. This work generalizes the previous work where independence among such channels was assumed. A person-by-person optimization (PBPO) procedure to obtain the solution is presented along with an illustrative example.

In this correspondence, we study some information theoretical characteristics of vector Gaussian interference channels. Resorting to the superposition code technique, a lower bound of the sum capacity for the vector Gaussian interference channel is obtained. Alternatively, orthogonal transmission via frequency division multiplexing is considered and we establish the concavity of sum rate as the bandwidth allocation factor for the vector channel case. Numerical examples indicate that the achievable sum rate via the superposition code compares favorably with orthogonal transmission: the lower bound obtained via the superposition code dominates the best achievable sum rate through orthogonal transmission. This improvement holds for all interference power levels, a sharp contrast to that of the scalar counterpart

Motivated by the delay and resource constraints omnipresent in most wireless sensor network applications, we design channel-optimized scalar quantizers for a canonical decentralized detection system. Aimed at minimizing the error probability of the fusion center output, we first establish the optimality of monotone likelihood ratio partition of the observation space for the local quantizer design. We then devise an iterative algorithm to construct distributed quantizers that are person-by-person optimal. The channel-optimized approach is shown to offer better performance compared with various alternatives. It also exhibits inherent adaptivity in resource (bit) allocation in response to varying channel conditions.

Distributed detection has been intensively studied in the past. In this correspondence, we consider the design of local decision rules in the presence of nonideal transmission channels between the sensors and the fusion center. Under the conditional independence assumption among multiple sensor observations, we show that the optimal local decisions that minimize the error probability at the fusion center amount to a likelihood-ratio test (LRT) given a particular constraint on the fusion rule. This constraint turns out to be quite general and is easily satisfied for most sensible fusion rules. A design example using a parallel sensor fusion structure with binary-symmetric channels (BSCs) between local sensors and the fusion center is given to illustrate the usefulness of the result in obtaining optimal thresholds for local sensor observations. The study that incorporates the transmission channel in the sensor system design may have potential applications in the emerging field of wireless sensor networks.

We develop an expression for the minimum extra bandwidth needed for a frequency-division multiple-access (FDMA) system to out perform its code-division (CDMA) counterpart uniformly (that is, for all rate n-tuples) in a Gaussian multiple-access channel (MAC). For equal-power sources, the behavior of this factor is as an iterated logarithm of the number of users; hence it increases slowly yet is unbounded. Asymmetric power cases are also studied and it is shown that the equal power scenario provides the least bandwidth expansion factor assuming constant constraint on total power.

Page's (1954) test is optimal for detecting a permanent change in distribution, in the sense that it minimizes the worst case average delay to detection given an average distance between false alarms. When used to detect transient signals, however, it in fact becomes the generalized likelihood ratio test (GLRT). Since a GLRT is in almost all cases ad hoc, Page's test used as such cannot be said to be optimal in any explicit sense. This article discusses the development of the min-max test, via the new ideas of Baygun and Hero (see ibid., vol.41, p.688-703, 1995) for the detection of a transient.