A distributed binary hypothesis testing problem is studied with one observer and two decision centers. Achievable type-II error exponents are derived for testing against conditional independence when the observer communicates with the two decision centers over one common and two individual noise-free bit pipes and when it communicates with them over a noisy broadcast channel (BC). The results are based on a coding and testing scheme that splits the observations into subblocks, so that transmitter and receivers can independently apply to each subblock either Gray-Wyner coordination coding with side-information or hybrid joint sourcechannel coding with side-information, followed by a Neyman-Pearson test over the subblocks at the receivers. This approach allows to avoid introducing further error exponents that one would expect from the receivers’ decoding operations related to binning or the noisy transmission channel. The derived exponents are shown to be optimal in some special cases when communication is over noise-free links. The results reveal a tradeoff between the type-II error exponents at the two decision centers.

Coding and testing schemes for binary hypothesis testing over noisy networks are proposed and their corresponding type-II error exponents are derived. When communication is over a discrete memoryless channel (DMC), our scheme combines Shimokawa-Han-Amari’s hypothesis testing scheme with Borade-Nakiboglu-Zheng’s unequal error protection (UEP) for channel coding where source and channel codewords are simultaneously decoded. The resulting exponent is optimal for the newly introduced class of generalized testing against conditional independence. When communication is over a multi-access channel (MAC), our scheme combines hybrid coding with UEP. The resulting error exponent over the MAC is optimal in the case of generalized testing against conditional independence with independent observations at the two sensors when the MAC decomposes into two individual DMCs. In this case, separate source-channel coding is sufficient and no UEP is required. This same conclusion holds also under arbitrarily correlated sensor observations when testing is against independence.

We revisit the distributed hypothesis testing (or hypothesis testing with communication constraints) problem from the viewpoint of privacy. Instead of observing the raw data directly, the transmitter observes a sanitized or randomized version of it. We impose an upper bound on the mutual information between the raw and randomized data. Under this scenario, the receiver, which is also provided with side information, is required to make a decision on whether the null or alternative hypothesis is in effect. We first provide a general lower bound on the type-II exponent for an arbitrary pair of hypotheses. Next, we show that if the distribution under the alternative hypothesis is the product of the marginals of the distribution under the null (i.e., testing against independence), then the exponent is known exactly. Moreover, we show that the strong converse property holds. Using ideas from Euclidean information theory, we also provide an approximate expression for the exponent when the communication rate is low and the privacy level is high. Finally, we illustrate our results with a binary and a Gaussian example.

This paper studies the rate-distortion-perception (RDP) tradeoff for a memoryless source model in the asymptotic limit of large block-lengths. The perception measure is based on a divergence between the distributions of the source and reconstruction sequences conditioned on the encoder output, first proposed by Mentzer et al. We consider the case when there is no shared randomness between the encoder and the decoder and derive, for the case of discrete memoryless sources, a single-letter characterization of the RDP function. This is in contrast to the marginal-distribution metric case (introduced by Blau and Michaeli), whose RDP characterization remains open when there is no shared randomness. The achievability scheme is based on lossy source coding with a posterior reference map. For the case of continuous valued sources under the squared error distortion measure and the squared quadratic Wasserstein perception measure, we also derive a single-letter characterization and show that the decoder can be restricted to a noise-adding mechanism. Interestingly, the RDP function characterized for the case of zero perception loss coincides with that of the marginal metric and further zero perception loss can be achieved with a 3-dB penalty in minimum distortion. Finally we specialize to the case of Gaussian sources, and derive the RDP function for Gaussian vector case and propose a reverse water-filling type solution. We also partially characterize the RDP function for a mixture of Gaussian vector sources.

In this paper, we study the one-receiver two-eavesdropper Broadcast Channel (BC) with three degraded message sets. A common message is sent to three receivers. Another message is sent to the first and second receivers and needs to be kept secret from the third receiver (second eavesdropper). The third message is sent to the first receiver and needs to be kept secret from the second and third receivers (first and second eavesdroppers). First, we consider perfect secrecy conditions at the eavesdroppers, where we find an achievable perfect secrecy region. In the achievability scheme, we use superposition coding which divides the available randomness into different levels. These levels are used to mislead the eavesdroppers. The proposed coding scheme determines the perfect secrecy capacity region of the one-receiver two-eavesdropper BC with three degraded message sets, when the receivers exhibit a degradedness order. Next, we find an achievable rate-equivocation region using the rate splitting technique and indirect decoding. We show that for the two-receiver one-eavesdropper BC with three degraded message sets where we relax the secrecy condition at the second receiver, our coding scheme is optimal when the second receiver is a degraded version of the first receiver and it is less noisy than the third receiver.