We revisit the hypothesis testing with communication constraints problem, also called distributed hypothesis testing, 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 decoder, which is also provided with side information, is required to make a decision on whether the null or alternative hypothesis is in effect. First, we provide a general lower bound on the type-II exponent for arbitrary hypotheses, privacy mechanism, rates, and leakage parameters. Second, we consider the testing against independence scenario in which the distribution under the alternative hypothesis is the product of the marginals of the distribution under the null hypothesis. In this setup, we show that the exponent is known exactly and the strong converse property holds. Finally, the trade-offs between the exponent, compression rate, and leakage parameter are illustrated through a binary example.

In this paper, asymptotic expansions for the two-user Gaussian multiple access channel with degraded message sets under long-term power constraints and non-vanishing error probabilities ε ∊ [0,1) are studied. The ε-capacity region is established and bounds on the second-order terms are derived.

International audience

In this paper, the fundamental limits of simultaneous information and energy transmission in the two-user Gaussian multiple access channel with feedback are fully characterized. A simple achievability scheme based on power-splitting and Ozarow's scheme is shown to be optimal. Finally, the maximum individual information rates and the information sum-capacity that are achievable given a minimum energy rate constraint of b energy-units per channel use at the input of the energy harvester are identified. An interesting conclusion is that for a fixed information transmission rate, feedback can at most double the energy transmission rate with respect to the case without feedback.

We show that the rate regions achieved by linear-feedback coding schemes over dual multi-antenna Gaussian multi-access channels (MACs) and broadcast channels (BCs) with independent noises coincide. By dual here we mean: (1) the channel matrices of the MAC and the BC are transposes of each other and (2) the same total input-power constraint P is imposed on both the channels. We also present multi-letter expressions for the linear-feedback capacity regions of the two channels, i.e., for the set of all rates that are achievable with the linear-feedback coding schemes. We identify a sub-class of MAC and BC linear-feedback coding schemes that achieve the respective linear-feedback capacity regions, and within these subclasses, we identify pairs of MAC and BC coding schemes that achieve the same rate regions. In the two-user case, when the transmitters or the receiver are single-antenna, the capacity region for the Gaussian MAC is known [20], [15] and the capacity-achieving scheme is a linear-feedback coding scheme. With our results, we can thus determine the linear-feedback capacity region of the two-user Gaussian BC when either transmitter or receivers are single-antenna and we can identify the corresponding linear-feedback capacity-achieving coding schemes. Our results show that the control-theory inspired linear-feedback coding scheme by Elia [11], Wu et al. [30], and Ardestanizadeh et al. [1] is sumrate optimal among all the linear-feedback coding schemes for the symmetric single-antenna Gaussian BC with equal channel gains. More generally, we show that the linear-feedback sum-capacity of the scalar Gaussian BC with independent noises is achieved using a simple rearrangement of Ozarow's MAC encodings and decodings. In the K 3-user case, Kramer [16] and Ardestanizadeh et al. [2] determined the linear-feedback sum-capacity for the symmetric single-antenna Gaussian MAC with equal channel gains. Using our duality result, in this paper, we identify the linear-feedback sum-capacity for the K 3-user single-antenna Gaussian BC with equal channel gains. It is equal to the sum-rate achieved by Ardestanizadeh et al.'s linear-feedback coding scheme [1].

We show that for the multi-antenna Gaussian MAC and BC with perfect feedback, the largest achievable regions with linear-feedback schemes (called linear-feedback capacity regions) coincide when the same total input-power constraint is imposed on both channels and when the MAC channel matrices are the transposes of the BC channel matrices.