A distributed binary hypothesis testing (HT) problem involving two parties, one referred to as the observer and the other as the detector is studied. The observer observes a discrete memoryless source (DMS) and communicates its observations to the detector over a discrete memoryless channel (DMC). The detector observes another DMS correlated with that at the observer, and performs a binary HT on the joint distribution of the two DMS's using its own observed data and the information received from the observer. The trade-off between the type I error probability and the type II error-exponent of the HT is explored. Single-letter lower bounds on the optimal type II error-exponent are obtained by using two different coding schemes, a separate HT and channel coding scheme and a joint HT and channel coding scheme based on hybrid coding for the matched bandwidth case. Exact single-letter characterization of the same is established for the special case of testing against conditional independence, and it is shown to be achieved by the separate HT and channel coding scheme. An example is provided where the joint scheme achieves a strictly better performance than the separation based scheme. arXiv:1802.07665v8 [cs.IT] 3 Dec 2019showed that for the case of a single-observer, the quantize-bin-test scheme achieves the optimal error-exponent for testing against conditional independence (TACI), in which, V = (E, Z) and Q U EZ = P U Z P E|Z . Extensions of the distributed HT problem has also been considered in several other interesting scenarios involving multiple detectors [9], multiple observers [10], interactive HT [11], [12], collaborative HT [13], HT with lossy source reconstruction [14], HT over a multi-hop relay network [16], etc., in which, the authors obtain a single-letter characterization of the optimal error-exponent in some special cases.While the works mentioned above have studied the unsymmetric case of focusing on the error-exponent for a constraint on the type I error probability, other works have analyzed the trade-off between the type I and type II error probabilities in the exponential sense. In this direction, the optimal trade-off between the type I and type II error-exponents in the centralized scenario is obtained in [17]. The distributed version of this problem is first studied in [18], where inner bounds on the above trade-off are established. This problem has also been explored from an information-geometric perspective for the zero-rate compression scenario in [19] and [20], which provide further insights into the geometric properties of the optimal trade-off between the two exponents. A Neyman-Pearson like test in the zero-rate compression scenario is proposed in [21], which, in addition to achieving the optimal trade-off between the two exponents, also achieves the optimal second order asymptotic performance among all symmetric (type-based) encoding schemes. However, the optimal trade-off between the type I and type II error-exponents for the general distributed HT problem remains open. Recently, an in...
Traditionally, the capacity region of a coherent fading multiple access channel (MAC) is analyzed in two popular contexts. In the first, a centralized system with full channel state information at the transmitters (CSIT) is assumed, and the transmit power and data-rate can be jointly chosen for every fading vector realization. On the other hand, in fastfading links with distributed CSIT, the lack of full CSI is compensated by performing ergodic averaging over sufficiently many channel realizations. Notice that the distributed CSI may necessitate decentralized power-control for optimal data-transfer. Apart from these two models, the case of slow-fading links and distributed CSIT, though relevant to many systems, has received much less attention.In this paper, a block-fading AWGN MAC with full CSI at the receiver and distributed CSI at the transmitters is considered. The links undergo independent fading, but otherwise have arbitrary fading distributions. The channel statistics and respective long-term average transmit powers are known to all parties. We first consider the case where each encoder has knowledge only of its own link quality, and not of others. For this model, we compute the adaptive capacity region, i.e. the collection of average rate-tuples under block-wise coding/decoding such that the ratetuple for every fading realization is inside the instantaneous MAC capacity region. The key step in our solution is an optimal rate allocation function for any given set of distributed power control laws at the transmitters. This also allows us to structurally characterize the optimal power control for a wide class of fading models. Further extensions are also proposed for the case where each encoder has additional partial CSI about the other links.
A distributed binary hypothesis testing problem, in which multiple observers transmit their observations to a detector over noisy channels, is studied. Given its own side information, the goal of the detector is to decide between two hypotheses for the joint distribution of the data. Single-letter upper and lower bounds on the optimal type 2 error exponent (T2-EE), when the type 1 error probability vanishes with the block-length are obtained. These bounds coincide and characterize the optimal T2-EE when only a single helper is involved. Our result shows that the optimal T2-EE depends on the marginal distributions of the data and the channels rather than their joint distribution. However, an operational separation between HT and channel coding does not hold, and the optimal T2-EE is achieved by generating channel inputs correlated with observed data.
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