By proving a strong converse, we strengthen the weak converse result by Salehkalaibar, Wigger and Wang (2017) concerning hypothesis testing against independence over a two-hop network with communication constraints. Our proof follows by judiciously combining two recently proposed techniques for proving strong converse theorems, namely the strong converse technique via reverse hypercontractivity by Liu, van Handel, and Verdú (2017) and the strong converse technique by Tyagi and Watanabe (2018), in which the authors used a change-of-measure technique and replaced hard Markov constraints with soft information costs. The techniques used in our paper can also be applied to prove strong converse theorems for other multiterminal hypothesis testing against independence problems.
A distributed binary hypothesis testing (HT) problem over a noisy (discrete and memoryless) channel studied previously by the authors is investigated from the perspective of the strong converse property. It was shown by Ahlswede and Csiszár that a strong converse holds in the above setting when the channel is rate-limited and noiseless. Motivated by this observation, we show that the strong converse continues to hold in the noisy channel setting for a special case of HT known as testing against independence (TAI). The proof utilizes the blowing up lemma and the recent change of measure techniq…
The main contribution of this paper is a strong converse result for $K$-hop distributed hypothesis testing against independence with multiple (intermediate) decision centers under a Markov condition. Our result shows that the set of type-II error exponents that can simultaneously be achieved at all the terminals does not depend on the maximum permissible type-I error probabilities. Our strong converse proof is based on a change of measure argument and on the asymptotic proof of specific Markov chains. This proof method can also be used for other converse proofs, and is appealing because it doe…
The paper presents exponentially-strong converses for source-coding, channel coding, and hypothesis testing problems. More specifically, it presents alternative proofs for the well-known exponentially-strong converse bounds for almost lossless source-coding with side-information and for channel coding over a discrete memoryless channel (DMC). These alternative proofs are solely based on a change of measure argument on the sets of conditionally or jointly typical sequences that result in a correct decision, and on the analysis of these measures in the asymptotic regime of infinite blocklengths.…
Coding and testing schemes and the corresponding achievable type-II error exponents are presented for binary hypothesis testing over two-hop relay networks. The schemes are based on cascade source coding techniques and {unanimous decision-forwarding}, the latter meaning that a terminal decides on the null hypothesis only if all previous terminals have decided on the null hypothesis. If the observations at the transmitter, the relay, and the receiver form a Markov chain in this order, then, without loss in performance, the proposed cascade source code can be replaced by two independent point-to…
We consider a multi-hop distributed hypothesis testing problem with multiple decision centers (DCs) for testing against independence and where the observations obey some Markov chain. For this system, we characterize the fundamental type-II error exponents region, i.e., the type-II error exponents that the various DCs can achieve simultaneously, under expected rate-constraints. Our results show that this fundamental exponents region is boosted compared to the region under maximum-rate constraints, and that it depends on the permissible type-I error probabilities. When all DCs have equal permis…
We study a hypothesis testing problem with a privacy constraint over a noisy channel and derive the performance of optimal tests under the Neyman-Pearson criterion. The fundamental limit of interest is the privacy-utility tradeoff (PUT) between the exponent of the type-II error probability and the leakage of the information source subject to a constant constraint on the type-I error probability. We provide an exact characterization of the asymptotic PUT for any non-vanishing type-I error probability. Our result implies that tolerating a larger type-I error probability cannot improve the PUT. S…
The classical problem in network coding theory considers communication over multicast networks. Multiple transmitters send independent messages to multiple receivers which decode the same set of messages. In this work, computation over multicast networks is considered: each receiver decodes an identical function of the original messages. For a countably infinite class of two-transmitter two-receiver single-hop linear deterministic networks, the computing capacity is characterized for a linear function (modulo-2 sum) of Bernoulli sources. Inspired by the geometric concept of interference alignm…
The problem of distributed testing against independence with variable-length coding is considered when the \emph{average} and not the \emph{maximum} communication load is constrained as in previous works. The paper characterizes the optimum type-II error exponent of a single sensor single decision center system given a maximum type-I error probability when communication is either over a noise-free rate-$R$ link or over a noisy discrete memoryless channel (DMC) with stop-feedback. Specifically, let $ε$ denote the maximum allowed type-I error probability. Then the optimum exponent of the system …
This paper characterizes the optimal type-II error exponent for a distributed hypothesis testing-against-independence problem when the \emph{expected} rate of the sensor-detector link is constrained. Unlike for the well-known Ahlswede-Csiszar result that holds under a \emph{maximum} rate constraint and where a strong converse holds, here the optimal exponent depends on the allowed type-I error exponent. Specifically, if the type-I error probability is limited by $ε$, then the optimal type-II error exponent under an \emph{expected} rate constraint $R$ coincides with the optimal type-II error ex…
Although extensively investigated, the capacity of the two-hop half-duplex (HD) relay channel is not fully understood. In particular, a capacity expression which can be easily evaluated is not available and an explicit coding scheme which achieves the capacity is not known either. In this paper, we derive a new expression for the capacity of the two-hop HD relay channel by simplifying previously derived converse expressions. Compared to previous results, the new capacity expression can be easily evaluated. Moreover, we propose an explicit coding scheme which achieves the capacity. To achieve t…
Although extensively investigated, the capacity of the two-hop half-duplex (HD) relay channel is not fully understood. In particular, a capacity expression which can be evaluated straightforwardly is not available and an explicit coding scheme which achieves the capacity is not known either. In this paper, we derive a new expression for the capacity of the two-hop HD relay channel based on a simplified converse. Compared to previous results, this capacity expression can be easily evaluated. Moreover, we propose an explicit coding scheme which achieves the capacity. To achieve the capacity, the…
This paper develops upper bounds on the end-to-end transmission capacity of multi-hop wireless networks. Potential source-destination paths are dynamically selected from a pool of randomly located relays, from which a closed-form lower bound on the outage probability is derived in terms of the expected number of potential paths. This is in turn used to provide an upper bound on the number of successful transmissions that can occur per unit area, which is known as the transmission capacity. The upper bound results from assuming independence among the potential paths, and can be viewed as the ma…
This paper studies low-latency streaming codes for the multi-hop network. The source is transmitting a sequence of messages (streaming messages) to a destination through a chain of relays where each hop is subject to packet erasures. Every source message has to be recovered perfectly at the destination within a delay constraint of $T$ time slots. In any sliding window of $T+1$ time slots, we assume no more than $N_j$ erasures introduced by the $j$'th hop channel. The capacity in case of a single relay (a three-node network) was derived by Fong [1], et al. While the converse derived for the thr…
We study a class of $K$-encoder hypothesis testing against conditional independence problems. Under the criterion that stipulates minimization of the Type II error subject to a (constant) upper bound $ε$ on the Type I error, we characterize the set of encoding rates and exponent for both discrete memoryless and memoryless vector Gaussian settings. For the DM setting, we provide a converse proof and show that it is achieved using the Quantize-Bin-Test scheme of Rahman and Wagner. For the memoryless vector Gaussian setting, we develop a tight outer bound by means of a technique that relies on th…
This paper investigates low-latency streaming codes for a three-node relay network. The source transmits a sequence of messages (streaming messages) to the destination through the relay between them, where the first-hop channel from the source to the relay and the second-hop channel from the relay to the destination are subject to packet erasures. Every source message must be recovered perfectly at the destination subject to a fixed decoding delay of $T$ time slots. In any sliding window of $T+1$ time slots, we assume no more than $N_1$ and $N_2$ erasures are introduced by the first-hop channe…
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 hy…
Covert communication, also known as low probability of detection (LPD) communication, prevents the adversary from knowing that a communication is taking place. Recent work has demonstrated that, in a three-party scenario with a transmitter (Alice), intended recipient (Bob), and adversary (Warden Willie), the maximum number of bits that can be transmitted reliably from Alice to Bob without detection by Willie, when additive white Gaussian noise (AWGN) channels exist between all parties, is on the order of the square root of the number of channel uses. In this paper, we begin consideration of ne…
We consider three channel models: the wiretap channel with $M$ helpers, the $K$-user multiple access wiretap channel, and the $K$-user interference channel with an external eavesdropper, when no eavesdropper's channel state information (CSI) is available at the transmitters. In each case, we establish the optimal sum secure degrees of freedom (s.d.o.f.) by providing achievable schemes and matching converses. We show that the unavailability of the eavesdropper's CSIT does not reduce the s.d.o.f. of the wiretap channel with helpers. However, there is loss in s.d.o.f. for both the multiple access…
We study the secure degrees of freedom (d.o.f.) of one-hop wireless networks by considering four fundamental Gaussian network structures: wiretap channel, broadcast channel with confidential messages, interference channel with confidential messages, and multiple access wiretap channel. The secure d.o.f. of the canonical Gaussian wiretap channel with no helpers is zero. It has been known that a strictly positive secure d.o.f. can be obtained in the Gaussian wiretap channel by using a helper which sends structured cooperative signals. We show that the exact secure d.o.f. of the Gaussian wiretap …
