Distributed Hypothesis Testing with Concurrent Detections

IEEE Trans. Inform. Theory

Wang

2019

Self Cite

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 decisionforwarding, 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-point source codes, one for each hop. The decoupled scheme (combined with decision-forwarding) is shown to attain the optimal type-II error exponents for various instances of "testing against conditional independence." The same decoupling is shown to be optimal also for some instances of "testing against independence," when the observations at the transmitter, the receiver, and the relay form a Markov chain in this order, and when the relay-to-receiver link is of sufficiently high rate. For completeness, the paper also presents an analysis of the Shimokawa-Han-Amari binning scheme for the point-to-point hypothesis testing setup.S. Salehkalaibar is with the In the second part of the manuscript, we focus on two cases: the first is where X n → Y n → Z n forms a Markov chain under both hypotheses, and the second is where X n → Z n → Y n forms a Markov chain under both hypotheses. The first case models an extreme situation where the relay lies in between the transmitter and the receiver, and thus the signals at the sensor and the receiver are conditionally independent given the signal at the relay. In such a situation, the two-hop network models, for example, short-range wireless communication where the sensor's signal only reaches the relay but not the more distant receiver. The second case models a situation where the receiver lies in between the sensor and the relay, and thus the signals at the transmitter and the relay are conditionally independent given the signal at the receiver. In such a situation, the two-hop network models, for example, communication in a cellular system where the relay is a powerful base station and all communication goes through this base station.We show that, in the first case where X n → Y n → Z n , our schemes simplify considerably in the sense that the source coding scheme for the two-hop relay network decouples into two independent point-to-point source coding schemes. In other words, it suffices to send quantization information about X n from the transmitter to the relay and, independently thereof, to send quantization information about Y n from the relay to the receiver (while also employing unanimous decision-forwarding) This contrasts the general scheme where the relay combines the quantization information about X n with its own observation Y n to create some kind of jointly processed quantization information to send to the receiver. The receiver error exponent achieved by the simplified scheme...

“…. ., such that the corresponding sequences of type-I and type-II error probabilities at the relay α y,n : = Pr[Ĥ y = 1|H = 0], (7) β y,n : = Pr[Ĥ y = 0|H = 1], (8) and at the receiver…”

Section: Detailed Problem Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Hypothesis Testing Over the Two-Hop Relay Network

Salehkalaibar

IEEE Trans. Inform. Theory

Wang

2019

Self Cite

“…The finite length regime was investigated in [28]. The optimal Type-II error exponents of zerorate hypothesis testing in an interactive setup and in a cascaded-encoders network were presented respectively in [29] and [13], [16], [23], [30]. In particular, in our previous work [16], we proved such a result for the singlesensor two-detectors setup.…”

Section: Introductionmentioning

confidence: 79%

“…In contrast, a tradeoff arises under concurrent detection if the sensor can distinguish the two hypotheses but can only send a single bit to the detectors. A comparison with the optimal exponents regions without cooperation [16], allows us to exactly quantify the benefits of detector cooperation in this setup with fixed communication alphabets' sizes. All results summarized in this paragraph remain valid when the alphabets' sizes are not fixed but grow sublinearly in the length of the observed sequences.…”

Section: A Main Contributions and Organizationmentioning

confidence: 99%

“…The latter scheme was shown to achieve the optimal exponent in the special case of testing against conditional independence by Rahman and Wagner [4]. This line of work has also been extended to networks with multiple sensors [2], [4]- [8], multiple detectors [9], interactive terminals [10]- [12], multi-hop networks [5], [13]- [16], noisy channels [17], [18], and scenarios with privacy constraints [19]- [22]. In this paper, we consider the single-sensor two-detectors system shown in Fig.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Distributed Hypothesis Testing: Cooperation and Concurrent Detection

Escamilla

IEEE Trans. Inform. Theory

Zaidi

2020

Self Cite

A single-sensor two-detectors system is considered where the sensor communicates with both detectors and Detector 1 communicates with Detector 2, all over noise-free rate-limited links. The sensor and both detectors observe discrete memoryless source sequences whose joint probability mass function depends on a binary hypothesis. The goal at each detector is to guess the binary hypothesis in a way that, for increasing observation lengths, the probability of error under one of the hypotheses decays to zero with largest possible exponential decay, whereas the probability of error under the other hypothesis can decay to zero or to a small positive number arbitrarily slow. For the setting with positive communication rates from the sensor to the detectors and when both detectors are interested in maximizing the error exponent under the same hypothesis, we characterize the set of all possible exponents in a special case of testing against independence. In this case the cooperation link allows Detector 2 to increase its Type-II error exponent by an amount that is equal to the exponent attained at Detector 1. We also provide a general inner bound on the set of achievable error exponents that shows a tradeoff between the exponents at the two detectors in most cases. When the two detectors aim at maximizing the error exponent under different hypotheses and the distribution at the Sensor is different under the two hypotheses, then we show that such a tradeoff does not exist. We propose a general scheme that allows each detector to attain the same exponent as if it was the only detector in the system. For the setting with zerorate communication on both links, we exactly characterize the set of possible exponents and the gain brought up by cooperation, in function of the number of bits that are sent over the two links. Notice that, for this setting, tradeoffs between the exponents achieved at the two detectors arise only in few particular cases. In all other cases, each detector achieves the same performance as if it were the only detector in the system.

Distributed Hypothesis Testing with Collaborative Detection

Escamilla

Zaidi²,

2018 56th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

2018

Self Cite

A detection system with a single sensor and two detectors is considered, where each of the terminals observes a memoryless source sequence, the sensor sends a message to both detectors and the first detector sends a message to the second detector. Communication of these messages is assumed to be error-free but rate-limited. The joint probability mass function (pmf) of the source sequences observed at the three terminals depends on an M-ary hypothesis (M ≥ 2), and the goal of the communication is that each detector can guess the underlying hypothesis. Detector k, k = 1, 2, aims to maximize the error exponent under hypothesis i k , i k ∈ {1, . . . , M}, while ensuring a small probability of error under all other hypotheses. We study this problem in the case in which the detectors aim to maximize their error exponents under the same hypothesis (i.e., i1 = i2) and in the case in which they aim to maximize their error exponents under distinct hypotheses (i.e., i1 = i2). For the setting in which i1 = i2, we present an achievable exponents region for the case of positive communication rates, and show that it is optimal for a specific case of testing against independence. We also characterize the optimal exponents region in the case of zero communication rates. For the setting in which i1 = i2, we characterize the optimal exponents region in the case of zero communication rates.