Sequential measurement-dependent noisy search

Chiu, Sung-En; Javidi, Tara

doi:10.1109/itw.2016.7606828

Cited by 12 publications

(8 citation statements)

References 9 publications

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“…, I n (k * n )}. Note that for this strategy, at every n, the noise is Z n ∼ N (0, |S n |δσ 2 ) and the worst noise intensity is N (0, αBσ 2 2 ). The posterior probability ρ n+1 (i) at time n+1 when Y n = y is obtained by the following Bayesian update:…”

Section: B Achievability: Adaptive Search Strategymentioning

confidence: 99%

“…Our prior work [4] by utilizing a (suboptimal) hard decoding of Gaussian observation Y n , strengthens [3] and [2] by also accounting for the regime in which B grows. While the analysis in [4] strengthens the nonasymptotic bounds in [2] with Bernoulli noise it failed to provide tight analysis for our problem with Gaussian observations. In this paper, by strengthening our analysis in [4] we extend the prior work in three ways: (i) we consider the soft Gaussian observation Y n , (ii) we obtain nonasymptotic achievability and converse analysis, and (iii) we characterize tight non-asymptotic adaptivity gain in the two asymptotically distinct regimes of B → ∞ and δ → 0.…”

Section: Introductionmentioning

confidence: 97%

“…On the other hand, we show that as the search width B expands while keeping search resolution δ fixed, the adaptivity gain grows in the number of locations as O B δ log B δ . The problem of searching for a target under a binary measurement dependent noise, whose crossover probability increases with the weight of the measurement vector was studied by [3] and analyzed under sort PM strategy in [2]. In particular, [3] and [2] provide asymptotic analysis of the adaptivity gain for the case where B = 1 and δ approaches zero.…”

Section: Introductionmentioning

confidence: 99%

“…The problem of searching for a target under a binary measurement dependent noise, whose crossover probability increases with the weight of the measurement vector was studied by [3] and analyzed under sort PM strategy in [2]. In particular, [3] and [2] provide asymptotic analysis of the adaptivity gain for the case where B = 1 and δ approaches zero. Our prior work [4] by utilizing a (suboptimal) hard decoding of Gaussian observation Y n , strengthens [3] and [2] by also accounting for the regime in which B grows.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, [3] and [2] provide asymptotic analysis of the adaptivity gain for the case where B = 1 and δ approaches zero. Our prior work [4] by utilizing a (suboptimal) hard decoding of Gaussian observation Y n , strengthens [3] and [2] by also accounting for the regime in which B grows. While the analysis in [4] strengthens the nonasymptotic bounds in [2] with Bernoulli noise it failed to provide tight analysis for our problem with Gaussian observations.…”

Section: Introductionmentioning

confidence: 99%

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Improved Target Acquisition Rates With Feedback Codes

Lalitha

Ronquillo

Javidi

2018

IEEE J. Sel. Top. Signal Process.

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This paper considers the problem of acquiring an unknown target location (among a finite number of locations) via a sequence of measurements, where each measurement consists of simultaneously probing a group of locations. The resulting observation consists of a sum of an indicator of the target's presence in the probed region, and a zero mean Gaussian noise term whose variance is a function of the measurement vector. An equivalence between the target acquisition problem and channel coding over a binary input additive white Gaussian noise (BAWGN) channel with state and feedback is established.Utilizing this information theoretic perspective, a two-stage adaptive target search strategy based on the sorted Posterior Matching channel coding strategy is proposed. Furthermore, using information theoretic converses, the fundamental limits on the target acquisition rate for adaptive and non-adaptive strategies are characterized. As a corollary to the non-asymptotic upper bound of the expected number of measurements under the proposed two-stage strategy, and to non-asymptotic lower bound of the expected number of measurements for optimal non-adaptive search strategy, a lower bound on the adaptivity gain is obtained. The adaptivity gain is further investigated in different asymptotic regimes of interest.Preliminary versions of this work were presented at the 50th Asilomar Conference on Signals, Systems, and Computers, and at 2017 International Symposium on Information Theory.A. Lalitha N. Ronquillo, and T. Javidi are with the Z n (S n ) is equivalent to channel coding over a binary additive white Gaussian noise (BAWGN) channel with state and feedback (in Section 4.6 [1]). This allows us not only to retrofit the known channel coding schemes based on sorted Posterior Matching (sort PM) [2] as adaptive search strategies, but also to obtain information theoretic converses to characterize fundamental limits on the target acquisition rate under both adaptive and non-adaptive strategies. As a corollary to the non-asymptotic analysis of our sorted Posterior-Matching-based adaptive strategy and our converse for non-adaptive strategy, we obtain a lower bound on the adaptivity gain. A. Our ContributionsOur main results are inspired by the analogy between target acquisition under measurement dependent noise and channel coding with state and feedback. This connection was utilized in [3] under a Bernoulli noise model. In this paper, in Proposition 1, we formalize the connection between our target acquisition problem with Gaussian measurement dependent noise and channel coding over a BAWGN channel with state. Here, the channel state denotes the variance of the measurement dependent noise |S n |δσ 2 . Since feedback codes i.e., adapting the codeword to the past channel outputs, are known to increase the capacity of a channel with state and feedback. This motivates us to use adaptivity when searching, i.e., to utilize past observations {Y 1 , Y 2 , . . . , Y n−1 } when selecting the next measurement vector S n . Furthermore, this informati...

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Section: B Achievability: Adaptive Search Strategymentioning

confidence: 99%