Bit-wise Sequential Coding with Feedback

Chiu, Sung-En; Lalitha, Anusha; Javidi, Tara

doi:10.1109/isit.2018.8437681

Cited by 5 publications

(7 citation statements)

References 7 publications

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“…where E RC (q) = max 0≤ρ≤1 E 0 (ρ, q) − ρ × log 2 (128) 28 and (33), and the upper bound on the bisection algorithm is provided by [1].…”

Section: Posterior Updatementioning

confidence: 99%

“…Our analysis follows similarly to [28], [2] which analyzed a feedback coding scheme and an abstract adaptive target search algorithm, respectively. The analysis is based on the behavior of the posterior of the AoA π i (t) := P(φ = θ i | y 1:t , w 1:t ) for i = 1, 2, ..., 1 δ , (51) over time t = 1, 2, .... Recall that the stopping time of hieP M is given by…”

Section: Appendix B Average Log-likelihood and The Extrinsic Jensen-smentioning

confidence: 99%

“…have been shown to be useful for analyzing adaptive systems [2], [29], [30], [31] with the Bayes' rule dynamics on the posterior distribution. Particularly, the functional average log-likelihood [30] has shown its usefulness in analyzing the behaviour of the posterior in feedback coding systems [28], dynamic spectrum sensing [10], hypothesis testing [32], active learning [32], etc. Here, we review some useful concepts through the context of AoA estimation with sequential beamforming:…”

Section: Appendix B Average Log-likelihood and The Extrinsic Jensen-smentioning

confidence: 99%

“…Let γ h be the hieP M feedback coding scheme. By the same method in [28], the EJS can be lower bounded by EJS(π(t), γ h ) ≥ I(1/3; p[l t+1 ]), ∀ t (66) EJS(π(t), γ h ) ≥πC 1 (p[log 2 (1/δ)]), ∀ max i π i ≥π (67) (for completeness, we include the proof of equation (66) (68) The gap from I(1/3; p [1]) to I(1/3; p[l]) is done similarly to [2]: we need to further show that hieP M is able to zoom-in to higher level beamforming and effectively obtain less noisy measurements (p By the time homogeneity of the Markov Chain π(t) together with Lemma 2, we can upper bound the two terms associated with the "good" event F C n and the "bad" but low probability event E t in (69) as Et E[τ ,δ | π(t)] dP ≤ P(E t )× for n > (l +1) log 2…”

Section: A Proof Of Theoremmentioning

confidence: 99%

See 3 more Smart Citations

Active Learning and CSI Acquisition for mmWave Initial Alignment

Chiu

Ronquillo

Javidi

2019

IEEE J. Select. Areas Commun.

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106

133

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Millimeter wave (mmWave) communication with large antenna arrays is a promising technique to enable extremely high data rates due to large available bandwidth in mmWave frequency bands. In addition, given the knowledge of an optimal directional beamforming vector, large antenna arrays have been shown to overcome both the severe signal attenuation in mmWave as well as the interference problem. However, fundamental limits on achievable learning rate of an optimal beamforming vector remain.This paper considers the problem of adaptive and sequential optimization of the beamforming vectors during the initial access phase of communication. With a single-path channel model, the problem is reduced to actively learning the Angle-of-Arrival (AoA) of the signal sent from the user to the Base Station (BS). Drawing on the recent results in the design of a hierarchical beamforming codebook [1], sequential measurement dependent noisy search strategies [2], and active learning from an imperfect labeler [3], an adaptive and sequential alignment algorithm is proposed.For any given resolution and error probability of the estimated AoA, an upper bound on the expected search time of the proposed algorithm is derived via Extrinsic Jensen-Shannon Divergence. The upper bound demonstrates that the search time of the proposed algorithm asymptotically matches the performance of the noiseless bisection search up to a constant factor, in effect, characterizing the AoA acquisition rate. Furthermore, the upper bound shows that the acquired AoA error probability decays exponentially fast with the search time with an exponent that is a decreasing function of the acquisition rate.Numerically, the proposed algorithm is compared with prior work where a significant improvement of the system communication rate is observed. Most notably, in the relevant regime of low (−10dB to +5dB) raw SNR, this establishes the first practically viable solution for initial access and, hence, the first demonstration of stand-alone mmWave communication.

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“…where E RC (q) = max 0≤ρ≤1 E 0 (ρ, q) − ρ × log 2 (128) 28 and (33), and the upper bound on the bisection algorithm is provided by [1].…”

Section: Posterior Updatementioning

confidence: 99%

Section: Appendix B Average Log-likelihood and The Extrinsic Jensen-smentioning

confidence: 99%

Section: Appendix B Average Log-likelihood and The Extrinsic Jensen-smentioning

confidence: 99%

Section: A Proof Of Theoremmentioning

confidence: 99%

See 2 more Smart Citations

Active Learning and CSI Acquisition for mmWave Initial Alignment

Chiu

Ronquillo

Javidi

2019

IEEE J. Select. Areas Commun.

Self Cite

106

133

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show abstract

“…Remark 5. The hierarchical query geometry H not only is connected but also is of a hierarchical structure, which is suitable for the applications such as heavy hitter detection in networking [12] (monitoring pre-fix IP addresses) and bit-wise coding [16]. Furthermore, the query cardinality is only |H| = O( 1 δ ), rendering hieP M a great candidate for beamforming applications [11].…”

Section: B Hierarchical Posterior Matchingmentioning

confidence: 99%

Low Complexity Sequential Search with Size-Dependent Measurement Noise

Chiu¹,

Javidi²

2020

Preprint

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This paper considers a target localization problem where at any given time an agent can choose a region to query for the presence of the target in that region. The measurement noise is assumed to be increasing with the size of the query region the agent chooses. Motivated by practical applications such as initial beam alignment in array processing, heavy hitter detection in networking, and visual search in robotics, we consider practically important complexity constraints/metrics: time complexity, computational and memory complexity, query geometry, and cardinality of possible query sets.Two novel search strategy, dyaP M and hieP M , are proposed. In contrast to previously proposed algorithms, dyaP M and hieP M are of a connected query geometry (i.e. query set is always a connected set). We also demonstrated how they can be implemented with low computational and memory complexity. Additionally, hieP M has a hierarchical structure and has a low cardinality of possible query sets. These make hieP M suitable for applications such as beamforming in array processing where the extra computation of the query set construction dictates a codebook-based approach (the choice of query set is constrained to a pre-computed small query set collection), and the limit of memory enforces a smaller codebook size.Through a unified analysis with Extrinsic Jensen Shannon (EJS) Divergence, dyaP M is shown to be asymptotically optimal in search time complexity (asymptotic in both resolution (rate) and error (reliability)). On the other hand, hieP M is shown to be near-optimal in rate. In addition, via numerical examples, both hieP M and dyaP M are shown to outperform prior work in the non-asymptotic regime.

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Fundamental limitations

Bavafa-Toosi¹

2019

Introduction to Linear Control Systems

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Bit-wise Sequential Coding with Feedback

Cited by 5 publications

References 7 publications

Active Learning and CSI Acquisition for mmWave Initial Alignment

Active Learning and CSI Acquisition for mmWave Initial Alignment

Low Complexity Sequential Search with Size-Dependent Measurement Noise

Fundamental limitations

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