[Paper Review] Distributed Binary Detection with Lossy Data Compression

Gil Katz, Pablo Piantanida+1 more|arXiv (Cornell University)|Jan 6, 2016

Wireless Communication Security Techniques12 references3 citations

TL;DR

This paper proposes a rate-error-distortion trade-off framework for distributed binary detection with lossy compression in a two-node system, where a central receiver detects hypotheses using rate-limited, compressed data from a remote source. The key contribution is the characterization of the optimal rate-error-distortion region for 'testing against independence' and the derivation of an improved achievable region using non-asymptotic binning, with explicit expressions provided for binary symmetric sources.

ABSTRACT

Consider the problem where a statistician in a two-node system receives rate-limited information from a transmitter about marginal observations of a memoryless process generated from two possible distributions. Using its own observations, this receiver is required to first identify the legitimacy of its sender by declaring the joint distribution of the process, and then depending on such authentication it generates the adequate reconstruction of the observations satisfying an average per-letter distortion. The performance of this setup is investigated through the corresponding rate-error-distortion region describing the trade-off between: the communication rate, the error exponent induced by the detection and the distortion incurred by the source reconstruction. In the special case of testing against independence, where the alternative hypothesis implies that the sources are independent, the optimal rate-error-distortion region is characterized. An application example to binary symmetric sources is given subsequently and the explicit expression for the rate-error-distortion region is provided as well. The case of "general hypotheses" is also investigated. A new achievable rate-error-distortion region is derived based on the use of non-asymptotic binning, improving the quality of communicated descriptions. Further improvement of performance in the general case is shown to be possible when the requirement of source reconstruction is relaxed, which stands in contrast to the case of general hypotheses.

Motivation & Objective

• To model a distributed detection system where a central receiver must authenticate a remote transmitter and reconstruct its observations under rate and distortion constraints.
• To analyze the trade-off between communication rate, detection error exponent, and source reconstruction distortion in a two-node network with lossy compression.
• To characterize the optimal rate-error-distortion region for the special case of 'testing against independence', where the sources are assumed independent under the alternative hypothesis.
• To improve performance in general hypotheses by introducing non-asymptotic binning techniques, reducing error probability in detection.
• To investigate the impact of relaxing source reconstruction requirements on performance gains in the general hypothesis case.

Proposed method

• Uses a two-node system where a transmitter sends rate-limited, compressed descriptions of its observations to a central receiver for hypothesis testing.
• Applies lossy source coding with a distortion constraint to reconstruct the transmitter's observations at the receiver.
• Employs non-asymptotic binning to improve the reliability of compressed descriptions, reducing decoding errors in detection.
• Derives an achievable rate-error-distortion region using type-based analysis and typical sequences, with error probabilities bounded via large deviations.
• Introduces a novel error exponent analysis for unintended sequence decoding, based on conditional typicality and mutual information terms.
• Uses the Kullback-Leibler divergence and mutual information to quantify the error exponent and distortion trade-offs in the asymptotic regime.

Experimental results

Research questions

• RQ1 What is the optimal trade-off between communication rate, detection error exponent, and reconstruction distortion in a distributed binary detection system with lossy compression?
• RQ2 How does the performance of the system change when the hypothesis test is 'testing against independence' compared to general hypotheses?
• RQ3 Can non-asymptotic binning techniques improve the error exponent and reduce detection error in distributed detection with lossy compression?
• RQ4 What is the impact of relaxing the source reconstruction requirement on the achievable rate-error-distortion region in general hypothesis testing?
• RQ5 How does the choice of compression strategy affect the error exponent and distortion in the joint detection and reconstruction problem?

Key findings

• For the 'testing against independence' case, the optimal rate-error-distortion region is characterized using the Kullback-Leibler divergence and mutual information terms.
• The error exponent for the second-type error is shown to be bounded below by $\max_{Q_{U|X}^\star} \left\{ R - I(P_X; Q_{U|X}^\star) + I(P_Y; Q_{U|Y}^\star) \right\} $, with an arbitrarily small error term as $\delta \to 0^+$.
• The use of non-asymptotic binning leads to a tighter bound on the error probability of unintended sequence decoding, improving the achievable rate-error-distortion region.
• Performance gains are observed when the source reconstruction constraint is relaxed in the general hypothesis case, in contrast to the 'testing against independence' scenario.
• For binary symmetric sources, the paper provides an explicit expression for the rate-error-distortion region, enabling quantitative analysis of system trade-offs.
• The derived error exponent analysis shows that the optimal detection performance is independent of the Type-I error constraint $\epsilon$ in the asymptotic regime, consistent with Stein's Lemma.