Enhanced processing power in the cloud allows constrained devices to offload costly computations: for instance, complex data analytics tasks can be computed by remote servers. Remote execution calls for a new compression paradigm that optimizes performance on the analytics task within a rate constraint, instead of the traditional rate-distortion framework which focuses on source reconstruction. This paper considers a simple binary hypothesis testing scenario where the resource constrained client (transmitter) performs fixed-length single-shot compression on data sampled from one of two distributions; the server (receiver) performs a hypothesis test on multiple received samples to determine the correct source distribution. To this end, the task-aware compression problem is formulated as finding the optimal source coder that maximizes the asymptotic error performance of the hypothesis test on the server side under a rate constraint. A new source coding strategy based on a greedy optimization procedure is proposed and it is shown that that the proposed compression scheme outperforms universal fixed-length single-shot coding scheme for a range of rate constraints.
In this paper, we consider sequential testing over a single-sensor, a single-decision center setup. At each time instant $t$, the sensor gets $k$ samples $(k>0)$ and describes the observed sequence until time $t$ to the decision center over a zero-rate noiseless link. The decision center sends a single bit of feedback to the sensor to request for more samples for compression/testing or to stop the transmission. We have characterized the optimal exponent of type-II error probability under the constraint that type-I error probability does not exceed a given threshold $ε\in (0,1)$ and also when t…
We study the problem of source and message compression in the one-shot setting for the point-to-point and multi-party scenarios (with and without side information). We derive achievability results for these tasks in a unified manner, using the techniques of convex-split, which was introduced in [Anshu,Devabathini and Jain 2014] and position-based decoding introduced in [Anshu, Jain and Warsi 2017], which in turn uses hypothesis testing between distributions. These results are in terms of smooth max divergence and smooth hypothesis testing divergence. As a by-product of the tasks studied in thi…
We revisit the task of visible compression of an ensemble of quantum states with entanglement assistance in the one-shot setting. The protocols achieving the best compression use many more qubits of shared entanglement than the number of qubits in the states in the ensemble. Other compression protocols, with potentially larger communication cost, have entanglement cost bounded by the number of qubits in the given states. This motivates the question as to whether entanglement is truly necessary for compression, and if so, how much of it is needed. Motivated by questions in communication complex…
This paper investigates the problem of variable-length lossy source coding allowing a positive excess distortion probability and an overflow probability of codeword lengths. Novel one-shot achievability and converse bounds of the optimal rate are established by a new quantity based on the smooth max entropy (the smooth Rényi entropy of order zero). To derive the achievability bounds, we give an explicit code construction based on a distortion ball instead of using the random coding argument. The basic idea of the code construction is similar to the optimal code construction in the variable-len…
In this paper we revisit the binary hypothesis testing problem with one-sided compression. Specifically we assume that the distribution in the null hypothesis is a mixture distribution of iid components. The distribution under the alternative hypothesis is a mixture of products of either iid distributions or finite order Markov distributions with stationary transition kernels. The problem is studied under the Neyman-Pearson framework in which our main interest is the maximum error exponent of the second type of error. We derive the optimal achievable error exponent and under a further sufficie…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is reduced to the problem of determining the reliability function of channel codes designed for detection (in analogy to a similar result which connects the reliability function of distributed lossless compression and ordinary channel codes). Second, a single-letter random-coding bound based on a hierarchical ensemble, as well as a single-letter expurgated bound, are…
This paper presents a one shot analysis of the lossy compression problem under average distortion constraints. We calculate the exact expected distortion of a random code. The result is given as an integral formula using a newly defined functional $\tilde{D}(z,Q_Y)$ where $Q_Y$ is the random coding distribution and $z\in [0,1]$. When we plug in the code distribution as $Q_Y$, this functional produces the average distortion of the code, thus provide a converse result utilizing the same functional. Two alternative formulas are provided for $\tilde{D}(z,Q_Y)$, the first involves a supremum over s…
Privacy amplification (PA) is an indispensable component in classical and quantum cryptography. Error correction (EC) and data compression (DC) algorithms are also indispensable in classical and quantum information theory. We here study these three algorithms (PA, EC, and DC) in the presence of quantum side information, and show that they all become equivalent in the one-shot scenario. As an application of this equivalence, we take previously known security bounds of PA, and translate them into coding theorems for EC and DC which have not been obtained previously. Further, we apply these resul…
