On Lossless Coding With Coded Side Information

This paper considers the problem, first introduced by Ahlswede and Korner in 1975, of lossless source coding with coded side information. Specifically, let X and Y be two random variables such that X is desired losslessly at the decoder while Y serves as side information. The random variables are encoded independently, and both descriptions are used by the decoder to reconstruct X. Ahlswede and Korner describe the achievable rate region in terms of an auxiliary random variable. This paper gives a partial solution for an optimal auxiliary random variable, thereby describing part of the rate region explicitly in terms of the distribution of X and Y

On networks with side information

In this paper, we generalize the lossless coded side information problem from the three-node network of Ahlswede and K¨orner to more general network scenarios. We derive inner and outer bounds on the achievable rate region in the general network scenario and show that they are tight for some families of networks. Our approach demonstrates how solutions to canonical source coding problems can be used to derive bounds for more complex networks and reveals an interesting connection between networks with side information, successive refinement, and network coding

On Approximating the Rate Region for Source Coding with Coded Side Information

The achievable rate region for the problem of lossless source coding with coded side information was derived by Ahlswede and Körner in 1975. While the Ahlswede-Körner bound completely characterizes the achievable rate region when the source and side information are memoryless, calculating this bound for a given memoryless joint probability mass function on the source and side information requires an optimization over all possible auxiliary random variables meeting a given Markov condition and alphabet size constraint. This optimization turns out to be surprisingly difficult even for very simple distributions on the source and side information. We here propose a (1 + ε)-approximation algorithm for the given rate region. The proposed technique involves quantization of a space of conditional distributions followed by linear programming. The resulting algorithm guarantees performance within a multiplicative factor (1 + ε) of the optimal performance - even when that optimal performance is unknown

A strong converse for a collection of network source coding problems

We prove a strong converse for particular source coding problems: the Ahlswede-Korner (coded side information) problem, lossless source coding for multicast networks with side-information at the end nodes, and the Gray-Wyner problem. Source and side-information sequences are drawn i.i.d. according to a given distribution on a finite alphabet. The strong converse discussed here states that when a given rate vector R is not D-achievable, the probability of observing distortion D for any sequence of block codes at rate R must decrease exponentially to 0 as the block length grows without bound. This strong converse implies the prior strong converses for the point-to-point network, Slepian-Wolf problem, and Ahlswede-Korner (coded side information) problem

Malleable coding for updatable cloud caching

In software-as-a-service applications provisioned through cloud computing, locally cached data are often modified with updates from new versions. In some cases, with each edit, one may want to preserve both the original and new versions. In this paper, we focus on cases in which only the latest version must be preserved. Furthermore, it is desirable for the data to not only be compressed but to also be easily modified during updates, since representing information and modifying the representation both incur cost. We examine whether it is possible to have both compression efficiency and ease of alteration, in order to promote codeword reuse. In other words, we study the feasibility of a malleable and efficient coding scheme. The tradeoff between compression efficiency and malleability cost-the difficulty of synchronizing compressed versions-is measured as the length of a reused prefix portion. The region of achievable rates and malleability is found. Drawing from prior work on common information problems, we show that efficient data compression may not be the best engineering design principle when storing software-as-a-service data. In the general case, goals of efficiency and malleability are fundamentally in conflict.This work was supported in part by an NSF Graduate Research Fellowship (LRV), Grant CCR-0325774, and Grant CCF-0729069. This work was presented at the 2011 IEEE International Symposium on Information Theory [1] and the 2014 IEEE International Conference on Cloud Engineering [2]. The associate editor coordinating the review of this paper and approving it for publication was R. Thobaben. (CCR-0325774 - NSF Graduate Research Fellowship; CCF-0729069 - NSF Graduate Research Fellowship)Accepted manuscrip

Secure Multiterminal Source Coding with Side Information at the Eavesdropper

The problem of secure multiterminal source coding with side information at the eavesdropper is investigated. This scenario consists of a main encoder (referred to as Alice) that wishes to compress a single source but simultaneously satisfying the desired requirements on the distortion level at a legitimate receiver (referred to as Bob) and the equivocation rate --average uncertainty-- at an eavesdropper (referred to as Eve). It is further assumed the presence of a (public) rate-limited link between Alice and Bob. In this setting, Eve perfectly observes the information bits sent by Alice to Bob and has also access to a correlated source which can be used as side information. A second encoder (referred to as Charlie) helps Bob in estimating Alice's source by sending a compressed version of its own correlated observation via a (private) rate-limited link, which is only observed by Bob. For instance, the problem at hands can be seen as the unification between the Berger-Tung and the secure source coding setups. Inner and outer bounds on the so called rates-distortion-equivocation region are derived. The inner region turns to be tight for two cases: (i) uncoded side information at Bob and (ii) lossless reconstruction of both sources at Bob --secure distributed lossless compression. Application examples to secure lossy source coding of Gaussian and binary sources in the presence of Gaussian and binary/ternary (resp.) side informations are also considered. Optimal coding schemes are characterized for some cases of interest where the statistical differences between the side information at the decoders and the presence of a non-zero distortion at Bob can be fully exploited to guarantee secrecy.Comment: 26 pages, 16 figures, 2 table

Morphological filter for lossless image subsampling

We present a morphological filter for lossless image subsampling for a given downsampling-upsampling strategy. This filter is applied in a multiresolution decomposition and results in a more efficient scheme for image coding purposes than other lossy sampling schemes. Its main advantage is a greatly reduced computational load compared to multiresolution schemes performed with linear filters.Peer ReviewedPostprint (published version