Malleable Coding: Compressed Palimpsests

A malleable coding scheme considers not only compression efficiency but also the ease of alteration, thus encouraging some form of recycling of an old compressed version in the formation of a new one. Malleability cost is the difficulty of synchronizing compressed versions, and malleable codes are of particular interest when representing information and modifying the representation are both expensive. We examine the trade-off between compression efficiency and malleability cost under a malleability metric defined with respect to a string edit distance. This problem introduces a metric topology to the compressed domain. We characterize the achievable rates and malleability as the solution of a subgraph isomorphism problem. This can be used to argue that allowing conditional entropy of the edited message given the original message to grow linearly with block length creates an exponential increase in code length. Index Terms data compression, distributed databases, concurrency control, Gray codes, subgraph isomorphism This work was supported in part by the NSF Graduate Research Fellowship, Grant CCR-0325774, and Grant CCF-0729069. L. R. Varshney is with the Department of Electrical Engineering and Computer Science, the Laboratory for Information and Decision Systems, and the Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: [email protected]). J. Kusuma is with Schlumberger Technology Corporation, Sugar Land, TX 77478 USA (e-mail: [email protected]). V. K. Goyal is with the Department of Electrical Engineering and Computer Science and the Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA 02139 USA (e-mail: [email protected]). July 11, 2011 DRAFT 1