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

On palimpsests in neural memory: an information theory viewpoint

The finite capacity of neural memory and the reconsolidation phenomenon suggest it is important to be able to update stored information as in a palimpsest, where new information overwrites old information. Moreover, changing information in memory is metabolically costly. In this paper, we suggest that information-theoretic approaches may inform the fundamental limits in constructing such a memory system. In particular, we define malleable coding, that considers not only representation length but also ease of representation update, thereby encouraging some form of recycling to convert an old codeword into 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 tradeoff between compression efficiency and malleability cost, under a malleability metric defined with respect to a string edit distance. This introduces a metric topology to the compressed domain. We characterize the exact set of achievable rates and malleability as the solution of a subgraph isomorphism problem. This is all done within the optimization approach to biology framework.Accepted manuscrip

Malleable Coding with Fixed Reuse

In cloud computing, storage area networks, remote backup storage, and similar settings, stored data is modified with updates from new versions. Representing information and modifying the representation are both expensive. Therefore it is desirable for the data to not only be compressed but to also be easily modified during updates. A malleable coding scheme considers both compression efficiency and ease of alteration, promoting codeword reuse. We examine the trade-off between compression efficiency and malleability cost-the difficulty of synchronizing compressed versions-measured as the length of a reused prefix portion. Through a coding theorem, the region of achievable rates and malleability is expressed as a single-letter optimization. Relationships to common information problems are also described

More Efficient Algorithms and Analyses for Unequal Letter Cost Prefix-Free Coding

There is a large literature devoted to the problem of finding an optimal (min-cost) prefix-free code with an unequal letter-cost encoding alphabet of size. While there is no known polynomial time algorithm for solving it optimally there are many good heuristics that all provide additive errors to optimal. The additive error in these algorithms usually depends linearly upon the largest encoding letter size. This paper was motivated by the problem of finding optimal codes when the encoding alphabet is infinite. Because the largest letter cost is infinite, the previous analyses could give infinite error bounds. We provide a new algorithm that works with infinite encoding alphabets. When restricted to the finite alphabet case, our algorithm often provides better error bounds than the best previous ones known.Comment: 29 pages;9 figures

Evolutionary Approaches to Minimizing Network Coding Resources

We wish to minimize the resources used for network coding while achieving the desired throughput in a multicast scenario. We employ evolutionary approaches, based on a genetic algorithm, that avoid the computational complexity that makes the problem NP-hard. Our experiments show great improvements over the sub-optimal solutions of prior methods. Our new algorithms improve over our previously proposed algorithm in three ways. First, whereas the previous algorithm can be applied only to acyclic networks, our new method works also with networks with cycles. Second, we enrich the set of components used in the genetic algorithm, which improves the performance. Third, we develop a novel distributed framework. Combining distributed random network coding with our distributed optimization yields a network coding protocol where the resources used for coding are optimized in the setup phase by running our evolutionary algorithm at each node of the network. We demonstrate the effectiveness of our approach by carrying out simulations on a number of different sets of network topologies.Comment: 9 pages, 6 figures, accepted to the 26th Annual IEEE Conference on Computer Communications (INFOCOM 2007

Weak universality in sensory tradeoffs

For many organisms, the number of sensory neurons is largely determined during development, before strong environmental cues are present. This is despite the fact that environments can fluctuate drastically both from generation to generation and within an organism's lifetime. How can organisms get by by hard-coding the number of sensory neurons? We approach this question using rate-distortion theory. A combination of simulation and theory suggests that when environments are large, the rate-distortion function---a proxy for material costs, timing delays, and energy requirements---depends only on coarse-grained environmental statistics that are expected to change on evolutionary, rather than ontogenetic, timescales

Source Coding for Quasiarithmetic Penalties

Huffman coding finds a prefix code that minimizes mean codeword length for a given probability distribution over a finite number of items. Campbell generalized the Huffman problem to a family of problems in which the goal is to minimize not mean codeword length but rather a generalized mean known as a quasiarithmetic or quasilinear mean. Such generalized means have a number of diverse applications, including applications in queueing. Several quasiarithmetic-mean problems have novel simple redundancy bounds in terms of a generalized entropy. A related property involves the existence of optimal codes: For ``well-behaved'' cost functions, optimal codes always exist for (possibly infinite-alphabet) sources having finite generalized entropy. Solving finite instances of such problems is done by generalizing an algorithm for finding length-limited binary codes to a new algorithm for finding optimal binary codes for any quasiarithmetic mean with a convex cost function. This algorithm can be performed using quadratic time and linear space, and can be extended to other penalty functions, some of which are solvable with similar space and time complexity, and others of which are solvable with slightly greater complexity. This reduces the computational complexity of a problem involving minimum delay in a queue, allows combinations of previously considered problems to be optimized, and greatly expands the space of problems solvable in quadratic time and linear space. The algorithm can be extended for purposes such as breaking ties among possibly different optimal codes, as with bottom-merge Huffman coding.Comment: 22 pages, 3 figures, submitted to IEEE Trans. Inform. Theory, revised per suggestions of reader