New Results on Generalized Caching

We report a number of new results in generalized caching. This problem arises in modern computer networks in which data objects of various sizes are transmitted frequently. First it is shown that its optimal solution is NP-complete. Then we explore two methods of obtaining nearly optimal answers based on the dynamic programming algorithm that we provided in [5]. These methods enable a trade-off between optimality and speed. It is also shown that LFD (the longest forward distance algorithm which is the optimal policy in the classical case), is no longer optimal but is competitive. We also prove that LRU remains competitive in the generalized case. This is an extension of a famous results by Sleator and Tarjan [12] on LRU. Finally, it is confirmed in the general case that prefetch does not reduce the total cost if cost reflects only the number of bytes transmitted

Examples of minimal-memory, non-catastrophic quantum convolutional encoders

One of the most important open questions in the theory of quantum convolutional coding is to determine a minimal-memory, non-catastrophic, polynomial-depth convolutional encoder for an arbitrary quantum convolutional code. Here, we present a technique that finds quantum convolutional encoders with such desirable properties for several example quantum convolutional codes (an exposition of our technique in full generality will appear elsewhere). We first show how to encode the well-studied Forney-Grassl-Guha (FGG) code with an encoder that exploits just one memory qubit (the former Grassl-Roetteler encoder requires 15 memory qubits). We then show how our technique can find an online decoder corresponding to this encoder, and we also detail the operation of our technique on a different example of a quantum convolutional code. Finally, the reduction in memory for the FGG encoder makes it feasible to simulate the performance of a quantum turbo code employing it, and we present the results of such simulations.Comment: 5 pages, 2 figures, Accepted for the International Symposium on Information Theory 2011 (ISIT 2011), St. Petersburg, Russia; v2 has minor change

Using Commutative Encryption to Share a Secret

It is shown how to use commutative encryption to share a secret. Suppose Alice wants to share a secret with Bob such that Bob cannot decrypt the secret unless a group of trustees agree. It is assumed that Alice, Bob and the trustees communicate over insecure channels. This paper presents a scheme that uses modular exponentiation and does not require key exchange. The security of the scheme rest of the difficulty of the discrete logarithm problem

Statistical Multiplexing of Semi-Markov Modulated Sources

It is shown that when a continuous buffer is driven by a semi-Markox modulated fluid flow source(s), the stationary distribution of the buffer content is governed by the same differential equation describing the distribution for continuous time Markov modulated fluid source(s) [1]. It is also shown that the same techniques can be utilized to decompose and solve the eigenvalue problem associated with the differential equation [6]. Finally it is shown that the stationary distribution of buffer content depends only on the mean time spent by each multiplexed semi-Markov source in each state

A Proposed Bus Arbitration Scheme for Multimedia Workstations

The integration of video and audio into computers requires the support of continuous streams at the hardware level. This paper proposes a bus bandwidth management and access arbitration scheme for a multimedia workstation. It is assumed that a multimedia workstation consists of several specialized processing modules which are linked by a packet-switched bus. Using the proposed scheme, the bus can support a mix of real-time continuous media streams and random transactions while fulfilling special requirements corresponding to each traffic type. Specifically, the bus provides very fast response to random transactions and serves continuous media streams in such a way that no piece of data falls behind its deadline. Furthermore, the performance with respect to continuous media traffic is maintained independent of time variations of randomm traffic. Practical implementation guidelines are provided. Finally, the performance of the proposed scheme is compared with other possible approaches

Optimal Solution of Off-line and On-line Generalized Caching

Network traffic can be reduced significantly if caching is utilized effectively. As an effort in this direction we study the replacement problem that arises in caching of multimedia objects. The size of objects and the cost of cache misses are assumed non-uniform. The non-uniformity of size is inherent in multimedia objects, and the non-uniformity of cost is due to the non-uniformity of size and the fact that the objects are scattered throughout the network. Although a special case of this problem, i.e. the case of uniform size and cost, has been extensively studied, the general case needs a great deal of study. We present a dynamic programming method of optimally solving the off-line and on-line versions of this problem, and discuss the complexity of this method

Minimal-memory requirements for pearl-necklace encoders of quantum convolutional codes

One of the major goals in quantum information processing is to reduce the overhead associated with the practical implementation of quantum protocols, and often, routines for quantum error correction account for most of this overhead. A particular technique for quantum error correction that may be useful for protecting a stream of quantum information is quantum convolutional coding. The encoder for a quantum convolutional code has a representation as a convolutional encoder or as a pearl-necklace encoder. In the pearl-necklace representation, it has not been particularly clear in the research literature how much quantum memory such an encoder would require for implementation. Here, we offer an algorithm that answers this question. The algorithm first constructs a weighted, directed acyclic graph where each vertex of the graph corresponds to a gate string in the pearl-necklace encoder, and each path through the graph represents a path through noncommuting gates in the encoder. We show that the weight of the longest path through the graph is equal to the minimal amount of memory needed to implement the encoder. A dynamic programming search through this graph determines the longest path. The running time for the construction of the graph and search through it is quadratic in the number of gate strings in the pearl-necklace encoder. © 2012 IEEE

Minimal-memory, noncatastrophic, polynomial-depth quantum convolutional encoders

Quantum convolutional coding is a technique for encoding a stream of quantum information before transmitting it over a noisy quantum channel. Two important goals in the design of quantum convolutional encoders are to minimize the memory required by them and to avoid the catastrophic propagation of errors. In a previous paper, we determined minimal-memory, noncatastrophic, polynomial-depth encoders for a few exemplary quantum convolutional codes. In this paper, we elucidate a general technique for finding an encoder of an arbitrary quantum convolutional code such that the encoder possesses these desirable properties. We also provide an elementary proof that these encoders are nonrecursive. Finally, we apply our technique to many quantum convolutional codes from the literature. © 1963-2012 IEEE