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.

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.

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 appears 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-Rötteler 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.

This paper studies a generalized version of the well-known page replacement problem. It assumes that page sizes and page fault penalties are nonuniform. This problem arises in distributed information systems, in particular the World Wide Web. It is shown that finding an optimal solution of this problem is an NP-complete problem. A dynamic programming algorithm that finds an optimal solution is presented. Since this algorithm is inefficient, we explore modified algorithms that allow a trade-off between optimality and speed.

An efficient bandwidth management and access arbitration scheme for an I/O bus in a multimedia workstation is presented. It assumes that a multimedia workstation consists of a number of processing modules which are interconnected by a packet bus. The scheme is efficient in the sense that it allows the bus to support both continuous media transfers and regular random transactions in such a way that continuous streams can meet their real-time constraints independently of random traffic, and random traffic is not delayed significantly by continuous traffic except when traffic load is very high. Implementation guidelines are provided to show that the scheme is practical. Finally, the performance of this scheme is compared with alternative solutions through simulation.