Robert J. McEliece

On the inherent intractability of certain coding problems (Corresp.)

MEMBER, IEEE, AND HENK C. A. V~ TILBORG The fact that the general decoding problem for linear codes and the general problem of finding the weights of a linear code are both NP-complete is shown. This strongly suggests, but does not rigorously imply, that no algorithm for either of these problems which runs in polynomial time exists.

Channels with block interference

A new class of channel models with memory is presented in order to study various kinds of interference phenomena. It is shown, among other things, that when all other parameters are held fixed, channel capacity C is an {\em increasing} function of the memory length, while the cutoff rate R_{0} generally is a {\em decreasing} function. Calculations with various explicit coding schemes indicate that C is better than R_{0} as a performance measure for these channel models. As a partial resolution of this C versus R_{0} paradox, the conjecture is offered that R_{0} is more properly a measure of coding delay rather than of coding complexity.

New upper bounds on the rate of a code via the Delsarte-MacWilliams inequalities

With the Delsarte-MacWilliams inequalities as a starting point, an upper bound is obtained on the rate of a binary code as a function of its minimum distance. This upper bound is asymptotically less than Levenshteins bound, and so also Eliass.

Channel assignment in cellular radio

Some heuristic channel-assignment algorithms for cellular systems are described. These algorithms have yielded optimal, or near-optimal assignments, in many cases. The channel-assignment problem can be viewed as a generalized graph-coloring problem, and these algorithms have been developed, in part, by suitably adapting some of the ideas previously introduced in heuristic graph-coloring algorithms. The channel-assignment problem is formulated as a minimum-span problem, i.e. a problem wherein the requirement is to find the minimum bandwidth necessary to satisfy a given demand. Examples are presented, and algorithm performance results are discussed.<<ETX>>

Weights of irreducible cyclic codes

With any fixed prime number p and positive integer N , not divisible by p , there is associated an infinite sequence of cyclic codes. In a previous article it was shown that a theorem of Davenport-Hasse reduces the calculation of the weight distributions for this whole sequence of codes to a single calculation (essentially that of calculating the weight distribution for the simplest code of the sequence). The primary object of this paper is the development of machinery which simplifies this remaining calculation. Detailed examples are given. In addition, tables are presented which essentially solve the weight distribution problem for all such binary codes with N

Dynamic channel assignment in cellular radio

Dynamic channel assignment algorithms for cellular systems are developed. The algorithms are compared with an easily simulated bound. Using this bound, it is demonstrated that in the case of homogeneous spatial traffic distribution, some of these algorithms are virtually unbeatable by any channel assignment algorithm. These algorithms are shown to be feasible for implementation in current cellular systems. For the examples considered, in the interesting range of blocking probabilities (2-4%), the dynamic channel assignment algorithms yielded an increase of 60-80% in the carried traffic over the best-known fixed channel assignment.<<ETX>>

Lower bounds on data collection time in sensory networks

Data collection, i.e., the aggregation at the user location of information gathered by sensor nodes, is a fundamental function of sensory networks. Indeed, most sensor network applications rely on data collection capabilities, and consequently, an inefficient data collection process may adversely affect the performance of the network. In this paper, we study via simple discrete mathematical models, the time performance of the data collection and data distribution tasks in sensory networks. Specifically, we derive the minimum delay in collecting sensor data for networks of various topologies such as line, multiline, and tree and give corresponding optimal scheduling strategies. Furthermore, we bound the data collection time on general graph networks. Our analyses apply to networks equipped with directional or omnidirectional antennas and simple comparative results of the two systems are presented.

Iterative algebraic soft-decision list decoding of Reed-Solomon codes

In this paper, we present an iterative soft-decision decoding algorithm for Reed-Solomon (RS) codes offering both complexity and performance advantages over previously known decoding algorithms. Our algorithm is a list decoding algorithm which combines two powerful soft-decision decoding techniques which were previously regarded in the literature as competitive, namely, the Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation based on adaptive parity-check matrices, recently proposed by Jiang and Narayanan. Building on the Jiang-Narayanan algorithm, we present a belief-propagation-based algorithm with a significant reduction in computational complexity. We introduce the concept of using a belief-propagation-based decoder to enhance the soft-input information prior to decoding with an algebraic soft-decision decoder. Our algorithm can also be viewed as an interpolation multiplicity assignment scheme for algebraic soft-decision decoding of RS codes.

Packets distribution algorithms for sensor networks

In this paper, we study, via simple discrete mathematical models, the problems of data distribution and data collection in wireless sensor networks. The work that follows continues the work presented by the authors in (C. Florens et al., 2002) where the focus was on sensor networks equipped with unidirectional antenna elements. Here we shift our interest to networks equipped with omnidirectional antenna elements. In particular we show how the data distribution and collection tasks can be performed optimally (with respect to time) on tree networks and give the corresponding time performances of those strategies. We also present a strategy for general graph networks that performs within a factor of 3 of the optimal performance. Finally we compare the performance of a network equipped with omnidirectional antenna elements with one equipped with unidirectional antenna elements. We show the latter outperforms the former by 33% at most in tree networks. To that purpose we included relevant results on directional antenna sensor networks, partly obtained in (C.Florens et al., 2002).

Asynchronous multiple-access channel capacity

The capacity region for the discrete memoryless multiple-access channel without time synchronization at the transmitters and receivers is shown to be the same as the known capacity region for the ordinary multiple-access channel. The proof utilizes time sharing of two optimal codes for the ordinary multiple-access channel and uses maximum likelihood decoding over shifts of the hypothesized transmitter words.