Engineering topics
Publications and source records attributed to Mceliece, R. J..
Alternate symbol inversion is sometimes applied to the output of convolutional encoders to guarantee sufficient richness of symbol transition for the receiver symbol synchronizer. A bound is given for the length of the transition-free symbol stream in such systems, and those convolutional codes are characterized in which arbitrarily long transition free runs occur.
In a previous paper Pierce considered the problem of optical communication from a novel viewpoint, and concluded that performance will likely be limited by issues of coding complexity rather than by thermal noise. This paper reviews the model proposed by Pierce and presents some results on the analysis and design of codes for this application.
Motivated by a recent paper of Pierce, we consider the problem associated with coding for optical communications systems that use photon-counting techniques. Making certain realistic assumptions, we find that external noise sources are negligible, and that channel capacity (measured in nats per photon) is infinite. However, quantum effects made the design of an efficient system at rates above about 5 nats per photon very difficult.
The performance of certain block codes on a Gaussian channel is evaluated. The BCH codes are markedly superior to convolutional codes currently used for deep space missions. The algorithm is used to derive results, which provides a basis for a simple, almost optimum procedure for decoding these codes.
The design of an optimal merged keycode data base information retrieval system is detailed. A probability distribution of n-bit binary words that minimized false drops was developed for the case where the set of desired records was a subset of tagged records.
The zero error capacity of a discrete memoryless channel is defined as the largest rate at which information can be transmitted over the channel with zero error probability. One channel with five inputs and outputs whose zero capacity remained unsolved until very recently is considered. An extremely powerful and general technique phased in terms of graph theory, for studying combinatorial packing problems is presented. In particular, Delsarte's linear programming bound for cliques in association schemes appears as a special case of the Lovasz bound.
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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.
Using a general decoding technique of Solomon we evaluate the performance of certain block codes on a Gaussian channel. Quadratic residue codes of lengths 48 and 80 as well as BCH codes of length 128 and rates 1/2 and 1/3 are considered. All four of these codes perform quite favorably with respect to the constraint-length 7 rate 1/2 convolutional code presently used on NASA's Mariner-class spacecraft.
An example is provided of two convolutional codes that have the same transmission gain but whose dual codes do not. This shows that no analog of the MacWilliams identity for block codes can exist relating the transmission gains of a convolutional code and its dual.
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For applications to the problem of radio frequency interference identification, or in the search for extraterrestrial intelligence, it is important to have a basic understanding of signal detection algorithms. A general technique for assessing the asymptotic sensitivity of a broad class of signal detection algorithms is given. In these algorithms, the decision is based on the value of X sub 1 + X sub 2...+ X sub n where the X sub 1's are obtained by sampling and preliminary processing of a physical process.
An RFI channel to be a multiple-access channel is defined in which no sender can know when any other starts, and the problem of determining the relative phases of the senders at the receiver is studied. A new result is proved about binary DEBruijn sequences.
An upper bound on the rate of a binary code as a function of minimum code distance (using a Hamming code metric) is arrived at from Delsarte-MacWilliams inequalities. The upper bound so found is asymptotically less than Levenshtein's bound, and a fortiori less than Elias' bound. Appendices review properties of Krawtchouk polynomials and Q-polynomials utilized in the rigorous proofs.
The problem of computing the minimum distance of an arbitrary binary linear code is non-polynomial complete. This strongly suggests, but does not imply, that it is impossible to design a computer algorithm for computing the minimum distance of an arbitrary code whose running time is bounded by a polynomial in the number of inputs.
This paper discusses models for multiple-access communications which take into account the fact that the channel users may not be able to synchronize their transmissions. It is shown that for a broad class of such channels, the capacity region is the same as it would be with user synchronization. Some open problems are discussed.
For coded telemetry systems it is important to know the tradeoff between the error probability and the complexity of implementation. For systems using block codes, the block coding error exponent is a good way to estimate this tradeoff. The new upper bounds on the minimum distance of binary codes result in improved upper bounds on the coding error exponents for binary input memoryless channels.
A general technique, called decoding with multipliers, is presented that can be used to decode any linear code. The technique is applied to the (48,24) quadratic residue code and yields the first known practical decoding algorithm for this powerful code.