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Mceliece, R. J.

Publications and source records attributed to Mceliece, R. J..

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

A note on the wideband Gaussian broadcast channel

It is well known that for the Gaussian broadcast channel, timeshared coding is not as efficient as more sophisticated broadcast coding strategies. However, the relative advantage of broadcast coding over timeshared coding is shown to be small if the signal-to-noise ratios of both receivers are small. One surprising consequence of this is that for the wideband Gaussian broadcast channel, which is defined, broadcast coding offers no advantage over timeshared coding at all, and so timeshared coding is optimal.

Mceliece, R. J.↗
NASA NTRS1986

On the decode error probability for Reed-Solomon codes

Upper bounds on the decoder error probability for Reed-Solomon codes are derived. By definition, decoder error occurs when the decoder finds a codeword other than the transmitted codeword; this is in contrast to decoder failure, which occurs when the decoder fails to find any codeword at all. The results imply, for example, that for a t error correcting Reed-Solomon code of length q - 1 over GF(q), if more than t errors occur, the probability of decoder error is less than 1/t! In particular, for the Voyager Reed-Solomon code, the probability of decoder error given a word error is smaller than 3 x 10 to the minus 14th power. Thus, in a typical operating region with probability 100,000 of word error, the probability of undetected word error is about 10 to the minus 14th power.

Mceliece, R. J.↗
NASA NTRS1985

Error and erasure probabilities for Galileo uplink code

The Galileo uplink Frame Erasure probability and Undetected Frame Error probability are derived. The performance meets desired specification under normal operations. The Galileo command system will work well even in an emergency condition, where the bit error rate into the command decoder is 1.00 X 0.001 (although Galileo's command threshold error rate is 1.00 X 0.00001).

Berner, J. B.↗
NASA NTRS1985

The number of stable points of an infinite-range spin glass memory

A rigorous asymptotic expression for the number of stable points of an infinite-range spin glass with independently identically distributed (i.i.d) zero-mean gaussian exchange interactions is discussed. The result also applies tot he number of stable points of a Hopfield Memory (a kind of associative memory) when the memory connections are i.i.d. zero-mean gaussians. The result is that the number of stable points is asymptotic to a constant slightly larger than 1 times 2 to a power slightly larger thann/4, where n is the number of spins in the glass, or the length of the n-tuples to be remembered by the memory. The answer is easily derived using simple asymptotic techniques from an exact expression for the probability that an arbitrary plus or minus 1 n-tuple of spins is a fixed point. This expression is obtained from the fact that any distribution of joint zero-mean gaussians of given covariances is specified solely by these covariances. This is a far shorter derivation of the result than those existing.

Posner, E. C.↗
NASA NTRS1985

Symbol Stream Combining in a Convolutionally Coded System

Symbol stream combining has been proposed as a method for arraying signals received at different antennas. If convolutional coding and Viterbi decoding are used, it is shown that a Viterbi decoder based on the proposed weighted sum of symbol streams yields maximum likelihood decisions.

Mceliece, R. J.↗
NASA NTRS1984

Efficient Coding for Optical Communication

Possibility of using photon counting, rather than conventional linear amplification, for optical communications discussed. Study suggests combination of pulse-position modulation and Reed-Solomon coding gives signaling efficiency of 3 to 4 bits/photon.

Mceliece, R. J.↗
NASA NTRS1984

Node synchronization for the Viterbi decoder

At very low signal to noise ratios such as those that Voyager 2 will encounter at Uranus, the performance of the Reed-Solomon/Viterbi concatenated coding system could be seriously degraded by loss of node synchronization by the Viterbi decoder. This problem is described and now it can be almost completely avoided with a simple outboard hardware 'node synchronizer'. This device makes statistical decisions about node sync based on the hard quantized undecoded data stream. In a worst case Voyager-like environment, our method will detect and correct a true loss of node sync (thought to be a very rare event) within several hundred bits; many of these false alarms for our technique is on the order several years. Previously announced in STAR as N83-28028

Lorden, G.↗
NASA NTRS1984

An Easy-to-implement Coding Scheme for Multifrequency PPM

In implementing multifrequency PPM, a naturally arising question is: Let P be a fixed number; among all integer valued processes X1, X2, X3, with E ( X(n+1)-X(n) squared) less than or = P, which has the largest entropy? Earlier work by McEliece and Rodemich answered this question, but there is no obvious way to use this process to implement a code for multifrequency PPM. The present article describes an easy-to-implement process X1, X2, with E ( X(n+1)-X(n) squared) less than or = P, whose entropy is nearly as great as that of the McEliece-Rodemich process.

Mceliece, R. J.↗
NASA NTRS1983

A study of optimal abstract jamming strategies vs. noncoherent MFSK

The present investigation is concerned with the performance of uncoded MFSK modulation in the presence of arbitrary additive jamming, taking into account the objective to devise robust antijamming strategies. An abstract model is considered, giving attention to the signal strength as a nonnegative real number X, the employment of X as a random variable, its distribution function G(x), the transmitter's strategy G, the jamming noise as an M-dimensional random vector Z, and the error probability. A summary of previous work on the considered problem is provided, and the results of the current study are presented.

Mceliece, R. J.↗
NASA NTRS1981

RFI channels, 2

The cutoff parameters for a class of channel models exhibiting burst noise behavior were calculated and the performance of interleaved coding strategies was evaluated. It is concluded that, provided the channel memory is large enough and is properly exploited, interleaved coding is nearly optimal.

Mceliece, R. J.↗
NASA NTRS1981

The R sub 0 parameter for the Gaussian channel

The cutoff R sub 0 for the additive white Gaussian channel is first defined and then computed. This important channel parameter seems not to have been previously computed for this important channel model except in the case when the input is restricted to be binary.

Mceliece, R. J.↗
NASA NTRS1981

Practical codes for photon communication

It is shown that even assuming a noiseless model for photon communication for which capacity (measured in nats/photon) is infinite, it is unlikely that a signaling efficiency of even 10 nats/photon could be achieved in practice. Pulse-position modulation plus Reed-Solomon coding is shown to yield practical results in the range of 2 to 3 nats/photon. In addition, a channel model appropriate for the study of noiseless photon communication, referred to as a photon channel, is presented. The use of q-ary pulse position modulation (q-PPM) on the photon channel is investigated. It is shown that q-PPM channel capacity is log q nats/photon, and performance curves (error probability versus signaling efficiency) are given for coded and uncoded q-PPM.

Mceliece, R. J.↗
NASA NTRS1981

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.

Cover, T. M.↗
NASA NTRS1980

Interleaved block codes for the photon channel

It is shown that interleavel binary block codes combined with pulse position modulation give the best practical coded systems yet devised for optical communication with photon detection. Linear block codes rather than convolutional codes are considered.

Mceliece, R. J.↗
NASA NTRS1980

RFI channels

A class of channel models is presented which exhibit varying burst error severity much like channels encountered in practice. An information-theoretic analysis of these channel models is made, and conclusions are drawn that may aid in the design of coded communication systems for realistic noisy channels.

Mceliece, R. J.↗
NASA NTRS1979

Coding for optical channels with photon-counting

The problem of coding for Pierce's recent model for optical communications is studied. It was concluded that for any positive rate rho (measured in nats per photon), the best code of length n has an error probability bounded by an exponentially decaying function of n. Explicit practical schemes are shown for rho less than or = to 1; and evidence is given that rho approximating 1 may be the practical limit for optical communication.

Mceliece, R. J.↗