Showing papers by "Jack K. Wolf published in 1969"
TL;DR: This paper is a compendium of results based on a simple observation: two information symbols can be appended to certain nonbinary BCH codes without affecting the guaranteed minimum distance of these codes.
Abstract: This paper is a compendium of results based on a simple observation: two information symbols can be appended to certain nonbinary BCH codes without affecting the guaranteed minimum distance of these codes. We give two formulations which achieve this result; the second yields information regarding the weights of coset leaders for the original BCH codes. Single-error-correcting Reed-Solomon codes with the added information symbols yield perfect codes for the Hamming metric. We use these lengthened Reed-Solomon codes as building blocks for perfect single-error-correcting codes in another metric.
68 citations
TL;DR: It is shown that the optimal probability of error is attainable without the use of the feedback channel by using antipodal signals, and the signal energy never exceeds a fixed level.
Abstract: We consider binary communication over the additive white Gaussian noise channel with no bandwidth constraint on the channel input signals, assuming the availability of a noiseless delayless feedback link. Although the signals at time t can depend on the noise at times \tau and are therefore random functions, we require that the signal energy never exceed a fixed level. We show that the optimal probability of error is attainable without the use of the feedback channel by using antipodal signals.
24 citations
TL;DR: It is shown that the optimum threshold and the probability of error of the system can be accurately estimated by using EVT to obtain properties of the initial probability density functions on their "tails."
Abstract: The use of extreme-value theory (EVT) in the detection of a binary signal in additive, but statistically unknown, noise is considered. It is shown that the optimum threshold and the probability of error of the system can be accurately estimated by using EVT to obtain properties of the initial probability density functions on their "tails." Both constant signals and slowly fading signals are considered. In the case of a fading signal, the detector becomes adaptive. Detection of the constant signal, both with and without an initial learning period, is studied by computer simulation.
14 citations
TL;DR: The techniques of coding theory are used to improve the reliability of digital devices by introducing majority voting and parity bit checking, and computations are made for several binary addition circuits.
Abstract: The techniques of coding theory are used to improve the reliability of digital devices. Redundancy is added to the device by the addition of extra digits which are independently computed from the input digits. A decoding device examines the original outputs along with the redundant outputs. The decoder may correct any errors it detects, not correct but locate the defective logic gate or subsystem, or only issue a general error warning. Majority voting and parity bit checking are introduced, and computations are made for several binary addition circuits. A detailed summary of coding theory is presented. This includes a discussion of algebraic codes, binary group codes, nonbinary linear codes, and error locating codes.
5 citations
TL;DR: The probability of error is derived for m > n, a situation which arises when the channel bandwidth is insufficient to support the data rate and the channel signal-to-noise ratio increases linearly with n.
Abstract: The transmission of the linear sum of m biphase modulated signals in a time interval T is considered for an additive Gaussian white noise channel of bandwidth W . Previous analyses consider the case where m \leq n \equiv 2WT . In this paper, the probability of error is derived for m > n , a situation which arises when the channel bandwidth is insufficient to support the data rate. Two distinct problems are considered. In the first, termed uncoded transmission, all m signals are independently biphase modulated. It is shown, for this case, that if the channel signal-to-noise ratio increases linearly with n , the error probability can be made to go to zero approximately exponentially in n for any value of m/n . In the second problem, termed ceded transmission, only k of the signals are independently modulated. (The remaining (m - k) signals carry redundant information.) By using a suboptimum receiver, it is shown that for a fixed channel signal-to-noise ratio the error probability goes to 0 exponentially in n if k/n is less than some number C^{\ast} . For high signal-to-noise ratio, C^{\ast} is greater than 1 , a situation which could not occur if m \leq n .