For pt.IV see ibid., vol.SMC-13, no.5, p.964-72 (1983). The psychophysical properties of a multiple-channel neural-counting model are investigated. Each channel represents a peripheral afferent fiber (or a group of such fibers) and consists of a cascade of signal-processing transformations, each of which has a physiological correlate in the auditory system. The acoustic signal is passed by a mathematical construct (which may be a pure tone or Gaussian noise) through a series of transformations. Spontaneous neural activity is independently incorporated into each channel by means of an additive refractoriness-modified Poisson process. A union process at a more distal center in the nervous system is generated by a parallel collection of such channels with a density (in frequency) determined by the cochlear mapping function. The statistics of the union count (in a fixed time) are then processed at a decision center in a manner that depends on the psychophysical paradigm under consideration. This random count number is assumed to contain all of the information for the examples considered. The model has been used to calculate psychophysical functions for pure-tone loudness estimation, pure-tone and variable-bandwidth noise intensity discrimination, and variable-bandwidth noise loudness summation. The theoretical results are in good agreement with human psychophysical data.

An energy-based neural-counting model, incorporating refractoriness and spread of excitation, has recently been applied to intensity discrimination and loudness estimation for a variety of acoustic stimuli. In this model, refractoriness was the sole means of achieving the saturation effect of the afferent fiber's response. Though refractoriness (or an effect like it) should be included in a proper Poisson-based model to produce a neural count variance less than the count mean (in accordance with experiment), there is a strong additional saturation effect associated with the response of the receptor. This earlier model is now extended to incorporate the effects of receptor saturation and spontaneous neural activity. In this paper the behavior of individual neural channels is investigated. Theoretical firing-rate curves are obtained as a function of stimulus level and frequency (isointensity contours). These are found to be in good agreement with neurophysiological data. It is shown that it is possible to fit human psychophysical tuning curves with a double-tuned linear filter, by judicious choice of the tuning parameter Q.

A model that allows one to calculate information rates for optical communication systems that use photocount detection is presented. This model has its basis in the coherent states of the field. It consists of a source that places the field in a coherent state, a channel that can introduce additive Gaussian noise, and a photodetector that produces the number of photocounts in the detection interval as output symbols. The capability of introducing additive Gaussian noise can also be used to represent a physical source. The model is applied to several examples to illustrate its use. The rate of flow of information through the channel is calculated for a binary channel with and without additive Gaussian noise. The information rate for a noiseless channel is also obtained for the case in which the signals sent by a single-mode coherent source are selected from a Gaussian distribution.

A technique is described whereby it is possible to determine a set of waveforms that minimize the error rate for a digital communication system. The waveforms are generated from a finite set of orthogonal waveforms. Each character waveform has the same energy as any other character waveform. The technique may be applied to any channel where the source and channel statistics are known. It is also applied to the problem of maximizing the minimum distance between a set of points on ann-dimensional sphere. The solution of this problem can be used to minimize the error rate for a system disturbed by white Gaussian noise of very low average noise power per unit of bandwidth. In particular a possible solution for the spacing of ten points on a four-dimensional sphere is shown. It represents a considerable improvement over the best previous result.