# Accession Number:

## AD0420125

# Title:

## ERROR PROBABILITIES FOR UNCODED M-ARY TRANSMISSION OF D-ARY DATA,

# Descriptive Note:

# Corporate Author:

## LITTON SYSTEMS INC WALTHAM MASS

# Personal Author(s):

# Report Date:

## 1963-08-01

# Pagination or Media Count:

## 26.0

# Abstract:

The error probabilities for uncoded multiple alternative transmission of the output of a discrete data source are derived quite generally and numerically evaluated for a sample case. Specifically, the source emits D-ary equiprobable messages information digits which are represented by associated with an M-ary alphabet transmission digits so as to minimize the average symbol length in the M-ary representation. One of the M signals is transmitted and an M-ary decision made in the receiver. A sequence of these received digits is then reassociated into the information alphabet. For the particular case of phase-coherent reception in a non-fading additive Gaussian noise channel, comparison of different transmission alphabets different M for a given source given D is accomplished under the constraints of equal source data rate, average signal power, and average noise power. No bandwidth constraints are imposed. One of the major conclusions is that if the ratio of signal energy per bit interval to noise power density is less than 1n 2, the optimum transmission alphabet size to minimize the average D-ary error probability has M equal to D if however, this signal-to-noise ratio is larger than 1n 2, the larger M is, the lower is the value for the average error probability. Author