ON THE EQUIVALENCE OF FREE DISTANCE AND COLUMN DISTANCE OF A CONVOLUTIONAL CODE,

Abstract

A brief discussion of the role of coding theory in a communications system is followed by a description of convolutional codes and various distances measures. Two theorems and several corollaries concerning free distance are presented. The first theorem is essentially a correction of a counterexample to a conjecture relating free distance and column distance. The second demonstrates a necessary and sufficient condition for the free distance of a canonic systematic code to equal its order M' column distance. A corollary shows that the condition is a sufficient one for a nonsystematic code also. Two expressions for the probability of undetectable error of a specific code are presented. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1970
Accession Number
AD0704650

Entities

People

  • Frank Ellwood Bell Iii

Organizations

  • University of Illinois Urbana–Champaign

Tags

DTIC Thesaurus Topics

  • Probability

Fields of Study

  • Mathematics

Readers

  • Computer Programming and Software Development.
  • Mathematical Modeling and Probability Theory.