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