Title :
Correcting a specified set of likely error patterns
Author :
Tan, Narciso L. ; Welch, Lloyd R. ; Scholtz, Robert A.
Author_Institution :
David Sarnoff Res. Center, Princeton, NJ, USA
fDate :
1/1/1995 12:00:00 AM
Abstract :
The main concern of this article is to find linear codes which will correct a set of arbitrary error patterns. Although linear codes which have been designed for correcting random error patterns and burst error patterns can be used, we would like to find codes which will correct a specified set of error patterns with the fewest possible redundant bits. Here, to reduce the complexity involved in finding the code with the smallest redundancy which can correct a specified set of error patterns, algebraic codes whose parity check matrix exhibits a particular structure are considered. If the number of redundant bits is T, the columns of the parity check matrix must be increasing powers of a field element in GF(2T). Given a set of error patterns to be corrected, computations to determine the code rates possible for these type of codes and hence the redundancy for different codeword lengths are presented. Results for various sets of error patterns suggest that the redundancy of these algebraic codes is close to the minimum redundancy possible for the set of error patterns specified and for any codeword length
Keywords :
algebraic codes; error correction codes; linear codes; algebraic codes; burst error patterns; code rates; codeword lengths; complexity; error patterns correction; field element; linear codes; parity check matrix; random error patterns; redundancy; redundant bits; Artificial intelligence; Block codes; Delay effects; Error correction; Error correction codes; Information theory; Linear code; Parity check codes; Redundancy; Vectors;
Journal_Title :
Information Theory, IEEE Transactions on