Correcting a specified set of likely error patterns

摘要

The main concern of this article is to find linear codes whichwill correct a set of arbitrary error patterns. Although linear codeswhich have been designed for correcting random error patterns and bursterror patterns can be used, we would like to find codes which willcorrect a specified set of error patterns with the fewest possibleredundant bits. Here, to reduce the complexity involved in finding thecode with the smallest redundancy which can correct a specified set oferror patterns, algebraic codes whose parity check matrix exhibits aparticular structure are considered. If the number of redundant bits isT, the columns of the parity check matrix must be increasing powers of afield element in GF(2T). Given a set of error patterns to becorrected, computations to determine the code rates possible for thesetype of codes and hence the redundancy for different codeword lengthsare presented. Results for various sets of error patterns suggest thatthe redundancy of these algebraic codes is close to the minimumredundancy possible for the set of error patterns specified and for anycodeword length