Extending the Error Correction Capability of Linear Codes

Abstract : Linear transmission codes were developed under the assumption that the bit errors are independent and random. When these codes are applied to difital circuits, this assumption no longer holds. Using the past history of the bit failures, a linear transmission code that can detect k bit failures can be made to tolerate and correct up to (k-1) bit failures. Thus if the classical error correction bounds are assumed, a linear transmission code used in digital circuitry is under-utilized. For example, the single-error-correction, double-error-detection Hamming code could be used to correct up to two bit failures with some additional error correction circuitry. A simple algorithm for correcting these extra errors in linear codoes is presented. (Author)