Monte Carlo determination of bounds on error correcting codes.

Abstract

Analytical bounds on the capabilities of error correcting codes have been found for most known codes. There are only a limited number of coding theorists available for the solution of such problems; however, new coding techniques are constantly being proposed to meet new communication system problems. This paper develops and describes a Monte Carlo method for estimating bounds experimentally. A bound on the block error rate is developed for use in evaluating optimum codes. The random sampling technique evolved is used to evaluate the bounds on four representative error correcting codes. The close agreement between the theoretical and experimental results establishes confidence in the method's use to determine bounds and capabilities. The technique and problems described can also be used to simulate error correction in system coding studies.