On the relation between undetected errors and the error detection criteria of a Reed-Solomon decoder correcting errors and erasures

This paper makes an analysis based on tests, of the relation between the various error detection criteria used in the decoding of error-and-erasure correcting Reed-Solomon codes, and the undetected errors this decoder produces. A strong correlation is found to exist between the number of erasures ρ and the number of undetected errors: errata patterns with an even number of erasures cause a considerable larger number of undetected errors than patterns with an odd number of erasures. A suggestion how to improve the decoder probability of undetected error by discarding one erasure if ρ is even, and its effect on the degradation of the probability of correct decoding, is also discussed