We investigate the performance of single and multiple parity codes in magnetic recording systems. We evaluate the codes with respect to bit error rate as well as error correction code (ECC) failure rate. While multiple parity codes outperform the single parity code in bit error rate, their performance is worse with respect to the ECC failure rate.

This letter continues the investigation of methods for computing exact bounds on the path metric differences in maximum-likelihood sequence detectors based upon the Viterbi algorithm. New upper and lower estimates for these bounds are presented and recast in terms of a collection of linear programming problems. These estimates improve upon previously proposed linear programming bounds. The estimates are applied to derive exact bounds or provably close to exact bounds for several Viterbi detectors corresponding to coded and uncoded partial-response channels of practical interest in digital magnetic and optical recording.