Simplified calculation of likelihood metrics for Viterbi decoding in partial response systems

The recovery of recorded data using maximum likelihood sequence estimation has become well established in magnetic recording. The implementation of this method by means of the Viterbi algorithm involves the calculation of likelihood metrics which determine the most likely sequence of decoded data. From a theoretical point of view, the most important metric is the squared Euclidean distance metric. While several types of partial response systems permit a simple means of calculating this metric, there are also a number of cases where the calculation of this metric cannot avoid the use of multipliers or a squaring circuit. In this paper, we discuss alternative methods for calculating likelihood metrics which avoid the use of squaring operations and minimize or eliminate multiplication operations. These metrics retain the maximum likelihood property under certain conditions which are satisfied in typical recording applications. This paper discusses these conditions and the signal-to-noise ratios for which they hold. Both hard-decision decoding and “quasi-soft”-decision decoding are discussed