A graph based construction of high-rate soft decodable codes for partial response channels

In partial response systems with maximum likelihood sequence estimation a short list of error events dominate. In this paper we introduce a graph-based construction of high rate codes capable of correcting errors from a given list. We define a directed graph describing a universe of error-event-detecting codes, and construct a code by tracing a path through the graph that gives the best probability of error. We demonstrate a substantial SNR gain when these codes are used in a scheme which combines the error event detection and the list soft decoding.