| Ordered statistics decoding (OSD) is an important decoding algorithm for linear block codes, capable of approaching the maximum-likelihood decoding performance of some well-known codes. However, the OSD was mainly developed for a memoryless channel, where individual channel observations are independent from one another. Unfortunately not all important channels are memoryless, the recording channel in particular (e.g. hard-drives and tape) is modeled by an intersymbol interference (ISI) channel that has inherent memory. In this thesis, we generalize OSD techniques to apply on ISI channels.;First, we generalize two OSD algorithms for the ISI channel. We exploit bursty-type errors, that occur when ISI is present. Efficient methods are given to handle these errors, which occur in more complicated configurations (as compared to memoryless channels). The box-and-match (BMA) algorithm is also generalized for ISI channels. The BMA is an enhanced OSD-type decoder that achieves improved performance, while maintaining similar complexity. For our BMA, (improved) error correction guarantees are provided.;Next, we consider complexity reduction techniques for OSD-type algorithms applied to ISI channels. These techniques were first developed for memoryless channels, and are commonly known as codeword optimality tests. Prior techniques are limited only to memoryless channels, and we generalize here for ISI channels. Performance loss is observed when applying these optimality tests to ISI channels; this loss is observed to depend on the channel characteristics.;The last part relates to analysis. First, we present closed-form expressions for the probability distributions of the channel detector symbol reliabilities ; here the considered channel detector is a (sliding-window implemented) max-log-map. These symbol reliabilities are essential to OSD, as the OSD prioritizes high reliability symbols (i.e. symbols received with a small estimated probability of error). The probability of an OSD decoding error, depends on ordered symbol error probabilities, i.e., the error probability that a symbol, ordered according to its symbol reliability, is in error. Conjectured approximations are presented for the ordered symbol error probabilities.;All generalizations in this thesis, collapse down to the memoryless case, when the channel impulse response is set to the Kronecker delta function. |
