Trellis coding for partial response channels
The topic of this dissertation is trellis coding for partial response channels, which is used to increase the reliability of detection of the presence of noise.
Partial response channels of the form [special characters omitted], [special characters omitted] (where [special characters omitted] and [special characters omitted] are not both zero) have a spectral null at either DC or the Nyquist frequency or both. Codes used with channels that have a spectral null may not have finite truncation depth, meaning that a long Viterbi detector path memory is required. In Chapter 2, analysis of the channel null space is used to develop conditions for finite truncation depth, as well as a finite error event search and finite output runlength. These conditions are used in Chapter 3 to develop techniques for the design of finite truncation depth codes for partial response channels, and the techniques are illustrated by their application to the design of codes for the channel [special characters omitted] (EPR4) with 3dB of coding gain.
In Chapter 4, large Euclidean distance trellis codes for the partial response channels [special characters omitted], [special characters omitted], are presented. Some of these codes are based on DC-null repetition-2 (DCNR2) graphs, which are DC-null graphs with a repetition-2 constraint. Here the conditions obtained in Chapter 2 are illustrated and applied to obtain codes with finite truncation depth and finite output runlength.
Chapter 5 presents an generalized approach for reduced-complexity detection of trellis codes using a two-stage detection process, referred to as concatenated detection. First, the Viterbi algorithm is implemented on a detector trellis which is matched only to the channel. Second, the detected sequences produced by the first step are examined to see if they could have been generated by the trellis code. If not, the most likely error event is corrected.
Chapter 6 describes a low-complexity method for constructing a graph corresponding to a list of forbidden sequences such that the graph is the maxentropic graph which does not allow any sequence on the list. Normally these forbidden sequences are channel input sequences which can form error events with small Euclidean distance, thus constructing a code from this graph can result in performance gain.