# Dynamic Programming Algorithms for Maximum Likelihood Decoding

#### Abstract

of “Dynamic Programming Algorithms for Maximum Likelihood Decoding,” by Kevin Geoffrey Kochanek, Ph.D., Brown University, May 1998 The Viterbi algorithm is the traditional prototype dynamic programming algorithm for maximum likelihood decoding. Seen from the perspective of formal language theory, this algorithm recursively parses a trellis code’s regular grammar. This thesis discusses generalized Viterbi algorithms for the maximum likelihood decoding of codes generated by context-free grammars and transmitted across either memoryless or Markov communications channels. Among the codes representable by context-free grammars are iterated squaring constructions—including the Reed–Muller codes. Two additional strategies are introduced for handling large Reed–Muller-like codes. First, by systematically discarding information bits, a code’s grammatical and decoding complexities can be reduced to manageable levels without seriously reducing its information capacity. Second, a coarse-to-fine dynamic programming algorithm for the maximum likelihood decoding of Reed–Muller-like codes is presented; this algorithm almost uniformly outperforms the Viterbi algorithm. c © Copyright by Kevin Geoffrey Kochanek 1998 This dissertation by Kevin Geoffrey Kochanek is accepted in its present form by Division of Applied Mathematics as satisfying the dissertation requirement for the degree of Doctor of Philosophy Date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Stuart Geman Recommended to the Graduate Council Date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . David Mumford Date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Donald McClure Approved by the Graduate Council Date . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

### Cite this paper

@inproceedings{Kochanek2004DynamicPA, title={Dynamic Programming Algorithms for Maximum Likelihood Decoding}, author={Kevin Kochanek}, year={2004} }