Abstract
Abstract This paper presents a computational complexity measure of convolutional codes well suitable for software implementations of the Viterbi algorithm (VA) operating with hard decision. We investigate the number of arithmetic operations performed by the decoding process over the conventional and minimal trellis modules. A relation between the complexity measure defined in this work and the one defined by McEliece and Lin is investigated. We also conduct a refined computer search for good convolutional codes (in terms of distance spectrum) with respect to two minimal trellis complexity measures. Finally, the computational cost of implementation of each arithmetic operation is determined in terms of machine cycles taken by its execution using a typical digital signal processor widely used for low-power telecommunications applications.
Highlights
Convolutional codes are widely adopted due to their capacity to increase the reliability of digital communication systems with manageable encoding/decoding complexity [1]
Once the number of operations performed by the Viterbi algorithm (VA) over a trellis module is determined, we must obtain the individual cost of the arithmetic operations S, Cb, and Ci for a more appropriate complexity comparison
The search proposed in this paper considers both the trellis and merge complexities of the minimal trellis in order to obtain a list of good codes with more refined computational complexity values
Summary
Convolutional codes are widely adopted due to their capacity to increase the reliability of digital communication systems with manageable encoding/decoding complexity [1]. This measure is defined by considering the total number of sums and comparisons in M as well as the respective computational cost (complexity) of the implementation of these arithmetical operations using a given digital signal processor.
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