| Summary: | 碩士 === 國立中山大學 === 電機工程學系研究所 === 93 === Combined coding with modulation is an important topic. Conventionally, the free distance is taken as the principle criterion for computing the error probability for
coding or modulation. In many cases, distance spectrum needs to be provided for analyze the Maximum likelihood decoding. However, it is difficult for computing the
distance spectrum for a combined coding with modulation because of a nonlinear structure inside. In this thesis, we study the order of distance spectrum members to
find some limited number of members to present the whole distance spectrum.
In our previous work, we have built an augmented trellis for the combined coding with modulation. Applying the concept of difference by exclusive OR and regular subtraction to the augmented trellis, we build an improved virtual trellis. In this thesis, we expend the concept of subtraction to a pair relation. Thus, this augmented trellis is first composed of paired states and transition lines. Then, we use a partition principle to group the states and lines. Finally, the complex trellis is reduced to a reasonable structure. We therefore can apply distance spectrum computing algorithm to find the distance spectrum. The distance spectrum for different convolution codes and CPM systems are investigated by us. Experiments
results have demonstrate this distance spectrum is more accurate than before.
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