Capacity achieving probabilistic shaping for noisy and noiseless channels

TL;DRAbstract

In Shannon theory, the key step in calculating the capacity of a communication channel is to determine the channel input distribution that maximizes the mutual information between transmitted and received symbols. For many channels, this so called capacity-achieving distribution is not uniform. In digital communication systems, there is a binary interface that separates the system into a source-related part and a channel-related part. A natural question is how the bit stream at the binary interface can be mapped to channel input symbols in such a way that the resulting distribution is close to capacity-achieving. The topic of this thesis is to answer this question. In this thesis, dyadic distributions are considered. Dyadic distributions can be generated by parsing the bit stream at the binary interface by a prefix-free code. A device that implements this procedure is called a prefix-free matcher. In the first part of this thesis, three types of discrete memoryless channels are conside

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