Abstract / truncated to 115 words (read the full abstract)

A fundamental theorem in information theory – the data processing inequality – states that deterministic processing cannot increase the amount of information contained in a random variable or a stochastic process. The task of signal processing is to operate on the physical representation of information such that the intended user can access this information with little effort. In the light of the data processing inequality, this can be viewed as the task of removing irrelevant information, while preserving as much relevant information as possible. This thesis defines information loss for memoryless systems processing random variables or stochastic processes, both with and without a notion of relevance. These definitions are the basis of an information-theoretic systems ... toggle 11 keywords

information theory – equivocation – information loss – markov chains – state space aggregation – PCA – anti-aliasing filters – linear prediction – DPCM – system theory – lumpability

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