A mathematical theory of imperfect communication: Energy efficiency considerations in multi-level coding
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A novel framework is presented for the analysis of multi-level coding that takes into account degrees of freedom attended and ignored by the different levels of analysis. It can be shown that for a multi-level coding system, skipped or incomplete error correction at many levels can save energy and provide equally good results to perfect correction. This is the case for both discrete and continuous cases. This has relevance to approximate computing, and also to deep learning networks, which can readily be construed as multiple levels of inadequate error correction reacting to some input signal, but which are typically considered beyond analysis by traditional information theoretical methods. The finding also has significance in natural systems, e.g. neuronal signaling, vision, and molecular genetics, which can be characterized as relying on multiple layers of inadequate error correction.
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