A mathematical theory of imperfect communication: Energy efficiency considerations in multi-level coding

Is perfect error correction always worth the trouble? A framework is presented for the analysis of error detection and correction in multi-level systems of communication that takes into account degrees of freedom attended and ignored by different levels of analysis. It follows from this analysis 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 has relevance to approximate computing, and to questions of the robustness of machine learning applications. The finding also has significance in natural systems, such as neuronal signaling, vision, and molecular genetics, which are readily characterized as relying on multiple layers of inadequate error correction.