An Informative Interpretation of Decision Theory: The Information Theoretic Basis for Signal-to-Noise Ratio and Log Likelihood Ratio

Abstract

The signal processing concept of signal-to-noise ratio (SNR), in its role as a performance measure, is recast within the more general context of information theory, leading to a series of useful insights. Establishing generalized SNR (GSNR) as a rigorous information theoretic measure inherent in any set of observations significantly strengthens its quantitative performance pedigree while simultaneously providing a specific definition under general conditions. In turn, this directly leads to consideration of the log likelihood ratio (LLR): first, as the simplest possible information-preserving transformation (i.e., signal processing algorithm) and subsequently, as an absolute, comparable measure of information for any specific observation exemplar. The information accounting methodology that results permits practical use of both GSNR and LLR as diagnostic scalar performance measurements, directly comparable across alternative system/algorithm designs, applicable at any tap point within any processing string, in a form that is also comparable with the inherent performance bounds due to information conservation.