# 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. 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. Furthermore, 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.

- Authors:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Computer Science Mathematics Division

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1344244

- Grant/Contract Number:
- AC05-00OR22725

- Resource Type:
- Accepted Manuscript

- Journal Name:
- IEEE Access

- Additional Journal Information:
- Journal Volume: 1; Journal ID: ISSN 2169-3536

- Publisher:
- IEEE

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; data compression; decision theory; detection algorithms; information measures; information theory; Kullback-Leibler divergence; log likelihood ratio; performance evaluation; performance measures; self-scaling property; signal processing algorithms; signal to noise ratio; statistical anlaysis

### Citation Formats

```
Polcari, J. An Informative Interpretation of Decision Theory: The Information Theoretic Basis for Signal-to-Noise Ratio and Log Likelihood Ratio. United States: N. p., 2013.
Web. doi:10.1109/ACCESS.2013.2277930.
```

```
Polcari, J. An Informative Interpretation of Decision Theory: The Information Theoretic Basis for Signal-to-Noise Ratio and Log Likelihood Ratio. United States. doi:10.1109/ACCESS.2013.2277930.
```

```
Polcari, J. Fri .
"An Informative Interpretation of Decision Theory: The Information Theoretic Basis for Signal-to-Noise Ratio and Log Likelihood Ratio". United States. doi:10.1109/ACCESS.2013.2277930. https://www.osti.gov/servlets/purl/1344244.
```

```
@article{osti_1344244,
```

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

author = {Polcari, J.},

abstractNote = {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. 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. Furthermore, 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.},

doi = {10.1109/ACCESS.2013.2277930},

journal = {IEEE Access},

number = ,

volume = 1,

place = {United States},

year = {2013},

month = {8}

}

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