Fundamental performance limits of analog-to-digital compression
Abstract/Contents
- Abstract
- Analog-to-digital conversion is a fundamental operation in many electronic and communication systems. The principles describing the information loss as a result of transforming from continuous-time, continuous-amplitude signals to a sequence of bits lie at the intersection of sampling theory and quantization or lossy source coding theory. Classic results in sampling theory established the Nyquist rate of a signal, or, more precisely, its spectral occupancy, as the critical sampling rate above which the signal can be perfectly reconstructed from its samples. However, these results do not incorporate the quantization precision of the samples. Since it is impossible to obtain an exact digital representation of any continuous-amplitude sequence of samples, any digital representation of an analog signal will introduce some error, regardless of the sampling rate. This raises the question as to when sampling at the Nyquist rate is necessary. In other words, is it possible to achieve the same or better performance by sampling at a rate lower than Nyquist without any further assumptions about the input signal other than a limited bitrate to describe the samples? When only quantization or limited bitrate is considered, the minimal distortion in encoding a random process subject to this bitrate limitation is described by Shannon's distortion-rate function (DRF). However, this DRF is given in terms of an optimization over a family of conditional probability distributions subject to a mutual information constraint and does not explicitly incorporate sampling and other inaccuracies arising from signal processing with a limited time-resolution. In fact, the standard achievability scheme in source coding assumes that the encoder can access the realization of the analog process, or expand it with respect to an analog basis function, without any restriction on the time resolution. Since this restriction often occurs in practice, the following question arises: Given a finite number of samples per unit time from the analog process, what is the minimal distortion in recovering it from a digital encoding of these samples subject to a bitrate constraint ? The goal of this thesis is to address the two questions posed above by characterizing the minimal distortion that can be attained in recovering a random process using the most general form of quantization applied to its samples. By explicitly incorporating sampling into the minimum distortion optimization, the characterization of the minimal distortion bridges the missing theoretical gap between sampling theory and lossy data compression theory. By taking into account signal sampling and the associated distortion, the resulting distortion function generalizes and unifies sampling theory and source coding theory.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2017 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Kipnis, Alon |
|---|---|
| Associated with | Stanford University, Department of Electrical Engineering. |
| Primary advisor | Goldsmith, Andrea, 1964- |
| Thesis advisor | Goldsmith, Andrea, 1964- |
| Thesis advisor | El Gamal, Abbas A |
| Thesis advisor | Weissman, Tsachy |
| Advisor | El Gamal, Abbas A |
| Advisor | Weissman, Tsachy |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Alon Kipnis. |
|---|---|
| Note | Submitted to the Department of Electrical Engineering. |
| Thesis | Thesis (Ph.D.)--Stanford University, 2017. |
| Location | electronic resource |
Access conditions
- Copyright
- © 2017 by Alon Kipnis
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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