Fundamental distortion limits of analog-to-digital compression

Alon Kipnis, Yonina C. Eldar, Andrea J. Goldsmith

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Representing a continuous-time signal by a set of samples is a classical problem in signal processing. We study this problem under the additional constraint that the samples are quantized or compressed in a lossy manner under a limited bitrate budget. To this end, we consider a combined sampling and source coding problem in which an analog stationary Gaussian signal is reconstructed from its encoded samples. These samples are obtained by a set of bounded linear functionals of the continuous-time path, with a limitation on the average number of samples per unit time given in this setting. We provide a full characterization of the minimal distortion in terms of the sampling frequency, the bitrate, and the signal's spectrum. Assuming that the signal's energy is not uniformly distributed over its spectral support, we show that for each compression bitrate there exists a critical sampling frequency smaller than the Nyquist rate, such that the distortion in signal reconstruction when sampling at this frequency is minimal. Our results can be seen as an extension of the classical sampling theorem for bandlimited random processes in the sense that they describe the minimal amount of excess distortion in the reconstruction due to lossy compression of the samples and provide the minimal sampling frequency required in order to achieve this distortion. Finally, we compare the fundamental limits in the combined source coding and sampling problem to the performance of pulse code modulation, where each sample is quantized by a scalar quantizer using a fixed number of bits.

Original languageEnglish (US)
Article number8416707
Pages (from-to)6013-6033
Number of pages21
JournalIEEE Transactions on Information Theory
Volume64
Issue number9
DOIs
StatePublished - Sep 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Keywords

  • Gaussian processes
  • Sampling
  • analog to digital
  • lossy compression
  • nonuniform sampling
  • source coding
  • sub-Nyquist sampling

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