TY - GEN
T1 - Information rates of sampled Wiener processes
AU - Kipnis, Alon
AU - Eldar, Yonina C.
AU - Goldsmith, Andrea J.
N1 - Publisher Copyright:
© 2016 IEEE.
PY - 2016/8/10
Y1 - 2016/8/10
N2 - The minimal distortion attainable in recovering the waveform of a continuous-time Wiener process from an encoded version of its uniform samples is considered. We first introduce a combined sampling and source coding problem and prove an associated source coding theorem. We then derive an upper bound on the minimal distortion attainable under any sampling rate and a prescribed number of bits to encode the samples. We show that this bound is accurate to within a second order term in the sampling rate, and converges to the true distortion-rate function of the Wiener process as the sampling rate goes to infinity. For example, this bound implies that by providing a single bit per sample it is possible to achieve the optimal distortion-rate performance of the Wiener process, given by its distortion-rate function, to within a factor of 1.5. We conclude the distortion-rate function of the Wiener process is strictly smaller than the indirect distortion-rate function from its uniform samples obtained at any finite sampling rate. This is in contrast to stationary infinite bandwidth processes.
AB - The minimal distortion attainable in recovering the waveform of a continuous-time Wiener process from an encoded version of its uniform samples is considered. We first introduce a combined sampling and source coding problem and prove an associated source coding theorem. We then derive an upper bound on the minimal distortion attainable under any sampling rate and a prescribed number of bits to encode the samples. We show that this bound is accurate to within a second order term in the sampling rate, and converges to the true distortion-rate function of the Wiener process as the sampling rate goes to infinity. For example, this bound implies that by providing a single bit per sample it is possible to achieve the optimal distortion-rate performance of the Wiener process, given by its distortion-rate function, to within a factor of 1.5. We conclude the distortion-rate function of the Wiener process is strictly smaller than the indirect distortion-rate function from its uniform samples obtained at any finite sampling rate. This is in contrast to stationary infinite bandwidth processes.
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U2 - 10.1109/ISIT.2016.7541397
DO - 10.1109/ISIT.2016.7541397
M3 - Conference contribution
AN - SCOPUS:84985998051
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 740
EP - 744
BT - Proceedings - ISIT 2016; 2016 IEEE International Symposium on Information Theory
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2016 IEEE International Symposium on Information Theory, ISIT 2016
Y2 - 10 July 2016 through 15 July 2016
ER -