Canaux à Bande Limitée et Echantillonage: Compromis Fondamentaux – BSC

The goal of this project is to contribute to a better information theoretic understanding of the role of sampling in the context of communication. In particular, this project addresses two fundamental problems: capacity and capacity per unit cost for, possibly asynchronous, band-limited additive noise channels (see Fig. 1) as functions of fundamental parameter, e.g., P, W , and b. We shall focus mainly on additive white Gaussian noise channels in synchronous and asynchronous settings. Broad questions the project addresses include:
• When is oversampling with respect to Nyquist rate (i.e., fs > 2W ) beneficial in terms of capacity and capacity per unit cost?
• How does capacity vary as a function of the input power P and output quantization rate ? =W ×b?
• How to efficiently signal over a band-limited and sampling constrained channel?
Note that capacity per unit cost addresses only in part the energy problem as it characterizes the mini- mum energy needed to transmit one bit of information but ignores the energy spent at the receiver for sampling and quantifying the signal. A 100 MS/s ADC, such as in Wi-Fi receivers, consumes a few milliwatts and has a 12 to 16-bit quantization resolution. By contrast, a high speed ADC that can take giga-samples per second consumes multiple orders of magnitude more power, typically more that one watt, and has only 6 to 8 bits of resolution. Recently, fundamental lower bounds on the power of ADCs were derived that showed that it is typically linear in the sampling frequency fs and exponential in the resolution b. This motivates to investigate the following question:
• Suppose in addition to the input cost we impose an output sampling cost—say, a linear function of the sampling frequency fs. What is capacity per unit cost when both the input and the output cost are taken into account?

The rmain result obtained sor far addresses the issue of receiver sampling in asynchronou communication. In brief, this work addresses the problem of communicating with a receiver that is sampling constrained. We showed that even under a sampling constraint it is possible to achieve the same performance in terms of rate per unit cost (bits per joules at the transmitter) and communication delay as under full sampling. We furthermore characterized the minimum sampling rate for this to hold.

By investigating both capacity and capacity per unit cost for quantized output channels this project seeks to establish fundamental communication limits in terms of input-output power, channel bandwidth, sampling frequency, and resolution. This requires to look at communication channels at a more fundamental level: the physical continuous time channel. In turn, this will allow us to optimize not only transmission signals amplitudes but also their waveforms. Beyond establishing fundamental information theoretic limits, this project may also reveal insights into more efficient coding strategies.

« How to Quickly Detect a Change while Sleeping Almost all the Time » with V. Chandar, submitted to IEEE Trans. on Inform. Th., 2016


« How to quickly detect a change while sleeping most of the time », with V. Chandar, Asilomar 2016, invited paper.

« Asynchronous Capacity per Unit Cost under a Receiver Sampling Constraint »,with V. Chandar, ISIT 2015.

« Sequential Detection of Transient Changes in Stochastic Systems under a Sampling Constraint », with E. Ebrahimzadeh, ISIT 2015.

« Quickest Transient Change-Detection: Finding a Needle in a Haystack with a Minimum Number of Observations », with V. Chandar
ITA 2015, invited paper.