Abstract
This paper studies the discrete-time Poisson channel and the noiseless binary channel where, after recording a 1, the channel output is stuck at 0 for a certain period; this period is called the “dead time.” The communication capacities of these channels are analyzed, with main focus on the regime where the allowed average input power is close to zero, either because the bandwidth is large, or because the available continuous-time input power is low.
Highlights
For some detection systems that record arrivals, for example, a single-photon avalanche diode, after each recorded arrival, there comes a period during which the detector is not able to record any new arrivals.This period is often called the “dead time”; see, e.g., [1,2,3]
As a first step toward understanding communication channels with detector dead time, we have studied the noiseless binary channel and the discrete-time Poisson channel with dead time in the asymptotic regime where the allowed average input power approaches zero
In the scenario where continuous-time input power is fixed and bandwidth grows large, if dead time limits the maximum possible output rate, it incurs a penalty in the dominant term in capacity for both channels
Summary
For some detection systems that record arrivals, for example, a single-photon avalanche diode, after each recorded arrival, there comes a period during which the detector is not able to record any new arrivals. The noiseless binary channel with dead time can be thought of as a model for direct-detection optical channel with number states containing zero or one photon as inputs.. An exception is the Poisson channel in the wideband regime without feedback, for which we prove a lower bound, but we have not found a matching upper bound In this case, we suspect that dead time does incur a penalty on the dominant term in capacity. At the end of the paper, we summarize the results and discuss some future research directions The channel, whether it is noiseless or Poisson, is characterized by two parameters: β denotes the maximum allowed average input power per channel use, and d denotes the duration of each dead-time period in channel uses. Throughout this paper, log denotes the natural logarithm, and information is measured in nats
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