Probing Capacity

TL;DR

This paper introduces the concept of probing capacity, analyzing how optimal state probing by encoder and decoder can maximize reliable communication rates in channels with controllable state information, considering cost constraints.

Contribution

It characterizes the probing capacity for channels with cost-constrained probing actions and explores the trade-off between state observation and communication rate.

Findings

Encoder can observe a small fraction of states and still achieve maximum communication rate.

Probing actions can be optimized under cost constraints to maximize capacity.

Numerical examples illustrate the capacity-observation trade-off.

Abstract

We consider the problem of optimal probing of states of a channel by transmitter and receiver for maximizing rate of reliable communication. The channel is discrete memoryless (DMC) with i.i.d. states. The encoder takes probing actions dependent on the message. It then uses the state information obtained from probing causally or non-causally to generate channel input symbols. The decoder may also take channel probing actions as a function of the observed channel output and use the channel state information thus acquired, along with the channel output, to estimate the message. We refer to the maximum achievable rate for reliable communication for such systems as the 'Probing Capacity'. We characterize this capacity when the encoder and decoder actions are cost constrained. To motivate the problem, we begin by characterizing the trade-off between the capacity and fraction of channel states the encoder is allowed to observe, while the decoder is aware of channel states. In this setting of 'to observe or not to observe' state at the encoder, we compute certain numerical examples and note a pleasing phenomenon, where encoder can observe a relatively small fraction of states and yet communicate at maximum rate, i.e. rate when observing states at encoder is not cost constrained.