Simulation of a Channel with Another Channel

Abstract

In this paper, we study the problem of simulating a discrete memoryless channel (DMC) from another DMC under an average-case and an exact model. We present several achievability and infeasibility results, with tight characterizations in special cases. In particular for the exact model, we fully characterize when a binary symmetric channel (BSC) can be simulated from a binary erasure channel (BEC) when there is no shared randomness. We also provide infeasibility and achievability results for simulation of a binary channel from another binary channel in the case of no shared randomness. To do this, we use properties of Rényi capacity of a given order. We also introduce a notion of "channel diameter" which is shown to be additive and satisfy a data processing inequality.

Communication for Generating Correlation: A Unifying Survey

“…Note that the common randomness generation problem and the Wyner common information, respectively, entail simulating a uniformly distributed shared bits from a given distribution and viceversa. Also, a related setting where we seek to simulate a given channel using an available channel was considered in [85]. We do not review this problem here and restrict ourselves to the simple source model setting above.…”

Strong Coordination of Signals and Actions Over Noisy Channels With Two-Sided State Information

“…The difference in common randomness rate I(W ; XY |U V ) stems from the requirement in [11], which coordinates U n and V n but not necessarly (U n , X n , Y n , V n ).…”

“…Strong coordination in networks was first studied over error free links [3] and later extended to noisy communication links [11]. In the latter setting, the signals that are transmitted and received over the physical channel become a part of what can be observed, and one can therefore coordinate the actions of the devices with their communication signals [13,14].…”

Strong Coordination over Noisy Channels with Strictly Causal Encoding

“…The key idea of the achievability proof is to define a random binning for the target joint distribution, and a random coding scheme, each of which induces a joint distribution, and to prove that the two schemes have almost the same statistics. The proof uses the same techniques as in [10] inspired by [8], to deal with the strictly causal encoder, a block Markov structure is required for the random coding scheme. Before defining the coding scheme, we state some results that we use to prove the inner bound.…”