Achievability proof via output statistics of random binning

Abstract

This paper presents a new and ubiquitous framework for establishing achievability results in network information theory (NIT) problems. The framework is used to prove various new results. To express the main tool, consider a set of discrete memoryless correlated sources (DMCS). Assume that each source (except one, Z n ) is randomly binned at a finite rate. We find sufficient conditions on these rates such that the bin indices are nearly mutually independent of each other and of Z n . This is used in conjunction with the Slepian-Wolf (S-W) result to set up the framework. We begin by illustrating this method via examples from channel coding and rate-distortion (or covering problems). Next, we use the framework to prove a new result on the lossy transmission of a source over a broadcast channel. We also prove a new lower bound to a three receiver wiretap broadcast channel under a strong secrecy criterion. We observe that we can directly prove the strong notion of secrecy without resorting to the common techniques, e.g., the leftover hash lemma. We have also used our technique to solve the problem of two-node interactive channel simulation and the problem of coordination via a relay.

Information Complexity Density and Simulation of Protocols

“…The first subroutine is an interactive version of the classical Slepian-Wolf compression [45] for sending X to an observer of Y which is of optimal instantaneous rate. The second subroutine uses an idea that appeared first in [41] (see, also, [35], [54]) and reduces the number of bits communicated in the first by realizing a portion of the required communication by the shared public randomness. This is possible since we are not required to recover a given random variable Π, but only simulate it to within a fixed statistical distance.…”

Polar codes for covert communications over asynchronous Discrete Memoryless Channels

“…Our code construction exploits recent results on polar codes that suggest how information-theoretic proofs exploiting source coding with side information and privacy amplification as primitives [16,17] may be converted into polar coding schemes by a suitable identification of polarization sets [11,18]. Specifically, the approach consists in recognizing that both primitives have counterparts based on polar codes, see Lemma 3 and Lemma 4 of [11], as well as [19,20].…”

Nonasymptotic and Second-Order Achievability Bounds for Coding With Side-Information

“…Recently, Yassaee-Aref-Gohari (YAG) [34] proposed an alternative approach for channel simulation, in which they exploited the (multi-terminal version of) intrinsic randomness [7,Ch. 2] instead of channel resolvability.…”

“…This approach is coined output statistics of random binning (OSRB). Although their approach is also used to replace the Markov lemma [2], it was not a priori yet clear when [34] was published whether our bounds can be also derived from the OSRB approach [34]. One of difficulties to apply the OSRB approach for non-asymptotic analysis is that the amount of common randomness that can be used in the channel simulation is limited by the randomness of sources involved in a coding problem, which is not the case with the approach using the channel resolvability.…”