2 research outputs found
On the calculation of the minimax-converse of the channel coding problem
A minimax-converse has been suggested for the general channel coding problem
by Polyanskiy etal. This converse comes in two flavors. The first flavor is
generally used for the analysis of the coding problem with non-vanishing error
probability and provides an upper bound on the rate given the error
probability. The second flavor fixes the rate and provides a lower bound on the
error probability. Both converses are given as a min-max optimization problem
of an appropriate binary hypothesis testing problem. The properties of the
first converse were studies by Polyanskiy and a saddle point was proved. In
this paper we study the properties of the second form and prove that it also
admits a saddle point. Moreover, an algorithm for the computation of the saddle
point, and hence the bound, is developed. In the DMC case, the algorithm runs
in a polynomial time.Comment: Extended version of a submission to ISIT 201
Lossless Source Coding in the Point-to-Point, Multiple Access, and Random Access Scenarios
This paper treats point-to-point, multiple access and random access lossless
source coding in the finite-blocklength regime. A random coding technique is
developed, and its power in analyzing the third-order coding performance is
demonstrated in all three scenarios. Via a connection to composite hypothesis
testing, a new converse that tightens previously known converses for
Slepian-Wolf source coding is established. Asymptotic results include a
third-order characterization of the Slepian-Wolf rate region and a proof
showing that for dependent sources, the independent encoders used by
Slepian-Wolf codes can achieve the same third-order-optimal performance as a
single joint encoder. The concept of random access source coding, which
generalizes the multiple access scenario to allow for a subset of participating
encoders that is unknown a priori to both the encoders and the decoder, is
introduced. Contributions include a new definition of the probabilistic model
for a random access source, a general random access source coding scheme that
employs a rateless code with sporadic feedback, and an analysis demonstrating
via a random coding argument that there exists a deterministic code of the
proposed structure that simultaneously achieves the third-order-optimal
performance of Slepian-Wolf codes for all possible subsets of encoders.Comment: 42 pages, 10 figures. Part of this work was presented at ISIT'1