24 research outputs found
Polar coding for the Slepian-Wolf problem based on monotone chain rules
We give a polar coding scheme that achieves the full admissible rate region in the Slepian-Wolf problem without time-sharing. The method is based on a source polarization result using monotone chain rule expansions. © 2012 IEEE
An improved rate region for the classical-quantum broadcast channel
We present a new achievable rate region for the two-user binary-input
classical-quantum broadcast channel. The result is a generalization of the
classical Marton-Gelfand-Pinsker region and is provably larger than the best
previously known rate region for classical-quantum broadcast channels. The
proof of achievability is based on the recently introduced polar coding scheme
and its generalization to quantum network information theory.Comment: 5 pages, double column, 1 figure, based on a result presented in the
Master's thesis arXiv:1501.0373
Universal Polarization
A method to polarize channels universally is introduced. The method is based
on combining two distinct channels in each polarization step, as opposed to
Arikan's original method of combining identical channels. This creates an equal
number of only two types of channels, one of which becomes progressively better
as the other becomes worse. The locations of the good polarized channels are
independent of the underlying channel, guaranteeing universality. Polarizing
the good channels further with Arikan's method results in universal polar codes
of rate 1/2. The method is generalized to construct codes of arbitrary rates.
It is also shown that the less noisy ordering of channels is preserved under
polarization, and thus a good polar code for a given channel will perform well
over a less noisy one.Comment: Submitted to the IEEE Transactions on Information Theor
Polar Coding for the General Wiretap Channel
Information-theoretic work for wiretap channels is mostly based on random
coding schemes. Designing practical coding schemes to achieve
information-theoretic security is an important problem. By applying the two
recently developed techniques for polar codes, we propose a polar coding scheme
to achieve the secrecy capacity of the general wiretap channel.Comment: Submitted to IEEE ITW 201
Polar codes in network quantum information theory
Polar coding is a method for communication over noisy classical channels
which is provably capacity-achieving and has an efficient encoding and
decoding. Recently, this method has been generalized to the realm of quantum
information processing, for tasks such as classical communication, private
classical communication, and quantum communication. In the present work, we
apply the polar coding method to network quantum information theory, by making
use of recent advances for related classical tasks. In particular, we consider
problems such as the compound multiple access channel and the quantum
interference channel. The main result of our work is that it is possible to
achieve the best known inner bounds on the achievable rate regions for these
tasks, without requiring a so-called quantum simultaneous decoder. Thus, our
work paves the way for developing network quantum information theory further
without requiring a quantum simultaneous decoder.Comment: 18 pages, 2 figures, v2: 10 pages, double column, version accepted
for publicatio
Successive cancellation decoding of polar codes for the two-user binary-input MAC
This paper describes a successive cancellation decoder of polar codes for the two-user binary-input multi-access channel that achieves the full admissible rate region. The polar code for the channel is generated from monotone chain rule expansions of mutual information terms. © 2013 IEEE
Polarization of the Renyi Information Dimension with Applications to Compressed Sensing
In this paper, we show that the Hadamard matrix acts as an extractor over the
reals of the Renyi information dimension (RID), in an analogous way to how it
acts as an extractor of the discrete entropy over finite fields. More
precisely, we prove that the RID of an i.i.d. sequence of mixture random
variables polarizes to the extremal values of 0 and 1 (corresponding to
discrete and continuous distributions) when transformed by a Hadamard matrix.
Further, we prove that the polarization pattern of the RID admits a closed form
expression and follows exactly the Binary Erasure Channel (BEC) polarization
pattern in the discrete setting. We also extend the results from the single- to
the multi-terminal setting, obtaining a Slepian-Wolf counterpart of the RID
polarization. We discuss applications of the RID polarization to Compressed
Sensing of i.i.d. sources. In particular, we use the RID polarization to
construct a family of deterministic -valued sensing matrices for
Compressed Sensing. We run numerical simulations to compare the performance of
the resulting matrices with that of random Gaussian and random Hadamard
matrices. The results indicate that the proposed matrices afford competitive
performances while being explicitly constructed.Comment: 12 pages, 2 figure
Polar Coding for the Cognitive Interference Channel with Confidential Messages
In this paper, we propose a low-complexity, secrecy capacity achieving polar
coding scheme for the cognitive interference channel with confidential messages
(CICC) under the strong secrecy criterion. Existing polar coding schemes for
interference channels rely on the use of polar codes for the multiple access
channel, the code construction problem of which can be complicated. We show
that the whole secrecy capacity region of the CICC can be achieved by simple
point-to-point polar codes due to the cognitivity, and our proposed scheme
requires the minimum rate of randomness at the encoder