27 research outputs found
Polar codes for the two-user multiple-access channel
Arikan's polar coding method is extended to two-user multiple-access
channels. It is shown that if the two users of the channel use the Arikan
construction, the resulting channels will polarize to one of five possible
extremals, on each of which uncoded transmission is optimal. The sum rate
achieved by this coding technique is the one that correponds to uniform input
distributions. The encoding and decoding complexities and the error performance
of these codes are as in the single-user case: for encoding and
decoding, and for block error probability, where
is the block length.Comment: 12 pages. Submitted to the IEEE Transactions on Information Theor
Systematic polar coding
Cataloged from PDF version of article.Polar codes were originally introduced as a class
of non-systematic linear block codes. This paper gives encoding
and decoding methods for systematic polar coding that preserve
the low-complexity nature of non-systematic polar coding while
guaranteeing the same frame error rate. Simulation results are
given to show that systematic polar coding offers significant
advantages in terms of bit error rate performance
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
Channel Upgradation for Non-Binary Input Alphabets and MACs
Consider a single-user or multiple-access channel with a large output
alphabet. A method to approximate the channel by an upgraded version having a
smaller output alphabet is presented and analyzed. The original channel is not
necessarily symmetric and does not necessarily have a binary input alphabet.
Also, the input distribution is not necessarily uniform. The approximation
method is instrumental when constructing capacity achieving polar codes for an
asymmetric channel with a non-binary input alphabet. Other settings in which
the method is instrumental are the wiretap setting as well as the lossy source
coding setting.Comment: 18 pages, 2 figure
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 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
Polar Codes for Arbitrary Classical-Quantum Channels and Arbitrary cq-MACs
We prove polarization theorems for arbitrary classical-quantum (cq) channels.
The input alphabet is endowed with an arbitrary Abelian group operation and an
Ar{\i}kan-style transformation is applied using this operation. It is shown
that as the number of polarization steps becomes large, the synthetic
cq-channels polarize to deterministic homomorphism channels which project their
input to a quotient group of the input alphabet. This result is used to
construct polar codes for arbitrary cq-channels and arbitrary classical-quantum
multiple access channels (cq-MAC). The encoder can be implemented in operations, where is the blocklength of the code. A quantum successive
cancellation decoder for the constructed codes is proposed. It is shown that
the probability of error of this decoder decays faster than
for any .Comment: 30 pages. Submitted to IEEE Trans. Inform. Theory and in part to
ISIT201