13,528 research outputs found
Achieving the Uniform Rate Region of General Multiple Access Channels by Polar Coding
We consider the problem of polar coding for transmission over -user
multiple access channels. In the proposed scheme, all users encode their
messages using a polar encoder, while a multi-user successive cancellation
decoder is deployed at the receiver. The encoding is done separately across the
users and is independent of the target achievable rate. For the code
construction, the positions of information bits and frozen bits for each of the
users are decided jointly. This is done by treating the polar transformations
across all the users as a single polar transformation with a certain
\emph{polarization base}. We characterize the resolution of achievable rates on
the dominant face of the uniform rate region in terms of the number of users
and the length of the polarization base . In particular, we prove that
for any target rate on the dominant face, there exists an achievable rate, also
on the dominant face, within the distance at most
from the target rate. We then prove that the proposed MAC polar coding scheme
achieves the whole uniform rate region with fine enough resolution by changing
the decoding order in the multi-user successive cancellation decoder, as
and the code block length grow large. The encoding and decoding
complexities are and the asymptotic block error probability of
is guaranteed. Examples of achievable rates for
the -user multiple access channel are provided
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
Polar Codes for the m-User MAC
In this paper, polar codes for the -user multiple access channel (MAC)
with binary inputs are constructed. It is shown that Ar{\i}kan's polarization
technique applied individually to each user transforms independent uses of a
-user binary input MAC into successive uses of extremal MACs. This
transformation has a number of desirable properties: (i) the `uniform sum rate'
of the original MAC is preserved, (ii) the extremal MACs have uniform rate
regions that are not only polymatroids but matroids and thus (iii) their
uniform sum rate can be reached by each user transmitting either uncoded or
fixed bits; in this sense they are easy to communicate over. A polar code can
then be constructed with an encoding and decoding complexity of
(where is the block length), a block error probability of o(\exp(- n^{1/2
- \e})), and capable of achieving the uniform sum rate of any binary input MAC
with arbitrary many users. An application of this polar code construction to
communicating on the AWGN channel is also discussed
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
Scaling Exponent and Moderate Deviations Asymptotics of Polar Codes for the AWGN Channel
This paper investigates polar codes for the additive white Gaussian noise
(AWGN) channel. The scaling exponent of polar codes for a memoryless
channel with capacity characterizes the closest gap
between the capacity and non-asymptotic achievable rates in the following way:
For a fixed , the gap between the capacity
and the maximum non-asymptotic rate achieved by a length- polar code
with average error probability scales as , i.e.,
.
It is well known that the scaling exponent for any binary-input
memoryless channel (BMC) with is bounded above by ,
which was shown by an explicit construction of polar codes. Our main result
shows that remains to be a valid upper bound on the scaling exponent
for the AWGN channel. Our proof technique involves the following two ideas: (i)
The capacity of the AWGN channel can be achieved within a gap of
by using an input alphabet consisting of
constellations and restricting the input distribution to be uniform; (ii) The
capacity of a multiple access channel (MAC) with an input alphabet consisting
of constellations can be achieved within a gap of by
using a superposition of binary-input polar codes. In addition, we
investigate the performance of polar codes in the moderate deviations regime
where both the gap to capacity and the error probability vanish as grows.
An explicit construction of polar codes is proposed to obey a certain tradeoff
between the gap to capacity and the decay rate of the error probability for the
AWGN channel.Comment: 24 page
Achieving Marton's Region for Broadcast Channels Using Polar Codes
This paper presents polar coding schemes for the 2-user discrete memoryless
broadcast channel (DM-BC) which achieve Marton's region with both common and
private messages. This is the best achievable rate region known to date, and it
is tight for all classes of 2-user DM-BCs whose capacity regions are known. To
accomplish this task, we first construct polar codes for both the superposition
as well as the binning strategy. By combining these two schemes, we obtain
Marton's region with private messages only. Finally, we show how to handle the
case of common information. The proposed coding schemes possess the usual
advantages of polar codes, i.e., they have low encoding and decoding complexity
and a super-polynomial decay rate of the error probability.
We follow the lead of Goela, Abbe, and Gastpar, who recently introduced polar
codes emulating the superposition and binning schemes. In order to align the
polar indices, for both schemes, their solution involves some degradedness
constraints that are assumed to hold between the auxiliary random variables and
the channel outputs. To remove these constraints, we consider the transmission
of blocks and employ a chaining construction that guarantees the proper
alignment of the polarized indices. The techniques described in this work are
quite general, and they can be adopted to many other multi-terminal scenarios
whenever there polar indices need to be aligned.Comment: 26 pages, 11 figures, accepted to IEEE Trans. Inform. Theory and
presented in part at ISIT'1
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
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
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