172 research outputs found
An Upper Bound on the Cutoff Rate of Sequential Decoding
An upper bound is given on the cutoff rate of discrete memoryless channels. This upper bound, which coincides with a known lower bound, determines the cutoff rate, and settles a long-standing open problem. © 1988 IEE
Sequential decoding on intersymbol interference channels with application to magnetic recording
Ankara : Department of Electrical and Electronics Engineering and the Institute of Engineering and Sciences of Bilkent University, 1990.Thesis (Master's) -- Bilkent University, 1990.Includes bibliographical references leaves 27-28In this work we treat sequential decoding in the problem of sequence estimation on
intersymbol interference ( ISI ) channels. We consider the magnetic recording channel
as the particular ISI channel and investigate the coding gains that can be achieved with
sequential decoding for different information densities. Since the cutoff rate determines
this quantity , we find lower bounds to the cutoff rate.
The symmetric cutoff rate is computed as a theoretical lower bound and practical
lower bounds are found through simulations. Since the optimum decoding metric is
impractical, a sub-optimum metric has been used in the simulations. The results show
that this metric can not achieve the cutoff rate in general, but still its performance is
not far from that of the optimum metric.
We compare the results to those of Immink[9] and see that one can achieve positive
coding gains at information densities of practical interest where other practical codes
used in magnetic recording show coding loss.Alanyalı, MuratM.S
Divergence radii and the strong converse exponent of classical-quantum channel coding with constant compositions
There are different inequivalent ways to define the R\'enyi capacity of a
channel for a fixed input distribution . In a 1995 paper Csisz\'ar has shown
that for classical discrete memoryless channels there is a distinguished such
quantity that has an operational interpretation as a generalized cutoff rate
for constant composition channel coding. We show that the analogous notion of
R\'enyi capacity, defined in terms of the sandwiched quantum R\'enyi
divergences, has the same operational interpretation in the strong converse
problem of classical-quantum channel coding. Denoting the constant composition
strong converse exponent for a memoryless classical-quantum channel with
composition and rate as , our main result is that where is the -weighted sandwiched R\'enyi
divergence radius of the image of the channel.Comment: 46 pages. V7: Added the strong converse exponent with cost constrain
On the Origin of Polar Coding
Polar coding was conceived originally as a technique for boosting the cutoff rate of sequential decoding, along the lines of earlier schemes of Pinsker and Massey. The key idea in boosting the cutoff rate is to take a vector channel (either given or artificially built), split it into multiple correlated subchannels, and employ a separate sequential decoder on each subchannel. Polar coding was originally designed to be a low-complexity recursive channel combining and splitting operation of this type, to be used as the inner code in a concatenated scheme with outer convolutional coding and sequential decoding. However, the polar inner code turned out to be so effective that no outer code was actually needed to achieve the original aim of boosting the cutoff rate to channel capacity. This paper explains the cutoff rate considerations that motivated the development of polar coding. © 2015 IEEE
Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels
A method is proposed, called channel polarization, to construct code
sequences that achieve the symmetric capacity of any given binary-input
discrete memoryless channel (B-DMC) . The symmetric capacity is the highest
rate achievable subject to using the input letters of the channel with equal
probability. Channel polarization refers to the fact that it is possible to
synthesize, out of independent copies of a given B-DMC , a second set of
binary-input channels such that, as becomes
large, the fraction of indices for which is near 1
approaches and the fraction for which is near 0
approaches . The polarized channels are
well-conditioned for channel coding: one need only send data at rate 1 through
those with capacity near 1 and at rate 0 through the remaining. Codes
constructed on the basis of this idea are called polar codes. The paper proves
that, given any B-DMC with and any target rate , there
exists a sequence of polar codes such that
has block-length , rate , and probability of
block error under successive cancellation decoding bounded as P_{e}(N,R) \le
\bigoh(N^{-\frac14}) independently of the code rate. This performance is
achievable by encoders and decoders with complexity for each.Comment: The version which appears in the IEEE Transactions on Information
Theory, July 200
Properties and Construction of Polar Codes
Recently, Ar{\i}kan introduced the method of channel polarization on which
one can construct efficient capacity-achieving codes, called polar codes, for
any binary discrete memoryless channel. In the thesis, we show that decoding
algorithm of polar codes, called successive cancellation decoding, can be
regarded as belief propagation decoding, which has been used for decoding of
low-density parity-check codes, on a tree graph. On the basis of the
observation, we show an efficient construction method of polar codes using
density evolution, which has been used for evaluation of the error probability
of belief propagation decoding on a tree graph. We further show that channel
polarization phenomenon and polar codes can be generalized to non-binary
discrete memoryless channels. Asymptotic performances of non-binary polar
codes, which use non-binary matrices called the Reed-Solomon matrices, are
better than asymptotic performances of the best explicitly known binary polar
code. We also find that the Reed-Solomon matrices are considered to be natural
generalization of the original binary channel polarization introduced by
Ar{\i}kan.Comment: Master thesis. The supervisor is Toshiyuki Tanaka. 24 pages, 3
figure
Coded Adaptive Linear Precoded Discrete Multitone Over PLC Channel
Discrete multitone modulation (DMT) systems exploit the capabilities of
orthogonal subcarriers to cope efficiently with narrowband interference, high
frequency attenuations and multipath fadings with the help of simple
equalization filters. Adaptive linear precoded discrete multitone (LP-DMT)
system is based on classical DMT, combined with a linear precoding component.
In this paper, we investigate the bit and energy allocation algorithm of an
adaptive LP-DMT system taking into account the channel coding scheme. A coded
adaptive LPDMT system is presented in the power line communication (PLC)
context with a loading algorithm which accommodates the channel coding gains in
bit and energy calculations. The performance of a concatenated channel coding
scheme, consisting of an inner Wei's 4-dimensional 16-states trellis code and
an outer Reed-Solomon code, in combination with the proposed algorithm is
analyzed. Theoretical coding gains are derived and simulation results are
presented for a fixed target bit error rate in a multicarrier scenario under
power spectral density constraint. Using a multipath model of PLC channel, it
is shown that the proposed coded adaptive LP-DMT system performs better than
coded DMT and can achieve higher throughput for PLC applications
Strong Converse Theorems for Classes of Multimessage Multicast Networks: A R\'enyi Divergence Approach
This paper establishes that the strong converse holds for some classes of
discrete memoryless multimessage multicast networks (DM-MMNs) whose
corresponding cut-set bounds are tight, i.e., coincide with the set of
achievable rate tuples. The strong converse for these classes of DM-MMNs
implies that all sequences of codes with rate tuples belonging to the exterior
of the cut-set bound have average error probabilities that necessarily tend to
one (and are not simply bounded away from zero). Examples in the classes of
DM-MMNs include wireless erasure networks, DM-MMNs consisting of independent
discrete memoryless channels (DMCs) as well as single-destination DM-MMNs
consisting of independent DMCs with destination feedback. Our elementary proof
technique leverages properties of the R\'enyi divergence.Comment: Submitted to IEEE Transactions on Information Theory, Jul 18, 2014.
Revised on Jul 31, 201
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