15 research outputs found
Channel combining and splitting for cutoff rate improvement
The cutoff rate of a discrete memoryless channel (DMC) is often
used as a figure of merit, alongside the channel capacity . Given a
channel consisting of two possibly correlated subchannels , , the
capacity function always satisfies , while there are
examples for which . This fact that cutoff rate can
be ``created'' by channel splitting was noticed by Massey in his study of an
optical modulation system modeled as a 'ary erasure channel. This paper
demonstrates that similar gains in cutoff rate can be achieved for general
DMC's by methods of channel combining and splitting. Relation of the proposed
method to Pinsker's early work on cutoff rate improvement and to Imai-Hirakawa
multi-level coding are also discussed.Comment: 5 pages, 7 figures, 2005 IEEE International Symposium on Information
Theory, Adelaide, Sept. 4-9, 200
Re-proving Channel Polarization Theorems: An Extremality and Robustness Analysis
The general subject considered in this thesis is a recently discovered coding
technique, polar coding, which is used to construct a class of error correction
codes with unique properties. In his ground-breaking work, Ar{\i}kan proved
that this class of codes, called polar codes, achieve the symmetric capacity
--- the mutual information evaluated at the uniform input distribution ---of
any stationary binary discrete memoryless channel with low complexity encoders
and decoders requiring in the order of operations in the
block-length . This discovery settled the long standing open problem left by
Shannon of finding low complexity codes achieving the channel capacity.
Polar coding settled an open problem in information theory, yet opened plenty
of challenging problems that need to be addressed. A significant part of this
thesis is dedicated to advancing the knowledge about this technique in two
directions. The first one provides a better understanding of polar coding by
generalizing some of the existing results and discussing their implications,
and the second one studies the robustness of the theory over communication
models introducing various forms of uncertainty or variations into the
probabilistic model of the channel.Comment: Preview of my PhD Thesis, EPFL, Lausanne, 2014. For the full version,
see http://people.epfl.ch/mine.alsan/publication
Space-Time Signal Design for Multilevel Polar Coding in Slow Fading Broadcast Channels
Slow fading broadcast channels can model a wide range of applications in
wireless networks. Due to delay requirements and the unavailability of the
channel state information at the transmitter (CSIT), these channels for many
applications are non-ergodic. The appropriate measure for designing signals in
non-ergodic channels is the outage probability. In this paper, we provide a
method to optimize STBCs based on the outage probability at moderate SNRs.
Multilevel polar coded-modulation is a new class of coded-modulation techniques
that benefits from low complexity decoders and simple rate matching. In this
paper, we derive the outage optimality condition for multistage decoding and
propose a rule for determining component code rates. We also derive an upper
bound on the outage probability of STBCs for designing the
set-partitioning-based labelling. Finally, due to the optimality of the
outage-minimized STBCs for long codes, we introduce a novel method for the
joint optimization of short-to-moderate length polar codes and STBCs
Efficient systematic turbo polar decoding based on optimized scaling factor and early termination mechanism
In this paper, an efficient early termination (ET) mechanism for systematic turbo-polar code (STPC) based on optimal estimation of scaling factor (SF) is proposed. The gradient of the regression line which best fits the distance between a priori and extrinsic information is used to estimate the SF. The multiplication of the extrinsic information by the proposed SF presents effectiveness in resolving the correlation issue between intrinsic and extrinsic reliability information traded between the two typical parallel concatenated soft-cancellation (SCAN) decoders. It is shown that the SF has improved the conventional STPC by about 0.3 dB with an interleaver length of 64 bits, and about 1 dB over the systematic polar code (SPC) at a bit error rate (BER) of . A new scheme is proposed as a stopping criterion, which is mainly based on the estimated value of SF at the second component decoder and the decoded frozen bits for each decoding iteration. It is shown that the proposed ET results in halving the average number of iterations (ANI) without adding considerable complexity. Moreover, the modified codes present comparable results in terms of BER to the codes that utilize fix number of iterations
Polar codes based OFDM-PLC systems in the presence of middleton class-A noise
© 2016 IEEE. The performance of power line communication (PLC) systems suffer mainly from non-Gaussian noise, commonly referred to as impulsive noise. To reduce the effect of this noise, various channel coding techniques have been studied in the literature over PLC channels. Unlike existing works, in this paper we investigate the performance and robustness of polar codes over impulsive noise PLC channels for different codeword lengths and noise scenarios in orthogonal frequency division multiplexing (OFDM) systems. In particular, insightful comparisons between hard decision (HD) decoding and soft decision (SD) decoding for the proposed system are made. Furthermore, we investigate the blanking and clipping techniques with polar codes for impulsive noise mitigation. In addition, for the sake of comparison, results for LDPC coding are also presented. The results show that polar codes can considerably improve the performance of PLC systems. It will also be demonstrated that SD decoding offers better performance than HD decoding and that as the codeword length is increased, the performance can be further improved
Polar codes for classical-quantum channels
Holevo, Schumacher, and Westmoreland's coding theorem guarantees the
existence of codes that are capacity-achieving for the task of sending
classical data over a channel with classical inputs and quantum outputs.
Although they demonstrated the existence of such codes, their proof does not
provide an explicit construction of codes for this task. The aim of the present
paper is to fill this gap by constructing near-explicit "polar" codes that are
capacity-achieving. The codes exploit the channel polarization phenomenon
observed by Arikan for the case of classical channels. Channel polarization is
an effect in which one can synthesize a set of channels, by "channel combining"
and "channel splitting," in which a fraction of the synthesized channels are
perfect for data transmission while the other fraction are completely useless
for data transmission, with the good fraction equal to the capacity of the
channel. The channel polarization effect then leads to a simple scheme for data
transmission: send the information bits through the perfect channels and
"frozen" bits through the useless ones. The main technical contributions of the
present paper are threefold. First, we leverage several known results from the
quantum information literature to demonstrate that the channel polarization
effect occurs for channels with classical inputs and quantum outputs. We then
construct linear polar codes based on this effect, and the encoding complexity
is O(N log N), where N is the blocklength of the code. We also demonstrate that
a quantum successive cancellation decoder works well, in the sense that the
word error rate decays exponentially with the blocklength of the code. For this
last result, we exploit Sen's recent "non-commutative union bound" that holds
for a sequence of projectors applied to a quantum state.Comment: 12 pages, 3 figures; v2 in IEEE format with minor changes; v3 final
version accepted for publication in the IEEE Transactions on Information
Theor
Secure Channel Coding Schemes based on Polar Codes
In this paper, we propose two new frameworks for joint encryption encoding schemes based on polar codes, namely efficient and secure joint secret/public key encryption channel coding schemes. The issue of using new coding structure, i.e. polar codes in McEliece-like and RN-like schemes is addressed. Cryptanalysis methods show that the proposed schemes have an acceptable level of security with a relatively smaller key size in comparison with the previous works. The results indicate that both schemes provide an efficient error performance and benefit from a higher code rate which can approach the channel capacity for large enough polar codes. The most important property of the proposed schemes is that if we increase the block length of the code, we can have a higher code rate and higher level of security without significant changes in the key size of the scheme. The resulted characteristics of the proposed schemes make them suitable for high-speed communications, such as deep space communication systems
Polaractivation of Hidden Private Classical Capacity Region of Quantum Channels
We define a new phenomenon for communication over noisy quantum channels. The
investigated solution is called polaractivation and based on quantum polar
encoding. Polaractivation is a natural consequence of the channel polarization
effect in quantum systems and makes possible to open the hidden capacity
regions of a noisy quantum channel by using the idea of rate increment. While
in case of a classical channel only the rate of classical communication can be
increased, in case of a quantum channel the channel polarization and the rate
improvement can be exploited to open unreachable capacity regions. We
demonstrate the results for the opening of private classical capacity-domain.
We prove that the method works for arbitrary quantum channels if a given
criteria in the symmetric classical capacity is satisfied. We also derived a
necessary lower bound on the rate of classical communication for the
polaractivation of private classical capacity-domain.Comment: 49 pages, 13 figures (with supplemental material), minor changes,
Journal-ref: IEEE Symposium on Quantum Computing and Computational
Intelligence 2013 (IEEE QCCI 2013