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Contact:
Marcus Greferath
School of Math. Sciences
University College Dublin
Belfield, Dublin 4, Ireland
Phone:
+353-1-716-2588 (UCD)
+353-85-153-0951 (mobile)
Joachim Rosenthal
Institut of Mathematics
University of Zurich
Winterthurerstrasse 190
8057 Zurich, Switzerland
Phone:
+41-44-63 55884 (office)
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ITW 2010 Dublin
IEEE Information Theory Workshop
Dublin, August 30 - September 3, 2010
Polar and LDPC codes
Tue 31 Aug, 14.40-15.40, Room 1
Contributed session
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Eran Hof, Igal Sason, and Shlomo Shamai
Polar Coding for Reliable Communications over Parallel Channels
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Abstract:
A capacity-achieving polar coding scheme is introduced for reliable
communications over a set of parallel communication channels. They
are assumed to be arbitrarily-permuted memoryless binary-input and
output-symmetric (MBIOS) channels, and they form a set of
(stochastically) degraded channels. The general case where the
parallel channels are not necessarily degraded is addressed in the
full paper version, though the suggested scheme is
not capacity-achieving in the general case.
Tue 31 Aug, 14.40-15.00, Room 1
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Ryuhei Mori and Toshiyuki Tanaka
Non-Binary Polar Codes using Reed-Solomon Codes and Algebraic Geometry Codes
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Abstract:
Polar codes, introduced by Arιkan, achieve symmetric capacity of
any discrete memoryless channels under low encoding and decoding
complexity. Recently, non-binary polar codes have been
investigated. In this paper, we calculate error probability of
non-binary polar codes constructed on the basis of Reed-Solomon
matrices by numerical simulations. It is confirmed that 4-ary polar
codes have significantly better performance than binary polar codes
on binary-input AWGN channel. We also discuss an interpretation of
polar codes in terms of algebraic geometry codes, and further show
that polar codes using Hermitian codes have asymptotically good
performance.
Tue 31 Aug, 15.00-15.20, Room 1
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Naveen Goela, Satish Babu Korada, and Michael Gastpar
On LP Decoding of Polar Codes
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Abstract:
Polar codes are the first codes to provably achieve capacity on the
symmetric binary-input discrete memoryless channel (B-DMC) with low
encoding and decoding complexity. The parity check matrix of polar
codes is high-density and we show that linear program (LP) decoding
fails on the fundamental polytope of the parity check matrix. The
recursive structure of the code permits a sparse factor graph
representation. We define a new polytope based on the fundamental
polytope of the sparse graph representation. This new polytope
P is defined in a space of dimension O(N log N) where
N is the block length. We prove that the projection of
P in the original space is tighter than the fundamental
polytope based on the parity check matrix. The LP decoder over
P obtains the ML-certificate property. In the case of
the binary erasure channel (BEC), the new LP decoder is equivalent
to the belief propagation (BP) decoder operating on the sparse
factor graph representation, and hence achieves capacity. Simulation
results of SC (successive cancelation) decoding, LP decoding over
tightened polytopes, and (ML) maximum likelihood decoding are
provided. For channels other than the BEC, we discuss why LP
decoding over P with a linear objective function is
insufficient.
Tue 31 Aug, 15.20-15.40, Room 1
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