1,261 research outputs found
On the Construction and Decoding of Concatenated Polar Codes
A scheme for concatenating the recently invented polar codes with interleaved
block codes is considered. By concatenating binary polar codes with interleaved
Reed-Solomon codes, we prove that the proposed concatenation scheme captures
the capacity-achieving property of polar codes, while having a significantly
better error-decay rate. We show that for any , and total frame
length , the parameters of the scheme can be set such that the frame error
probability is less than , while the scheme is still
capacity achieving. This improves upon 2^{-N^{0.5-\eps}}, the frame error
probability of Arikan's polar codes. We also propose decoding algorithms for
concatenated polar codes, which significantly improve the error-rate
performance at finite block lengths while preserving the low decoding
complexity
An efficient length- and rate-preserving concatenation of polar and repetition codes
We improve the method in \cite{Seidl:10} for increasing the finite-lengh
performance of polar codes by protecting specific, less reliable symbols with
simple outer repetition codes. Decoding of the scheme integrates easily in the
known successive decoding algorithms for polar codes. Overall rate and block
length remain unchanged, the decoding complexity is at most doubled. A
comparison to related methods for performance improvement of polar codes is
drawn.Comment: to be presented at International Zurich Seminar (IZS) 201
Concatenated Polar Codes
Polar codes have attracted much recent attention as the first codes with low
computational complexity that provably achieve optimal rate-regions for a large
class of information-theoretic problems. One significant drawback, however, is
that for current constructions the probability of error decays
sub-exponentially in the block-length (more detailed designs improve the
probability of error at the cost of significantly increased computational
complexity \cite{KorUS09}). In this work we show how the the classical idea of
code concatenation -- using "short" polar codes as inner codes and a
"high-rate" Reed-Solomon code as the outer code -- results in substantially
improved performance. In particular, code concatenation with a careful choice
of parameters boosts the rate of decay of the probability of error to almost
exponential in the block-length with essentially no loss in computational
complexity. We demonstrate such performance improvements for three sets of
information-theoretic problems -- a classical point-to-point channel coding
problem, a class of multiple-input multiple output channel coding problems, and
some network source coding problems
Polar Coding for the Large Hadron Collider: Challenges in Code Concatenation
In this work, we present a concatenated repetition-polar coding scheme that
is aimed at applications requiring highly unbalanced unequal bit-error
protection, such as the Beam Interlock System of the Large Hadron Collider at
CERN. Even though this concatenation scheme is simple, it reveals significant
challenges that may be encountered when designing a concatenated scheme that
uses a polar code as an inner code, such as error correlation and unusual
decision log-likelihood ratio distributions. We explain and analyze these
challenges and we propose two ways to overcome them.Comment: Presented at the 51st Asilomar Conference on Signals, Systems, and
Computers, November 201
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