2,181 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
Optimal Threshold-Based Multi-Trial Error/Erasure Decoding with the Guruswami-Sudan Algorithm
Traditionally, multi-trial error/erasure decoding of Reed-Solomon (RS) codes
is based on Bounded Minimum Distance (BMD) decoders with an erasure option.
Such decoders have error/erasure tradeoff factor L=2, which means that an error
is twice as expensive as an erasure in terms of the code's minimum distance.
The Guruswami-Sudan (GS) list decoder can be considered as state of the art in
algebraic decoding of RS codes. Besides an erasure option, it allows to adjust
L to values in the range 1<L<=2. Based on previous work, we provide formulae
which allow to optimally (in terms of residual codeword error probability)
exploit the erasure option of decoders with arbitrary L, if the decoder can be
used z>=1 times. We show that BMD decoders with z_BMD decoding trials can
result in lower residual codeword error probability than GS decoders with z_GS
trials, if z_BMD is only slightly larger than z_GS. This is of practical
interest since BMD decoders generally have lower computational complexity than
GS decoders.Comment: Accepted for the 2011 IEEE International Symposium on Information
Theory, St. Petersburg, Russia, July 31 - August 05, 2011. 5 pages, 2 figure
Self-concatenated code design and its application in power-efficient cooperative communications
In this tutorial, we have focused on the design of binary self-concatenated coding schemes with the help of EXtrinsic Information Transfer (EXIT) charts and Union bound analysis. The design methodology of future iteratively decoded self-concatenated aided cooperative communication schemes is presented. In doing so, we will identify the most important milestones in the area of channel coding, concatenated coding schemes and cooperative communication systems till date and suggest future research directions
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