1,272 research outputs found
Fast syndrome-based Chase decoding of binary BCH codes through Wu list decoding
We present a new fast Chase decoding algorithm for binary BCH codes. The new
algorithm reduces the complexity in comparison to a recent fast Chase decoding
algorithm for Reed--Solomon (RS) codes by the authors (IEEE Trans. IT, 2022),
by requiring only a single Koetter iteration per edge of the decoding tree. In
comparison to the fast Chase algorithms presented by Kamiya (IEEE Trans. IT,
2001) and Wu (IEEE Trans. IT, 2012) for binary BCH codes, the polynomials
updated throughout the algorithm of the current paper typically have a much
lower degree.
To achieve the complexity reduction, we build on a new isomorphism between
two solution modules in the binary case, and on a degenerate case of the
soft-decision (SD) version of the Wu list decoding algorithm. Roughly speaking,
we prove that when the maximum list size is in Wu list decoding of binary
BCH codes, assigning a multiplicity of to a coordinate has the same effect
as flipping this coordinate in a Chase-decoding trial.
The solution-module isomorphism also provides a systematic way to benefit
from the binary alphabet for reducing the complexity in bounded-distance
hard-decision (HD) decoding. Along the way, we briefly develop the
Groebner-bases formulation of the Wu list decoding algorithm for binary BCH
codes, which is missing in the literature
Iterative Algebraic Soft-Decision List Decoding of Reed-Solomon Codes
In this paper, we present an iterative soft-decision decoding algorithm for
Reed-Solomon codes offering both complexity and performance advantages over
previously known decoding algorithms. Our algorithm is a list decoding
algorithm which combines two powerful soft decision decoding techniques which
were previously regarded in the literature as competitive, namely, the
Koetter-Vardy algebraic soft-decision decoding algorithm and belief-propagation
based on adaptive parity check matrices, recently proposed by Jiang and
Narayanan. Building on the Jiang-Narayanan algorithm, we present a
belief-propagation based algorithm with a significant reduction in
computational complexity. We introduce the concept of using a
belief-propagation based decoder to enhance the soft-input information prior to
decoding with an algebraic soft-decision decoder. Our algorithm can also be
viewed as an interpolation multiplicity assignment scheme for algebraic
soft-decision decoding of Reed-Solomon codes.Comment: Submitted to IEEE for publication in Jan 200
Iterative Soft Input Soft Output Decoding of Reed-Solomon Codes by Adapting the Parity Check Matrix
An iterative algorithm is presented for soft-input-soft-output (SISO)
decoding of Reed-Solomon (RS) codes. The proposed iterative algorithm uses the
sum product algorithm (SPA) in conjunction with a binary parity check matrix of
the RS code. The novelty is in reducing a submatrix of the binary parity check
matrix that corresponds to less reliable bits to a sparse nature before the SPA
is applied at each iteration. The proposed algorithm can be geometrically
interpreted as a two-stage gradient descent with an adaptive potential
function. This adaptive procedure is crucial to the convergence behavior of the
gradient descent algorithm and, therefore, significantly improves the
performance. Simulation results show that the proposed decoding algorithm and
its variations provide significant gain over hard decision decoding (HDD) and
compare favorably with other popular soft decision decoding methods.Comment: 10 pages, 10 figures, final version accepted by IEEE Trans. on
Information Theor
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
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