25 research outputs found
Optimal Thresholds for GMD Decoding with (L+1)/L-extended Bounded Distance Decoders
We investigate threshold-based multi-trial decoding of concatenated codes
with an inner Maximum-Likelihood decoder and an outer error/erasure
(L+1)/L-extended Bounded Distance decoder, i.e. a decoder which corrects e
errors and t erasures if e(L+1)/L + t <= d - 1, where d is the minimum distance
of the outer code and L is a positive integer. This is a generalization of
Forney's GMD decoding, which was considered only for L = 1, i.e. outer Bounded
Minimum Distance decoding. One important example for (L+1)/L-extended Bounded
Distance decoders is decoding of L-Interleaved Reed-Solomon codes. Our main
contribution is a threshold location formula, which allows to optimally erase
unreliable inner decoding results, for a given number of decoding trials and
parameter L. Thereby, the term optimal means that the residual codeword error
probability of the concatenated code is minimized. We give an estimation of
this probability for any number of decoding trials.Comment: Accepted for the 2010 IEEE International Symposium on Information
Theory, Austin, TX, USA, June 13 - 18, 2010. 5 pages, 2 figure
Solving Shift Register Problems over Skew Polynomial Rings using Module Minimisation
For many algebraic codes the main part of decoding can be reduced to a shift
register synthesis problem. In this paper we present an approach for solving
generalised shift register problems over skew polynomial rings which occur in
error and erasure decoding of -Interleaved Gabidulin codes. The algorithm
is based on module minimisation and has time complexity where
measures the size of the input problem.Comment: 10 pages, submitted to WCC 201
Decoding of Interleaved Reed-Solomon Codes Using Improved Power Decoding
We propose a new partial decoding algorithm for -interleaved Reed--Solomon
(IRS) codes that can decode, with high probability, a random error of relative
weight at all code rates , in time polynomial in the
code length . For , this is an asymptotic improvement over the previous
state-of-the-art for all rates, and the first improvement for in the
last years. The method combines collaborative decoding of IRS codes with
power decoding up to the Johnson radius.Comment: 5 pages, accepted at IEEE International Symposium on Information
Theory 201
On Error Decoding of Locally Repairable and Partial MDS Codes
We consider error decoding of locally repairable codes (LRC) and partial MDS
(PMDS) codes through interleaved decoding. For a specific class of LRCs we
investigate the success probability of interleaved decoding. For PMDS codes we
show that there is a wide range of parameters for which interleaved decoding
can increase their decoding radius beyond the minimum distance with the
probability of successful decoding approaching , when the code length goes
to infinity
Decoding Generalized Concatenated Codes Using Interleaved Reed-Solomon Codes
Generalized Concatenated codes are a code construction consisting of a number
of outer codes whose code symbols are protected by an inner code. As outer
codes, we assume the most frequently used Reed-Solomon codes; as inner code, we
assume some linear block code which can be decoded up to half its minimum
distance. Decoding up to half the minimum distance of Generalized Concatenated
codes is classically achieved by the Blokh-Zyablov-Dumer algorithm, which
iteratively decodes by first using the inner decoder to get an estimate of the
outer code words and then using an outer error/erasure decoder with a varying
number of erasures determined by a set of pre-calculated thresholds. In this
paper, a modified version of the Blokh-Zyablov-Dumer algorithm is proposed,
which exploits the fact that a number of outer Reed-Solomon codes with average
minimum distance d can be grouped into one single Interleaved Reed-Solomon code
which can be decoded beyond d/2. This allows to skip a number of decoding
iterations on the one hand and to reduce the complexity of each decoding
iteration significantly - while maintaining the decoding performance - on the
other.Comment: Proceedings of the 2008 IEEE International Symposium on Information
Theory, Toronto, ON, Canada, July 6 - 11, 2008. 5 pages, 2 figure
Decoding of Repeated-Root Cyclic Codes up to New Bounds on Their Minimum Distance
The well-known approach of Bose, Ray-Chaudhuri and Hocquenghem and its
generalization by Hartmann and Tzeng are lower bounds on the minimum distance
of simple-root cyclic codes. We generalize these two bounds to the case of
repeated-root cyclic codes and present a syndrome-based burst error decoding
algorithm with guaranteed decoding radius based on an associated folded cyclic
code. Furthermore, we present a third technique for bounding the minimum
Hamming distance based on the embedding of a given repeated-root cyclic code
into a repeated-root cyclic product code. A second quadratic-time probabilistic
burst error decoding procedure based on the third bound is outlined. Index
Terms Bound on the minimum distance, burst error, efficient decoding, folded
code, repeated-root cyclic code, repeated-root cyclic product cod