9,610 research outputs found
1 Burst List Decoding of Interleaved Reed–Solomon Codes
Abstract—It is shown that interleaved Reed–Solomon codes can be list-decoded for burst errors while attaining the generalized Reiger bound for list decoding. A respective decoding algorithm is presented which is (significantly) more efficient than a burst list decoder for a non-interleaved Reed–Solomon code with comparable parameters. Finally, it is shown through counterexamples that, unlike the special case of Reed–Solomon codes, interleaving does not always preserve the list decoding properties of the constituent code. Index Terms—Burst errors, interleaving, list decoding, Reed– Solomon codes, Reiger bound. I
On Burst Error Correction and Storage Security of Noisy Data
Secure storage of noisy data for authentication purposes usually involves the
use of error correcting codes. We propose a new model scenario involving burst
errors and present for that several constructions.Comment: to be presented at MTNS 201
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
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
A study of digital holographic filters generation. Phase 2: Digital data communication system, volume 1
An empirical study of the performance of the Viterbi decoders in bursty channels was carried out and an improved algebraic decoder for nonsystematic codes was developed. The hybrid algorithm was simulated for the (2,1), k = 7 code on a computer using 20 channels having various error statistics, ranging from pure random error to pure bursty channels. The hybrid system outperformed both the algebraic and the Viterbi decoders in every case, except the 1% random error channel where the Viterbi decoder had one bit less decoding error
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