A Note on Interleaved Reed-Solomon Codes Over Galois Rings

Collaborative decoding of interleaved Reed-Solomon (RS) codes was first proposed by Krachkovsky in 1997. Their work has since sparked off a series of papers from various authors on the subject. In this paper, we study the merits of multisequence-shift-register-synthesis-based collaborative decoding...

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Bibliographic Details
Published in:IEEE transactions on information theory Vol. 56; no. 4; pp. 1574 - 1581
Main Author: Armand, M.A.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.04.2010
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Applied sciences
Codes
codes over rings
Coding, codes
Collaboration
Collaborative decoding
Collaborative work
Cyclic redundancy check
Decoders
Decoding
Error analysis
Error probability
Errors
Exact sciences and technology
Galois fields
Galois rings
Geometry
Information theory
Information, signal and communications theory
Interleaved codes
interleaved Reed-Solomon (RS) codes
Mathematical analysis
Mathematical functions
multisequence shift register synthesis
Network synthesis
Probability
Reed-Solomon codes
Reproduction
Shift registers
Signal and communications theory
Studies
Telecommunications and information theory
Reed Solomon code
Performance evaluation
Finite field
Error probability
interleaved Reed-Solomon (RS) codes
Galois rings
codes over rings
Decoding
Failures
Collaborative decoding
Shift register
Algorithm complexity
Interleaved codes
multisequence shift register synthesis
ISSN:0018-9448, 1557-9654
Online Access:Get full text
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Summary:Collaborative decoding of interleaved Reed-Solomon (RS) codes was first proposed by Krachkovsky in 1997. Their work has since sparked off a series of papers from various authors on the subject. In this paper, we study the merits of multisequence-shift-register-synthesis-based collaborative decoding of interleaved RS codes formed from RS codes over Galois rings, in terms of key performance measures such as the probabilty of decoding failure and word error probability. In particular, we show that when ¿ is even and large but not exceeding ¿ (n -3+¿( n 2 -6 n +1))/2¿, a q ¿ -ary interleaved code formed from ¿/2 parallel copies of a length- n RS code of rate greater than 1-( ¿+3+(2/¿))/ n over a Galois ring of cardinality q 2 , can be on par with its finite field counterpart formed from ¿ parallel copies of an RS code of the same length and rate over F q , in terms of the word error probabilities of their respective decoders, while incurring lower decoding complexity.
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ISSN:0018-9448
1557-9654
DOI:10.1109/TIT.2010.2040943