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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Vydané v:	IEEE transactions on information theory Ročník 56; číslo 4; s. 1574 - 1581
Hlavný autor:	Armand, M.A.
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York, NY IEEE 01.04.2010 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	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
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Shrnutí:	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.
Bibliografia:	SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-2 content type line 23
ISSN:	0018-9448 1557-9654
DOI:	10.1109/TIT.2010.2040943