Title :
A Note on Interleaved Reed–Solomon Codes Over Galois Rings
Author_Institution :
Dept. of Electr. & Comput. Eng., Nat. Univ. of Singapore, Singapore, Singapore
fDate :
4/1/2010 12:00:00 AM
Abstract :
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 2-6n+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.
Keywords :
Galois fields; Reed-Solomon codes; computational complexity; probability; Galois rings; collaborative decoding; decoding complexity; decoding failure probability; interleaved Reed-Solomon codes; multisequence shift register synthesis; word error probability; Collaboration; Collaborative work; Cyclic redundancy check; Decoding; Error probability; Galois fields; Geometry; Interleaved codes; Network synthesis; Shift registers; Collaborative decoding; Galois rings; codes over rings; interleaved Reed–Solomon (RS) codes; multisequence shift register synthesis;
Journal_Title :
Information Theory, IEEE Transactions on
DOI :
10.1109/TIT.2010.2040943