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 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.