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Table 4 The usage number of four arithmetic operators per decoding of a single row/column vector required in the error correction of the proposed syndrome-based decoding algorithm (reference to Fig. 1)

From: An advanced low-complexity decoding algorithm for turbo product codes based on the syndrome

\(N_{c,t}^{\text {DEC}}\)AdditionMultiplicationComparisonModulo-2
 (c=1)(c=2)(c=3)(c=4)
NoHISOn2n2nkn(nk)
error(t=1)    
 HDD-basedn3nn(d+2)−k+1n(nk+1)
SingleHISO (t=2)    
errorSISOn(2p−1+2)n(2p−1+3)2p−1(2n+3)(2p−1−1)(n2nk+k+p)
 (t=3)  +n(d+1)−k−4+n(nk+1)
 BFHDD-n3nn(d+2)−kd+5n(nk+1)
DoubleHISO (t=4)    
errorSISOn(2p−1+2)n(2p−1+3)2p−1(2n+3)(2p−1−1)(n2nk+k+p)
 (t=5)  +n(d+1)−dk+n(nk+1)