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
| \(N_{c,t}^{\text {DEC}}\) | Addition | Multiplication | Comparison | Modulo-2 | |
|---|---|---|---|---|---|
| (c=1) | (c=2) | (c=3) | (c=4) | ||
| No | HISO | n | 2n | 2n−k | n(n−k) |
| error | (t=1) | ||||
| HDD-based | n | 3n | n(d+2)−k+1 | n(n−k+1) | |
| Single | HISO (t=2) | ||||
| error | SISO | n(2p−1+2) | n(2p−1+3) | 2p−1(2n+3) | (2p−1−1)(n2−nk+k+p) |
| (t=3) | +n(d+1)−k−4 | +n(n−k+1) | |||
| BFHDD- | n | 3n | n(d+2)−k−d+5 | n(n−k+1) | |
| Double | HISO (t=4) | ||||
| error | SISO | n(2p−1+2) | n(2p−1+3) | 2p−1(2n+3) | (2p−1−1)(n2−nk+k+p) |
| (t=5) | +n(d+1)−d−k | +n(n−k+1) | |||