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Table 1 Number of operations required to achieve a low BER in the TPCs and the iVTCs

From: Irregular Vector Turbo Codes with low complexity

Code

Mod

Iterations

Operations

\(\%{\Delta }\)

TPC

iVTC/R

TPC

iVTC

(63,57)

BPSK

3

6/0.77

8694

10,206

− 17.3

QPSK

7

9/0.77

20,286

15,309

24.5

16QAM

8

7/0.77

23,184

11,907

48.6

64QAM

2

4/0.77

5796

6804

− 17.3

(127,120)

BPSK

5

17/0.90

29,210

55,233

− 89.0

10/0.88

32,490

− 11.2

6/0.85

19,494

33.2

QPSK

10

11/0.90

58,420

35,739

38.8

38/0.88

123,462

− 111.3

18/0.85

58,482

− 0.1

16QAM

10

14/0.90

58,420

45,486

22.1

13/0.88

42,237

27.7

16/0.85

51,984

11.0

64QAM

7

9/0.90

40,894

29,241

28.4

13/0.88

42,237

3.2

14/0.85

45,486

− 11.2

(255,247)

BPSK

11

10/0.93

129,030

68,850

46.6

QPSK

15

15/0.93

175,950

103,275

41.3

16QAM

10

17/0.93

117,300

117,045

0.2

64QAM

8

11/0.93

93,840

75,735

19.2

  1. aThe (63, 57), (127, 120) and (255, 247)TPC have fixed code rates of 0.82, 0.89 and 0.94, respectively. \(\%{\Delta }\) in the table stands for the percentage change in the decoding operations with respect to TPC, R the iVTC code rate, operations as the number of operations and Mod as Modulation