IP Library › Granted Patent US 8,375,280
Granted Patent B2
US 8,375,280 · App. 12/260,340 · Granted Feb 12, 2013

Optimum distance spectrum feedforward tail-biting convolutional codes

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Quick Facts
Patent No.
US 8,375,280
App. No.
12/260,340
Granted
Feb 12, 2013
Kind
B2
Abstract

A method of generating a set of generator polynomials for use as a tail biting convolution code to operate on data transmitted over a channel comprises: (1) selecting valid combinations of generator polynomials to include in a pool of potential codes, each valid combination being a potential code; (2) determining first lines of a weight spectrum for each potential code in the pool and including potential codes of the pool having best first lines in a candidate set; (3) determining best codes of the candidate set based on the first L number of lines in the weight spectrum; (4) selecting an optimum code(s) from the best codes; and (5) configuring a shift register circuit(s) of a data transceiver to implement the optimum code(s).

Claims (4317)

1. A method of generating a set of generator polynomials for use as a tail biting convolution code to operate on data transmitted over a channel, the method comprising: (1) selecting valid combinations of generator polynomials to include in a pool of potential codes, each valid combination being a potential code; (2) determining first lines of a weight spectrum for each potential code in the pool and including potential codes of the pool having best first lines in a candidate set; (3) determining best codes of the candidate set based on a first L number of lines in the weight spectrum, L being an integer greater than one; (4) selecting an optimum code(s) from the best codes; (5) configuring a shift register circuit(s) of a data transceiver to implement the optimum code(s).

2. The method of claim 1 , further comprising using a free distance parameter and a multiplicity parameter for selecting the optimum code(s) from the best codes.

3. The method of claim 1 , further comprising using a free distance parameter and a bit multiplicity parameter for selecting the optimum code(s) from the best codes.

4. The method of claim 1 , further comprising using the shift register circuit configured in accordance with the optimum code to append error correction information to data transmitted over the channel.

5. A node of a communications network which participates in data transmissions over a channel, the node comprising: a transceiver configured to send and receive data over the channel; a shift register circuit configured to implement an optimum tail biting convolutional code for operating on the data transmitted over the channel, the optimum code having been generated by performing the acts of claim 1 .

6. The apparatus of claim 5 , further comprising: plural shift register circuits, each of the shift register circuits being configured to implement a respective different one of plural optimum tail biting convolutional codes, each of the plural optimum tail biting convolutional codes being of a different rate and having been generated by performing the acts of claim 1 ; a code activator configured to include one of the plural shift register circuits in a processing stream for a respective data transmission over the channel.

7. The apparatus of claim 5 , wherein the shift register circuit comprises an encoder configured to append error correction information to data transmitted over the channel.

8. The method of claim 1 , wherein the optimum code is expressed by a set of polynomials listed in any of Table 2-Table 21, polynomials being shown in octal notation in column G of Table 2-Table 21:

TABLE 1

NEW ODS FEEDFORWARD TBCC WITH

RATE ¼ AND CONSTRAINT LENGTH V = 2

#

permutation

equivalent

K

G

WS

codes

Note

3

(1, 1, 3, 5)

(6, 4, 6)

30

ODS-BER

6

(1, 3, 5, 7)

(8, 6, 6)

6

ODS-BER

8

(3, 5, 7, 7)

(10, 16, 24)

2

ODS-FER/BER

9

(3, 5, 7, 7)

(10, 18, 27)

2

ODS-FER/BER

TABLE 2

NEW ODS FEEDFORWARD TBCC WITH

RATE ¼ AND CONSTRAINT LENGTH V = 3

#

permutation

equivalent

K

G

WS

codes

Note

3

(4, 4, 14, 50)

(6, 4, 6)

372

ODS-BER

9

(44, 54, 64, 74)

(12, 12, 18)

1

ODS-BER

TABLE 3

NEW ODS FEEDFORWARD TBCC WITH

RATE ¼ AND CONSTRAINT LENGTH V = 4

#

permutation

equivalent

K

G

WS

codes

Note

3

(2, 2, 6, 42)

(6, 4, 6)

5238

ODS-BER

5

(2, 6, 16, 52)

(9, 10, 20)

1058

ODS-FER/BER

6

(2, 6, 26, 76)

(10, 9, 18)

120

ODS-FER/BER

10

(26, 36, 46, 56)

(14, 30, 60)

8

ODS-FER/BER

11

(46, 52, 56, 76)

(15, 22, 66)

2

ODS-BER

TABLE 4

NEW ODS FEEDFORWARD TBCC WITH

RATE ¼ AND CONSTRAINT LENGTH V = 5

#

permutation

equivalent

K

G

WS

codes

Note

3

(1, 1, 3, 41)

(6, 4, 6)

78273

ODS-BER

5

(1, 3, 7, 52)

(9, 10, 20)

17596

ODS-FER/BER

6

(1, 3, 13, 57)

(10, 9, 18)

2352

ODS-FER/BER

8

(1, 23, 45, 77)

(12, 8, 16)

72

ODS-FER/BER

9

(13, 17, 23, 56)

(14, 72, 261)

60

ODS-FER/BER

10

(27, 47, 57, 61)

(16, 285, 1350)

4

ODS-FER/BER

14

(45, 53, 73, 77)

(18, 84, 364)

2

ODS-BER

16

(47, 53, 67, 75)

(18, 48, 96)

2

ODS-FER

16

(45, 53, 73, 77)

(18, 48, 80)

2

ODS-BER

17

(47, 53, 67, 75)

(18, 51, 102)

2

ODS-FER

17

(45, 53, 73, 77)

(18, 51, 85)

2

ODS-BER

18

(47, 53, 67, 75)

(18, 54, 108)

2

ODS-FER

18

(45, 53, 73, 77)

(18, 54, 90)

2

ODS-BER

19

(45, 57, 67, 75)

(18, 57, 95)

2

ODS-FER/BER

20

(45, 57, 67, 75)

(18, 60, 100)

2

ODS-FER/BER

21

(45, 57, 67, 75)

(18, 63, 105)

2

ODS-FER/BER

24

(45, 57, 67, 75)

(18, 72, 120)

2

ODS-FER/BER

TABLE 5

NEW ODS FEEDFORWARD TBCC WITH

RATE ¼ AND CONSTRAINT LENGTH V = 6

#

permutation

equivalent

K

G

WS

codes

Note

2

(4, 4, 4, 410)

(5, 2, 2)

1279360

ODS-FER/BER

3

(4, 4, 14, 430)

(6, 3, 6)

791712

ODS-FER

(4, 4, 14, 410)

(6, 4, 6)

1209060

ODS-BER

4

(4, 14, 24, 414)

(8, 11, 24)

460800

ODS-FER/BER

5

(4, 14, 34, 444)

(9, 10, 20)

281250

ODS-FER/BER

6

(4, 14, 54, 570)

(10, 9, 18)

36408

ODS-FER/BER

7

(4, 34, 174, 524)

(12, 28, 84)

6339

ODS-FER/BER

8

(4, 34, 114, 674)

(12, 8, 16)

1256

ODS-FER/BER

9

(4, 274, 454, 764)

(14, 72, 234)

112

ODS-FER/BER

10

(4, 374, 454, 534)

(16, 285, 1140)

28

ODS-FER/BER

11

(204, 214, 724, 774)

(16, 66, 286)

12

ODS-FER/BER

12

(424, 474, 704, 724)

(17, 60, 324)

2

ODS-FER

12

(224, 324, 354, 554)

(17, 72, 312)

16

ODS-BER

13

(134, 564, 634, 724)

(19, 325, 1963)

6

ODS-FER/BER

14

(114, 534, 664, 764)

(19, 182, 1106)

6

ODS-FER/BER

15

(464, 534, 564, 674)

(20, 285, 1815)

2

ODS-FER

15

(444, 654, 674, 734)

(20, 288, 1800)

2

ODS-BER

16

(454, 554, 724, 774)

(20, 64, 224)

2

ODS-FER/BER

17

(454, 474, 724, 754)

(20, 34, 51)

2

ODS-FER/BER

18

(474, 554, 624, 764)

(20, 36, 54)

2

ODS-FER

18

(454, 474, 724, 754)

(20, 36, 54)

2

ODS-BER

20

(474, 554, 624, 764)

(20, 40, 60)

2

ODS-FER/BER

TABLE 6

NEW ODS FEEDFORWARD TBCC WITH

RATE ⅓ AND CONSTRAINT LENGTH V = 2

#

permutation

equivalent

K

G

WS

codes

Note

3

(1, 1, 5)

(4, 3, 3)

12

ODS-FER/BER

TABLE 7

NEW ODS FEEDFORWARD TBCC WITH

RATE ⅓ AND CONSTRAINT LENGTH V = 3

#

permutation

equivalent

K

G

WS

codes

Note

7

(4, 54, 74)

(8, 35, 91)

8

ODS-BER

9

(34, 54, 74)

(8, 9, 18)

4

ODS-FER

9

(24, 54, 64)

(8, 9, 9)

2

ODS-BER

TABLE 8

NEW ODS FEEDFORWARD TBCC WITH

RATE ⅓ AND CONSTRAINT LENGTH V = 4

#

permutation

equivalent

K

G

WS

codes

Note

6

(2, 16, 56)

(8, 45, 120)

30

ODS-FER/BER

7

(2, 46, 76)

(8, 21, 56)

10

ODS-FER/BER

8

(2, 56, 66)

(8, 1, 8)

10

ODS-FER/BER

9

(16, 46, 56)

(10, 99, 405)

6

ODS-FER/BER

(26, 52, 56)

4

10

(46, 66, 72)

(10, 46, 240)

2

ODS-FER

10

(26, 36, 46)

(10, 52, 220)

8

ODS-BER

11

(46, 62, 76)

(10, 11, 22)

1

ODS-FER

11

(16, 56, 72)

(10, 11, 22)

3

ODS-BER

12

(46, 52, 72)

(10, 12, 12)

2

ODS-BER

15

(46, 56, 72)

(11, 15, 15)

2

ODS-FER/BER

TABLE 9

NEW ODS FEEDFORWARD TBCC WITH

RATE ⅓ AND CONSTRAINT LENGTH V = 5

#

permutation

equivalent

K

G

WS

codes

Note

6

(1, 7, 53)

(8, 45, 120)

156

ODS-FER/BER

7

(1, 7, 57)

(8, 21, 56)

124

ODS-FER/BER

8

(1, 27, 66)

(8, 1, 8)

52

ODS-FER/BER

9

(1, 47, 75)

(10, 99, 333)

24

ODS-FER/BER

10

(33, 43, 53)

(10, 21, 90)

4

ODS-FER/BER

12

(13, 37, 53)

(12, 202, 1008)

12

ODS-BER

17

(47, 57, 65)

(13, 34, 68)

2

ODS-BER

TABLE 10

NEW ODS FEEDFORWARD TBCC WITH RATE ⅓ AND

CONSTRAINT LENGTH V = 6

#

permutation

equivalent

K

G

WS

codes

Note

3

(4, 4, 410)

(4, 3, 3)

42984

ODS-FER/BER

6

(4, 34, 530)

(8, 45, 120)

1326

ODS-FER/BER

7

(4, 34, 534)

(8, 21, 56)

751

ODS-FER/BER

8

(4, 134, 614)

(8, 1, 8)

314

ODS-FER/BER

9

(4, 74, 554)

(10, 99, 306)

112

ODS-FER/BER

10

(154, 214, 530)

(10, 21, 90)

40

ODS-FER

10

(4, 314, 674)

(10, 26, 80)

28

ODS-BER

13

(434, 574, 664)

( 12, 39, 338)

2

ODS-FER

13

(104, 554, 574)

( 12, 39, 156)

6

ODS-BER

17

(474, 634, 654)

( 14, 51, 306)

2

ODS-FER

17

(574, 654, 764)

( 14, 51, 170)

1

ODS-BER

21

(464, 564, 674)

( 15, 84, 210)

2

ODS-BER

22

(474, 564, 664)

( 15, 66, 154)

2

ODS-BER

TABLE 11

NEW ODS FEEDFORWARD TBCC WITH RATE ⅓ AND

CONSTRAINT LENGTH V = 7

# permutation

equivalent

K

G

WS

codes

Note

4

(2, 6, 406)

(6, 12, 24)

200704

ODS-FER/BER

5

(2, 16, 422)

(7, 15, 35)

49000

ODS-FER/BER

6

(2, 16, 452)

(8, 45, 120)

10584

ODS-FER/BER

7

(2, 16, 534)

(8, 21, 56)

6318

ODS-FER/BER

8

(2, 56, 432)

(8, 1, 8)

1224

ODS-FER/BER

9

(2, 36, 466)

(10, 99, 306)

736

ODS-FER/BER

10

(2, 216, 566)

(10, 21, 70)

128

ODS-FER/BER

11

(2, 456, 722)

(11, 33, 121)

8

ODS-FER/BER

12

(26, 126, 646)

(12, 178, 948)

48

ODS-FER

12

(2, 336, 516)

(12, 186, 732)

32

ODS-BER

13

(126, 232, 532)

(12, 39, 208)

20

ODS-FER

13

(276, 442, 776)

(12, 39, 130)

4

ODS-BER

14

(226, 422, 476)

( 13, 112, 672)

4

ODS-FER

14

(566, 716, 736)

( 13, 112, 616)

2

ODS-BER

15

(156, 332, 452)

( 14, 330, 2535)

12

ODS-FER

15

(146, 316, 722)

(14, 375, 2280)

12

ODS-BER

16

(316, 336, 452)

(14, 64, 480)

8

ODS-FER/BER

17

(266, 512, 746)

(15, 238, 1700)

4

ODS-FER/BER

18

(256, 662, 746)

(16, 837, 7146)

4

ODS-FER/BER

19

(232, 632, 766)

(16, 342, 2090)

4

ODS-FER/BER

20

(452, 476, 756)

(16, 130, 1120)

2

ODS-FER

20

(456, 476, 666)

(16, 180, 920)

2

ODS-BER

21

(526, 572, 636)

(16, 63, 378)

2

ODS-FER

21

(422, 726, 736)

(16, 84, 273)

2

ODS-BER

22

(456, 626, 772)

(16, 22, 44)

2

ODS-FER

22

(476, 572, 632)

(16, 22, 44)

2

ODS-BER

24

(472, 562, 676)

(16, 24, 48)

2

ODS-FER

24

(462, 532, 736)

(16, 27, 48)

2

ODS-BER

25

(462, 532, 736)

(16, 25, 25)

2

ODS-FER/BER

26

(462, 532, 736)

(16, 26, 26)

2

ODS-FER/BER

TABLE 12

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 2

#

permutation

equivalent

K

G

WS

codes

Note

2

(1, 4)

(2, 2, 2)

5

ODS-BER

5

(1, 7)

(4, 15, 30)

3

ODS-BER

7

(3, 7)

(4, 7, 14)

2

ODS-FER/BER

TABLE 13

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 3

#

permutation

equivalent

K

G

WS

codes

Note

2

(4, 40)

(2, 2, 2)

19

ODS-BER

5

(4, 74)

(4, 10, 20)

4

ODS-FER/BER

6

(14, 70)

(4, 9, 24)

2

ODS-BER

7

(4, 74)

(4, 7, 14)

4

ODS-FER/BER

12

(34, 54)

(6, 64, 192)

4

ODS-BER

TABLE 14

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 4

# permutation

equivalent

K

G

WS

codes

Note

2

(2, 40)

(2, 2, 2)

74

ODS-BER

5

(2, 56)

(4, 10, 20)

17

ODS-FER/BER

6

(2, 56)

(4, 6, 12)

10

ODS-FER/BER

7

(2, 66)

(4, 7, 14)

7

ODS-FER/BER

8

(2, 56)

(5, 24, 56)

10

ODS-FER/BER

9

(16, 54)

(6, 102, 450)

4

ODS-FER/BER

10

(16, 54)

(6, 90, 390)

4

ODS-FER/BER

16

(46, 66)

(7, 64, 256)

2

ODS-BER

18

(46, 56)

(7, 54, 126)

2

ODS-FER/BER

19

(46, 66)

(7, 38, 76)

2

ODS-BER

20

(46, 66)

(7, 40, 80)

2

ODS-BER

22

(46, 66)

(7, 44, 88)

2

ODS-BER

23

(46, 66)

(7, 46, 92)

2

ODS-BER

TABLE 15

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 5

#

permutation

equivalent

K

G

WS

codes

Note

2

(1, 40)

(2, 2, 2)

292

ODS-BER

6

(1, 53)

(4, 6, 12)

16

ODS-FER/BER

7

(1, 53)

(4, 7, 14)

28

ODS-FER/BER

8

(1, 53)

(5, 24, 56)

16

ODS-FER/BER

9

(7, 54)

(6, 102, 450)

16

ODS-FER/BER

10

(13, 53)

(6, 40, 180)

6

ODS-FER/BER

12

(23, 47)

(6, 20, 120)

4

ODS-FER/BER

18

(37, 53)

(8, 117, 684)

4

ODS-BER

20

(43, 73)

(8, 100, 340)

2

ODS-BER

21

(23, 67)

(8, 84, 189)

4

ODS-BER

22

(57, 63)

(8, 44, 132)

2

ODS-FER

23

(45, 77)

(8, 46, 92)

2

ODS-FER/BER

TABLE 16

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 6

#

permutation

equivalent

K

G

WS

codes

Note

5

(4, 464)

(4, 10, 20)

225

ODS-FER/BER

6

(4, 530)

(4, 6, 12)

82

ODS-FER/BER

7

(4, 434)

(4, 7, 14)

54

ODS-FER/BER

8

(4, 434)

(5, 24, 56)

50

ODS-FER/BER

9

(4, 474)

(6, 102, 306)

28

ODS-FER/BER

11

(274, 574)

(7, 176, 880)

4

ODS-FER/BER

(474, 674)

2

13

(134, 670)

(7, 117, 611)

4

ODS-FER/BER

15

(114, 714)

(8, 450, 3120)

6

ODS-FER/BER

17

(374, 444)

(8, 187, 1156)

2

ODS-BER

19

(464, 744)

(8, 19, 190)

2

ODS-FER

19

(634, 734)

(8, 38, 190)

2

ODS-BER

TABLE 17

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 7

#

permutation

equivalent

K

G

WS

codes

Note

2

(2, 400)

(2, 2, 2)

4624

ODS-BER

6

(2, 452)

(4, 6, 12)

324

ODS-FER/BER

7

(2, 434)

(4, 7, 14)

348

ODS-FER/BER

8

(2, 426)

(5, 24, 56)

68

ODS-FER/BER

9

(2, 456)

(6, 102, 306)

40

ODS-FER/BER

10

(2, 476)

(6, 40, 120)

16

ODS-FER/BER

11

(2, 556)

(7, 176, 616)

16

ODS-FER/BER

13

(56, 670)

(7, 117, 611)

6

ODS-FER/BER

14

(76, 654)

(8, 546, 3640)

2

ODS-FER/BER

(112, 472)

6

(256, 626)

4

(266, 602)

4

(316, 412)

4

15

(376, 412)

(8, 450, 2955)

4

ODS-FER/BER

16

(36, 564)

(8, 238, 1776)

2

ODS-FER/BER

17

(146, 534)

(8, 153, 1190)

4

ODS-FER

17

(176, 444)

(8, 187, 1156)

2

ODS-BER

18

(336, 646)

(8, 54, 468)

4

ODS-FER

18

(336, 676)

(8, 81, 432)

4

ODS-FER

19

(556, 736)

(8, 19, 152)

2

ODS-FER

21

(326, 576)

(10, 1722,

4

ODS-BER

15771)

22

(236, 626)

(10, 1298,

4

ODS-FER

13112)

22

(272, 634)

(10, 1364,

4

ODS-BER

12914)

24

(236, 652)

(10, 744, 6624)

4

ODS-BER

26

(276, 722)

(10, 143, 1118)

4

ODS-BER

27

(316, 466)

(10, 162, 567)

4

ODS-BER

28

(506, 772)

(10, 84, 224)

2

ODS-BER

31

(532, 746)

(10, 31, 124)

2

ODS-FER

31

(446, 756)

(10, 31, 62)

2

ODS-BER

32

(532, 746)

(10, 32, 128)

2

ODS-FER

33

(532, 746)

(10, 33, 132)

2

ODS-FER

33

(452, 766)

(10, 33, 66)

2

ODS-BER

34

(532, 746)

(10, 34, 136)

2

ODS-FER

35

(532, 746)

(10, 35, 140)

2

ODS-FER

35

(452, 766)

(10, 35, 70)

2

ODS-BER

36

(532, 746)

(10, 36, 144)

2

ODS-FER

36

(452, 766)

(10, 36, 72)

2

ODS-BER

37

(532, 746)

(10, 37, 148)

2

ODS-FER

38

(532, 746)

(10, 38, 152)

2

ODS-FER

TABLE 19

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 8

#

permutation

equivalent

K

G

WS

codes

Note

5

(1, 407)

(4, 10, 20)

3600

ODS-FER/BER

6

(1, 423)

(4, 6, 12)

1296

ODS-FER/BER

7

(1, 415)

(4, 7, 14)

1323

ODS-FER/BER

8

(1, 426)

(5, 24, 56)

624

ODS-FER/BER

9

(1, 447)

(6, 102, 306)

79

ODS-FER/BER

10

(1, 476)

(6, 40, 120)

4

ODS-FER/BER

11

(1, 556)

(7, 176, 616)

4

ODS-FER/BER

12

(1, 573)

(8, 759, 3036)

18

ODS-FER/BER

14

(1, 727)

(8, 546, 2184)

9

ODS-FER/BER

15

(177, 412)

( 8, 450, 2955)

4

ODS-FER/BER

16

(55, 727)

( 8, 238, 1744)

4

ODS-FER

16

(1, 557)

(8, 372, 1456)

18

ODS-BER

17

(433, 473)

(8, 153, 952)

2

ODS-FER/BER

18

(647, 657)

(8, 54, 324)

2

ODS-FER

18

(537, 737)

(8, 63, 324)

2

ODS-BER

19

(357, 737)

(8, 19, 38)

4

ODS-FER/BER

20

(303, 433)

( 9, 240, 2160)

4

ODS-FER/BER

21

(227, 615)

(10, 1680,

4

ODS-FER/BER

15729)

22

(133, 463)

(10, 1298,

6

ODS-BER

11704)

24

(475, 507)

( 10, 456, 4320)

2

ODS-BER

27

(67, 745)

(10, 54, 162)

8

ODS-BER

28

(233, 635)

( 11, 644, 7308)

4

ODS-BER

29

(233, 565)

( 11, 319, 3277)

4

ODS-FER/BER

32

(235, 557)

(12, 1568,

4

ODS-BER

15840)

38

(457, 755)

( 12, 380, 1520)

2

ODS-FER/BER

39

(463, 755)

( 12, 429, 1482)

2

ODS-BER

40

(463, 755)

( 12, 440, 1520)

2

ODS-BER

TABLE 20

NEW ODS FEEDFORWARD TBCC WITH RATE 1/5 AND

VARIOUS CONSTRAINT LENGTHS.

# permutation

equivalent

K

V

G

WS

codes

Note

12

2

(5, 5, 7, 7,7)

(13, 12, 12)

1

ODS-FER/BER

12

3

(54, 54, 64,

(16, 12, 24)

2

ODS-FER/BER

74, 74)

12

4

(52, 56, 66,

(20, 72, 216)

1

ODS-FER/BER

72, 76)

12

5

(37, 47, 55,

(22, 108, 504)

4

ODS-FER/BER

57, 65)

TABLE 21

NEW ODS FEEDFORWARD TBCC WITH RATE ⅖ AND

VARIOUS CONSTRAINT LENGTHS.

# permutation

equivalent

K

V

G

WS

codes

Note

12

3

(54, 64, 74) pl

(8, 51,

1

ODS-FER/BER

192)

12

4

(46, 56, 76) pl

(8, 15,

1

ODS-FER/BER

(62, 72, 76) pl

66)

1

12

5

(43, 57, 64) pl

(9, 78,

1

ODS-FER/BER

(13, 61, 75) p3

456)

3

(32, 43, 57) p3

2

5

(23, 55, 56) p2

(8, 6,

4

ODS-FER if

36)

p2 is used

5

(15, 57, 62) p2

(8, 6, 6)

3

ODS-BER if

p2 is used

12

6

(464, 474, 670) pl

(9, 72,

1

ODS-FER/BER

(544, 730, 744) p2

342)

1

(334, 464, 474) p3

2

12

7

(232, 236, 670) pl

(9, 72,

5

ODS-FER/BER

(232, 334, 474) p2

342)

3

(262, 730, 744) p2

1

(156, 232, 474) p3

6

(354, 362, 544) p3

 1.

9. A code generator comprising a computer which executes a computer program comprising instructions stored on a computer-readable medium which, when executed, performs the acts of: (1) selecting valid combinations of generator polynomials to include in a pool of potential codes, each valid combination being a potential code; (2) determining first lines of a weight spectrum for each potential code in the pool and including potential codes of the pool having best first lines in a candidate set; (3) determining best codes of the candidate set based on a first L number of lines in the weight spectrum, L being an integer greater than one; (4) selecting an optimum code(s) from the best codes; (5) outputting an identification of the optimum code(s).

10. The generator of claim 9 , wherein when executed the instructions further perform the act of using a free distance parameter and a multiplicity parameter for selecting the optimum code(s) from the best codes.

11. The generator of claim 9 , wherein when executed the instructions further perform the act of using a free distance parameter and a bit multiplicity parameter for selecting the optimum code(s) from the best codes.

12. A node of a communications network which participates in data transmissions over a channel, the node comprising: a transceiver for sending and receiving data over the channel; a shift register circuit configured to implement an optimum tail biting convolutional code for operating on the data transmitted over the channel, the optimum code being expressed by a set of polynomials listed in any of Table 2-Table 21, polynomials being shown in octal notation in column G of Table 2-Table 21:

TABLE 2

NEW ODS FEEDFORWARD TBCC WITH RATE ¼ AND

CONSTRAINT LENGTH V = 2

#

permutation

equivalent

K

G

WS

codes

Note

3

(1, 1, 3, 5)

(6, 4, 6)

30

ODS-BER

6

(1, 3, 5, 7)

(8, 6, 6)

6

ODS-BER

8

(3, 5, 7, 7)

(10, 16, 24)

2

ODS-FER/BER

9

(3, 5, 7, 7)

(10, 18, 27)

2

ODS-FER/BER

TABLE 3

NEW ODS FEEDFORWARD TBCC WITH RATE ¼ AND

CONSTRAINT LENGTH V = 3

#

permutation

equivalent

K

G

WS

codes

Note

3

(4, 4, 14, 50)

(6, 4, 6)

372

ODS-BER

9

(44, 54, 64, 74)

( 12, 12, 18)

1

ODS-BER

TABLE 4

NEW ODS FEEDFORWARD TBCC WITH RATE ¼ AND

CONSTRAINT LENGTH V = 4

#

permutation

equivalent

K

G

WS

codes

Note

3

(2, 2, 6, 42)

(6, 4, 6)

5238

ODS-BER

5

(2, 6, 16, 52)

(9, 10, 20)

1058

ODS-FER/BER

6

(2, 6, 26, 76)

(10, 9, 18)

120

ODS-FER/BER

10

(26, 36, 46, 56)

( 14, 30, 60)

8

ODS-FER/BER

11

(46, 52, 56, 76)

( 15, 22, 66)

2

ODS-BER

TABLE 5

NEW ODS FEEDFORWARD TBCC WITH RATE ¼ AND

CONSTRAINT LENGTH V = 5

#

permutation

equivalent

K

G

WS

codes

Note

3

(1, 1, 3, 41)

(6, 4, 6)

78273

ODS-BER

5

(1, 3, 7, 52)

(9, 10, 20)

17596

ODS-FER/BER

6

(1, 3, 13, 57)

(10, 9, 18)

2352

ODS-FER/BER

8

(1, 23, 45, 77)

(12, 8, 16)

72

ODS-FER/BER

9

(13, 17, 23, 56)

(14, 72, 261)

60

ODS-FER/BER

10

(27, 47, 57, 61)

( 16, 285, 1350)

4

ODS-FER/BER

14

(45, 53, 73, 77)

(18, 84, 364)

2

ODS-BER

16

(47, 53, 67, 75)

(18, 48, 96)

2

ODS-FER

16

(45, 53, 73, 77)

(18, 48, 80)

2

ODS-BER

17

(47, 53, 67, 75)

(18, 51, 102)

2

ODS-FER

17

(45, 53, 73, 77)

(18, 51, 85)

2

ODS-BER

18

(47, 53, 67, 75)

(18, 54, 108)

2

ODS-FER

18

(45, 53, 73, 77)

(18, 54, 90)

2

ODS-BER

19

(45, 57, 67, 75)

(18, 57, 95)

2

ODS-FER/BER

20

(45, 57, 67, 75)

(18, 60, 100)

2

ODS-FER/BER

21

(45, 57, 67, 75)

(18, 63, 105)

2

ODS-FER/BER

24

(45, 57, 67, 75)

(18, 72, 120)

2

ODS-FER/BER

TABLE 6

NEW ODS FEEDFORWARD TBCC WITH RATE ¼ AND

CONSTRAINT LENGTH V = 6

# permutation

equivalent

K

G

WS

codes

Note

2

(4, 4, 4, 410)

(5, 2, 2)

1279360

ODS-FER/BER

3

(4, 4, 14, 430)

(6, 3, 6)

791712

ODS-FER

(4, 4, 14, 410)

(6, 4, 6)

1209060

ODS-BER

4

(4, 14, 24, 414)

(8, 11, 24)

460800

ODS-FER/BER

5

(4, 14, 34, 444)

(9, 10, 20)

281250

ODS-FER/BER

6

(4, 14, 54, 570)

(10, 9, 18)

36408

ODS-FER/BER

7

(4, 34, 174, 524)

(12, 28, 84)

6339

ODS-FER/BER

8

(4, 34, 114, 674)

(12, 8, 16)

1256

ODS-FER/BER

9

(4, 274, 454,

(14, 72, 234)

112

ODS-FER/BER

764)

10

(4, 374, 454,

(16, 285, 1140)

28

ODS-FER/BER

534)

11

(204, 214, 724,

(16, 66, 286)

12

ODS-FER/BER

774)

12

(424, 474, 704,

(17, 60, 324)

2

ODS-FER

724)

12

(224, 324, 354,

(17, 72, 312)

16

ODS-BER

554)

13

(134, 564, 634,

(19, 325, 1963)

6

ODS-FER/BER

724)

14

(114, 534, 664,

(19, 182, 1106)

6

ODS-FER/BER

764)

15

(464, 534, 564,

(20, 285, 1815)

2

ODS-FER

674)

15

(444, 654, 674,

(20, 288, 1800)

2

ODS-BER

734)

16

(454, 554, 724,

(20, 64, 224)

2

ODS-FER/BER

774)

17

(454, 474, 724,

(20, 34, 51)

2

ODS-FER/BER

754)

18

(474, 554, 624,

(20, 36, 54)

2

ODS-FER

764)

18

(454, 474, 724,

(20, 36, 54)

2

ODS-BER

754)

20

(474, 554, 624,

(20, 40, 60)

2

ODS-FER/BER

764)

TABLE 7

NEW ODS FEEDFORWARD TBCC WITH RATE ⅓ AND

CONSTRAINT LENGTH V = 2

#

permutation

equivalent

K

G

WS

codes

Note

3

(1, 1, 5)

(4, 3, 3)

12

ODS-FER/BER

TABLE 8

NEW ODS FEEDFORWARD TBCC WITH RATE ⅓ AND

CONSTRAINT LENGTH V = 3

#

permutation

equivalent

K

G

WS

codes

Note

7

(4, 54, 74)

(8, 35, 91)

8

ODS-BER

9

(34, 54, 74)

(8, 9, 18)

4

ODS-FER

9

(24, 54, 64)

(8, 9, 9)

2

ODS-BER

TABLE 9

NEW ODS FEEDFORWARD TBCC WITH RATE ⅓ AND

CONSTRAINT LENGTH V = 4

#

permutation

equivalent

K

G

WS

codes

Note

6

(2, 16, 56)

(8, 45, 120)

30

ODS-FER/BER

7

(2, 46, 76)

(8, 21, 56)

10

ODS-FER/BER

8

(2, 56, 66)

(8, 1, 8)

10

ODS-FER/BER

9

(16, 46, 56)

(10, 99, 405)

6

ODS-FER/BER

(26, 52, 56)

4

10

(46, 66, 72)

(10, 46, 240)

2

ODS-FER

10

(26, 36, 46)

(10, 52, 220)

8

ODS-BER

11

(46, 62, 76)

(10, 11, 22)

1

ODS-FER

11

(16, 56, 72)

(10, 11, 22)

3

ODS-BER

12

(46, 52, 72)

(10, 12, 12)

2

ODS-BER

15

(46, 56, 72)

(11, 15, 15)

2

ODS-FER/BER

TABLE 10

NEW ODS FEEDFORWARD TBCC WITH RATE ⅓ AND

CONSTRAINT LENGTH V = 5

#

permutation

equivalent

K

G

WS

codes

Note

6

(1, 7, 53)

(8, 45, 120)

156

ODS-FER/BER

7

(1, 7, 57)

(8, 21, 56)

124

ODS-FER/BER

8

(1, 27, 66)

(8, 1, 8)

52

ODS-FER/BER

9

(1, 47, 75)

(10, 99, 333)

24

ODS-FER/BER

10

(33, 43, 53)

(10, 21, 90)

4

ODS-FER/BER

12

(13, 37, 53)

(12, 202, 1008)

12

ODS-BER

17

(47, 57, 65)

(13, 34, 68)

2

ODS-BER

TABLE 11

NEW ODS FEEDFORWARD TBCC WITH RATE ⅓ AND

CONSTRAINT LENGTH V = 6

#

permutation

equivalent

K

G

WS

codes

Note

3

(4, 4, 410)

(4, 3, 3)

42984

ODS-FER/BER

6

(4, 34, 530)

(8, 45, 120)

1326

ODS-FER/BER

7

(4, 34, 534)

(8, 21, 56)

751

ODS-FER/BER

8

(4, 134, 614)

(8, 1, 8)

314

ODS-FER/BER

9

(4, 74, 554)

(10, 99, 306)

112

ODS-FER/BER

10

(154, 214, 530)

(10, 21, 90)

40

ODS-FER

10

(4, 314, 674)

(10, 26, 80)

28

ODS-BER

13

(434, 574, 664)

(12, 39, 338)

2

ODS-FER

13

(104, 554, 574)

(12, 39, 156)

6

ODS-BER

17

(474, 634, 654)

(14, 51, 306)

2

ODS-FER

17

(574, 654, 764)

(14, 51, 170)

1

ODS-BER

21

(464, 564, 674)

(15, 84, 210)

2

ODS-BER

22

(474, 564, 664)

(15, 66, 154)

2

ODS-BER

TABLE 12

NEW ODS FEEDFORWARD TBCC WITH RATE ⅓ AND

CONSTRAINT LENGTH V = 7

# permutation

equivalent

K

G

WS

codes

Note

4

(2, 6, 406)

(6, 12, 24)

200704

ODS-FER/BER

5

(2, 16, 422)

(7, 15, 35)

49000

ODS-FER/BER

6

(2, 16, 452)

(8, 45, 120)

10584

ODS-FER/BER

7

(2, 16, 534)

(8, 21, 56)

6318

ODS-FER/BER

8

(2, 56, 432)

(8, 1, 8)

1224

ODS-FER/BER

9

(2, 36, 466)

(10, 99, 306)

736

ODS-FER/BER

10

(2, 216, 566)

(10, 21, 70)

128

ODS-FER/BER

11

(2, 456, 722)

(11, 33, 121)

8

ODS-FER/BER

12

(26, 126, 646)

(12, 178, 948)

48

ODS-FER

12

(2, 336, 516)

(12, 186, 732)

32

ODS-BER

13

(126, 232, 532)

(12, 39, 208)

20

ODS-FER

13

(276, 442, 776)

(12, 39, 130)

4

ODS-BER

14

(226, 422, 476)

(13, 112, 672)

4

ODS-FER

14

(566, 716, 736)

(13, 112, 616)

2

ODS-BER

15

(156, 332, 452)

(14, 330, 2535)

12

ODS-FER

15

(146, 316, 722)

(14, 375, 2280)

12

ODS-BER

16

(316, 336, 452)

(14, 64, 480)

8

ODS-FER/BER

17

(266, 512, 746)

(15, 238, 1700)

4

ODS-FER/BER

18

(256, 662, 746)

(16, 837, 7146)

4

ODS-FER/BER

19

(232, 632, 766)

(16, 342, 2090)

4

ODS-FER/BER

20

(452, 476, 756)

(16, 130, 1120)

2

ODS-FER

20

(456, 476, 666)

(16, 180, 920)

2

ODS-BER

21

(526, 572, 636)

(16, 63, 378)

2

ODS-FER

21

(422, 726, 736)

(16, 84, 273)

2

ODS-BER

22

(456, 626, 772)

(16, 22, 44)

2

ODS-FER

22

(476, 572, 632)

(16, 22, 44)

2

ODS-BER

24

(472, 562, 676)

(16, 24, 48)

2

ODS-FER

24

(462, 532, 736)

(16, 27, 48)

2

ODS-BER

25

(462, 532, 736)

(16, 25, 25)

2

ODS-FER/BER

26

(462, 532, 736)

(16, 26, 26)

2

ODS-FER/BER

TABLE 13

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 2

#

permutation

equivalent

K

G

WS

codes

Note

2

(1, 4)

(2, 2, 2)

5

ODS-BER

5

(1, 7)

(4, 15, 30)

3

ODS-BER

7

(3, 7)

(4, 7, 14)

2

ODS-FER/BER

TABLE 14

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 3

#

permutation

equivalent

K

G

WS

codes

Note

2

(4, 40)

(2, 2, 2)

19

ODS-BER

5

(4, 74)

(4, 10, 20)

4

ODS-FER/BER

6

(14, 70)

(4, 9, 24)

2

ODS-BER

7

(4, 74)

(4, 7, 14)

4

ODS-FER/BER

12

(34, 54)

(6, 64, 192)

4

ODS-BER

TABLE 15

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 4

# permutation

equivalent

K

G

WS

codes

Note

2

(2, 40)

(2, 2, 2)

74

ODS-BER

5

(2, 56)

(4, 10, 20)

17

ODS-FER/BER

6

(2, 56)

(4, 6, 12)

10

ODS-FER/BER

7

(2, 66)

(4, 7, 14)

7

ODS-FER/BER

8

(2, 56)

(5, 24, 56)

10

ODS-FER/BER

9

(16, 54)

(6, 102, 450)

4

ODS-FER/BER

10

(16, 54)

(6, 90, 390)

4

ODS-FER/BER

16

(46, 66)

(7, 64, 256)

2

ODS-BER

18

(46, 56)

(7, 54, 126)

2

ODS-FER/BER

19

(46, 66)

(7, 38, 76)

2

ODS-BER

20

(46, 66)

(7, 40, 80)

2

ODS-BER

22

(46, 66)

(7, 44, 88)

2

ODS-BER

23

(46, 66)

(7, 46, 92)

2

ODS-BER

TABLE 16

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 5

#

permutation

equivalent

K

G

WS

codes

Note

2

(1, 40)

(2, 2, 2)

292

ODS-BER

6

(1, 53)

(4, 6, 12)

16

ODS-FER/BER

7

(1, 53)

(4, 7, 14)

28

ODS-FER/BER

8

(1, 53)

(5, 24, 56)

16

ODS-FER/BER

9

(7, 54)

(6, 102, 450)

16

ODS-FER/BER

10

(13, 53)

(6, 40, 180)

6

ODS-FER/BER

12

(23, 47)

(6, 20, 120)

4

ODS-FER/BER

18

(37, 53)

(8, 117, 684)

4

ODS-BER

20

(43, 73)

(8, 100, 340)

2

ODS-BER

21

(23, 67)

(8, 84, 189)

4

ODS-BER

22

(57, 63)

(8, 44, 132)

2

ODS-FER

23

(45, 77)

(8, 46, 92)

2

ODS-FER/BER

TABLE 17

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 6

#

permutation

equivalent

K

G

WS

codes

Note

5

(4, 464)

(4, 10, 20)

225

ODS-FER/BER

6

(4, 530)

(4, 6, 12)

82

ODS-FER/BER

7

(4, 434)

(4, 7, 14)

54

ODS-FER/BER

8

(4, 434)

(5, 24, 56)

50

ODS-FER/BER

9

(4, 474)

(6, 102, 306)

28

ODS-FER/BER

11

(274, 574)

(7, 176, 880)

4

ODS-FER/BER

(474, 674)

2

13

(134, 670)

(7, 117, 611)

4

ODS-FER/BER

15

(114, 714)

(8, 450, 3120)

6

ODS-FER/BER

17

(374, 444)

(8, 187, 1156)

2

ODS-BER

19

(464, 744)

(8, 19, 190)

2

ODS-FER

19

(634, 734)

(8, 38, 190)

2

ODS-BER

TABLE 18

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 7

#

permutation

equivalent

K

G

WS

codes

Note

2

(2, 400)

(2, 2, 2)

4624

ODS-BER

6

(2, 452)

(4, 6, 12)

324

ODS-FER/BER

7

(2, 434)

(4, 7, 14)

348

ODS-FER/BER

8

(2, 426)

(5, 24, 56)

68

ODS-FER/BER

9

(2, 456)

(6, 102, 306)

40

ODS-FER/BER

10

(2, 476)

(6, 40, 120)

16

ODS-FER/BER

11

(2, 556)

(7, 176, 616)

16

ODS-FER/BER

13

(56, 670)

(7, 117, 611)

6

ODS-FER/BER

14

(76, 654)

(8, 546, 3640)

2

ODS-FER/BER

(112, 472)

6

(256, 626)

4

(266, 602)

4

(316, 412)

4

15

(376, 412)

(8, 450, 2955)

4

ODS-FER/BER

16

(36, 564)

(8, 238, 1776)

2

ODS-FER/BER

17

(146, 534)

(8, 153, 1190)

4

ODS-FER

17

(176, 444)

(8, 187, 1156)

2

ODS-BER

18

(336, 646)

(8, 54, 468)

4

ODS-FER

18

(336, 676)

(8, 81, 432)

4

ODS-FER

19

(556, 736)

(8, 19, 152)

2

ODS-FER

21

(326, 576)

(10, 1722,

4

ODS-BER

15771)

22

(236, 626)

(10, 1298,

4

ODS-FER

13112)

22

(272, 634)

(10, 1364,

4

ODS-BER

12914)

24

(236, 652)

(10, 744, 6624)

4

ODS-BER

26

(276, 722)

(10, 143, 1118)

4

ODS-BER

27

(316, 466)

(10, 162, 567)

4

ODS-BER

28

(506, 772)

(10, 84, 224)

2

ODS-BER

31

(532, 746)

(10, 31, 124)

2

ODS-FER

31

(446, 756)

(10, 31, 62)

2

ODS-BER

32

(532, 746)

(10, 32, 128)

2

ODS-FER

33

(532, 746)

(10, 33, 132)

2

ODS-FER

33

(452, 766)

(10, 33, 66)

2

ODS-BER

34

(532, 746)

(10, 34, 136)

2

ODS-FER

35

(532, 746)

(10, 35, 140)

2

ODS-FER

35

(452, 766)

(10, 35, 70)

2

ODS-BER

36

(532, 746)

(10, 36, 144)

2

ODS-FER

36

(452, 766)

(10, 36, 72)

2

ODS-BER

37

(532, 746)

(10, 37, 148)

2

ODS-FER

38

(532, 746)

(10, 38, 152)

2

ODS-FER

TABLE 19

NEW ODS FEEDFORWARD TBCC WITH RATE ½ AND

CONSTRAINT LENGTH V = 8

#

permutation

equivalent

K

G

WS

codes

Note

5

(1, 407)

(4, 10, 20)

3600

ODS-FER/BER

6

(1, 423)

(4, 6, 12)

1296

ODS-FER/BER

7

(1, 415)

(4, 7, 14)

1323

ODS-FER/BER

8

(1, 426)

(5, 24, 56)

624

ODS-FER/BER

9

(1, 447)

(6, 102, 306)

79

ODS-FER/BER

10

(1, 476)

(6, 40, 120)

4

ODS-FER/BER

11

(1, 556)

(7, 176, 616)

4

ODS-FER/BER

12

(1, 573)

(8, 759, 3036)

18

ODS-FER/BER

14

(1, 727)

(8, 546, 2184)

9

ODS-FER/BER

15

(177, 412)

(8, 450, 2955)

4

ODS-FER/BER

16

(55, 727)

(8, 238, 1744)

4

ODS-FER

16

(1, 557)

(8, 372, 1456)

18

ODS-BER

17

(433, 473)

(8, 153, 952)

2

ODS-FER/BER

18

(647, 657)

(8, 54, 324)

2

ODS-FER

18

(537, 737)

(8, 63, 324)

2

ODS-BER

19

(357, 737)

(8, 19, 38)

4

ODS-FER/BER

20

(303, 433)

(9, 240, 2160)

4

ODS-FER/BER

21

(227, 615)

(10, 1680,

4

ODS-FER/BER

15729)

22

(133, 463)

(10, 1298,

6

ODS-BER

11704)

24

(475, 507)

(10, 456, 4320)

2

ODS-BER

27

(67, 745)

(10, 54, 162)

8

ODS-BER

28

(233, 635)

(11, 644, 7308)

4

ODS-BER

29

(233, 565)

(11, 319, 3277)

4

ODS-FER/BER

32

(235, 557)

(12, 1568,

4

ODS-BER

15840)

38

(457, 755)

(12, 380, 1520)

2

ODS-FER/BER

39

(463, 755)

(12, 429, 1482)

2

ODS-BER

40

(463, 755)

(12, 440, 1520)

2

ODS-BER

TABLE 20

NEW ODS FEEDFORWARD TBCC WITH RATE 1/5 AND

VARIOUS CONSTRAINT LENGTHS.

# permutation

equivalent

K

V

G

WS

codes

Note

12

2

(5, 5, 7, 7,7)

(13, 12, 12)

1

ODS-FER/BER

12

3

(54, 54, 64,

(16, 12, 24)

2

ODS-FER/BER

74, 74)

12

4

(52, 56, 66,

(20, 72, 216)

1

ODS-FER/BER

72, 76)

12

5

(37, 47, 55,

(22, 108, 504)

4

ODS-FER/BER

57, 65)

TABLE 21

NEW ODS FEEDFORWARD TBCC WITH RATE ⅖ AND

VARIOUS CONSTRAINT LENGTHS.

# permutation

equivalent

K

V

G

WS

codes

Note

12

3

(54, 64, 74) pl

(8, 51,

1

ODS-FER/BER

192)

12

4

(46, 56, 76) pl

(8, 15,

1

ODS-FER/BER

(62, 72, 76) pl

66)

1

12

5

(43, 57, 64) pl

(9, 78,

1

ODS-FER/BER

(13, 61, 75) p3

456)

3

(32, 43, 57) p3

2

5

(23, 55, 56) p2

(8, 6,

4

ODS-FER if

36)

p2 is used

5

(15, 57, 62) p2

(8, 6, 6)

3

ODS-BER if

p2 is used

12

6

(464, 474, 670) pl

(9, 72,

1

ODS-FER/BER

(544, 730, 744) p2

342)

1

(334, 464, 474) p3

2

12

7

(232, 236, 670) pl

(9, 72,

5

ODS-FER/BER

(232, 334, 474) p2

342)

3

(262, 730, 744) p2

1

(156, 232, 474) p3

6

(354, 362, 544) p3

 1.

13. The apparatus of claim 12 , further comprising: plural shift register circuits, each of the shift register circuits being configured to implement a respective different one of plural optimum tail biting convolutional codes, each of the plural optimum tail biting convolutional codes being of a different rate and being expressed by a set of polynomials listed in any of Table 2-Table 21; a code activator configured to include one of the plural shift register circuits in a processing stream for a respective data transmission over the channel.

14. The apparatus of claim 13 , wherein the shift register circuit comprises an encoder configured to append error correction information to data transmitted over the channel.

15. A method of operating a node of a communications network, the method comprising:

configuring a shift register circuit of the node to implement an optimum tail biting convolutional code expressed by a set of polynomials listed in any of Table 2-Table 21, the polynomials being shown in octal notation in column G of Table 2-Table 21:

TABLE 2

NEW ODS FEEDFORWARD TBCC WITH RATE ¼ AND

CONSTRAINT LENGTH V = 2

#

permutation

equivalent

K

G

WS

codes

Note

3

(1, 1, 3, 5)

(6, 4, 6)

30

ODS-BER

6

(1, 3, 5, 7)

(8, 6, 6)

6

ODS-BER

8

(3, 5, 7, 7)

(10, 16, 24)

2

ODS-FER/BER

9

(3, 5, 7, 7)

(10, 18, 27)

2

ODS-FER/BER

TABLE 3

NEW ODS FEEDFORWARD TBCC WITH RATE ¼ AND

CONSTRAINT LENGTH V = 3

#

permutation

equivalent

K

G

WS

codes

Note

3

(4, 4, 14, 50)

(6, 4, 6)

372

ODS-BER

9

(44, 54, 64, 74)

(12, 12, 18)

1

ODS-BER

TABLE 4

NEW ODS FEEDFORWARD TBCC WITH RATE ¼ AND

CONSTRAINT LENGTH V = 4

#

permutation

equivalent

K

G

WS

codes

Note

3

(2, 2, 6, 42)

(6, 4, 6)

5238

ODS-BER

5

(2, 6, 16, 52)

(9, 10, 20)

1058

ODS-FER/BER

6

(2, 6, 26, 76)

(10, 9, 18)

120

ODS-FER/BER

10

(26, 36, 46, 56)

(14, 30, 60)

8

ODS-FER/BER

11

(46, 52, 56, 76)

(15, 22, 66)

2

ODS-BER

TABLE 5

NEW ODS FEEDFORWARD TBCC WITH RATE 1/4 AND

CONSTRAINT LENGTH V = 5

# permutation

equivalent

K

G

WS

codes

Note

3

(1, 1, 3, 41)

(6, 4, 6)

78273

ODS-BER

5

(1, 3, 7, 52)

(9, 10, 20)

17596

ODS-FER/BER

6

(1, 3, 13, 57)

(10, 9, 18)

2352

ODS-FER/BER

8

(1, 23, 45, 77)

(12, 8, 16)

72

ODS-FER/BER

9

(13, 17, 23, 56)

(14, 72, 261)

60

ODS-FER/BER

10

(27, 47, 57, 61)

(16, 285, 1350)

4

ODS-FER/BER

14

(45, 53, 73, 77)

(18, 84, 364)

2

ODS-BER

16

(47, 53, 67, 75)

(18, 48, 96)

2

ODS-FER

16

(45, 53, 73, 77)

(18, 48, 80)

2

ODS-BER

17

(47, 53, 67, 75)

(18, 51, 102)

2

ODS-FER

17

(45, 53, 73, 77)

(18, 51, 85)

2

ODS-BER

18

(47, 53, 67, 75)

(18, 54, 108)

2

ODS-FER

18

(45, 53, 73, 77)

(18, 54, 90)

2

ODS-BER

19

(45, 57, 67, 75)

(18, 57, 95)

2

ODS-FER/BER

20

(45, 57, 67, 75)

(18, 60, 100)

2

ODS-FER/BER

21

(45, 57, 67, 75)

(18, 63, 105)

2

ODS-FER/BER

24

(45, 57, 67, 75)

(18, 72, 120)

2

ODS-FER/BER

TABLE 6

NEW ODS FEEDFORWARD TBCC WITH RATE 1/4 AND

CONSTRAINT LENGTH V = 6

# permutation

equivalent

K

G

WS

codes

Note

2

(4, 4, 4, 410)

(5, 2, 2)

1279360

ODS-FER/BER

3

(4, 4, 14, 430)

(6, 3, 6)

791712

ODS-FER

(4, 4, 14, 410)

(6, 4, 6)

1209060

ODS-BER

4

(4, 14, 24, 414)

(8, 11, 24)

460800

ODS-FER/BER

5

(4, 14, 34, 444)

(9, 10, 20)

281250

ODS-FER/BER

6

(4, 14, 54, 570)

(10, 9, 18)

36408

ODS-FER/BER

7

(4, 34, 174, 524)

(12, 28, 84)

6339

ODS-FER/BER

8

(4, 34, 114, 674)

(12, 8, 16)

1256

ODS-FER/BER

9

(4, 274, 454,

(14, 72, 234)

112

ODS-FER/BER

764)

10

(4, 374, 454,

(16, 285, 1140)

28

ODS-FER/BER

534)

11

(204, 214, 724,

(16, 66, 286)

12

ODS-FER/BER

774)

12

(424, 474, 704,

(17, 60, 324)

2

ODS-FER

724)

12

(224, 324, 354,

(17, 72, 312)

16

ODS-BER

554)

13

(134, 564, 634,

(19, 325, 1963)

6

ODS-FER/BER

724)

14

(114, 534, 664,

(19, 182, 1106)

6

ODS-FER/BER

764)

15

(464, 534, 564,

(20, 285, 1815)

2

ODS-FER

674)

15

(444, 654, 674,

(20, 288, 1800)

2

ODS-BER

734)

16

(454, 554, 724,

(20, 64, 224)

2

ODS-FER/BER

774)

17

(454, 474, 724,

(20, 34, 51)

2

ODS-FER/BER

754)

18

(474, 554, 624,

(20, 36, 54)

2

ODS-FER

764)

18

(454, 474, 724,

(20, 36, 54)

2

ODS-BER

754)

20

(474, 554, 624,

(20, 40, 60)

2

ODS-FER/BER

764)

TABLE 7

NEW ODS FEEDFORWARD TBCC WITH RATE 1/3 AND

CONSTRAINT LENGTH V = 2

# permutation

equivalent

K

G

WS

codes

Note

3

(1, 1, 5)

(4, 3, 3)

12

ODS-FER/BER

TABLE 8

NEW ODS FEEDFORWARD TBCC WITH RATE 1/3 AND

CONSTRAINT LENGTH V = 3

# permutation

equivalent

K

G

WS

codes

Note

7

(4, 54, 74)

(8, 35, 91)

8

ODS-BER

9

(34, 54, 74)

(8, 9, 18)

4

ODS-FER

9

(24, 54, 64)

(8, 9, 9)

2

ODS-BER

TABLE 9

NEW ODS FEEDFORWARD TBCC WITH RATE 1/3 AND

CONSTRAINT LENGTH V = 4

# permutation

equivalent

K

G

WS

codes

Note

6

(2, 16, 56)

(8, 45, 120)

30

ODS-FER/BER

7

(2, 46, 76)

(8, 21, 56)

10

ODS-FER/BER

8

(2, 56, 66)

(8, 1, 8)

10

ODS-FER/BER

9

(16, 46, 56)

(10, 99, 405)

6

ODS-FER/BER

(26, 52, 56)

4

10

(46, 66, 72)

(10, 46, 240)

2

ODS-FER

10

(26, 36, 46)

(10, 52, 220)

8

ODS-BER

11

(46, 62, 76)

(10, 11, 22)

1

ODS-FER

11

(16, 56, 72)

(10, 11, 22)

3

ODS-BER

12

(46, 52, 72)

(10, 12, 12)

2

ODS-BER

15

(46, 56, 72)

(11, 15, 15)

2

ODS-FER/BER

TABLE 10

NEW ODS FEEDFORWARD TBCC WITH RATE 1/3 AND

CONSTRAINT LENGTH V = 5

# permutation

equivalent

K

G

WS

codes

Note

6

(1, 7, 53)

(8, 45, 120)

156

ODS-FER/BER

7

(1, 7, 57)

(8, 21, 56)

124

ODS-FER/BER

8

(1, 27, 66)

(8, 1, 8)

52

ODS-FER/BER

9

(1, 47, 75)

(10, 99, 333)

24

ODS-FER/BER

10

(33, 43, 53)

(10, 21, 90)

4

ODS-FER/BER

12

(13, 37, 53)

(12, 202, 1008)

12

ODS-BER

17

(47, 57, 65)

(13, 34, 68)

2

ODS-BER

TABLE 11

NEW ODS FEEDFORWARD TBCC WITH RATE 1/3 AND

CONSTRAINT LENGTH V = 6

# permutation

equivalent

K

G

WS

codes

Note

3

(4, 4, 410)

(4, 3, 3)

42984

ODS-FER/BER

6

(4, 34, 530)

(8, 45, 120)

1326

ODS-FER/BER

7

(4, 34, 534)

(8, 21, 56)

751

ODS-FER/BER

8

(4, 134, 614)

(8, 1, 8)

314

ODS-FER/BER

9

(4, 74, 554)

(10, 99, 306)

112

ODS-FER/BER

10

(154, 214, 530)

(10, 21, 90)

40

ODS-FER

10

(4, 314, 674)

(10, 26, 80)

28

ODS-BER

13

(434, 574, 664)

(12, 39, 338)

2

ODS-FER

13

(104, 554, 574)

(12, 39, 156)

6

ODS-BER

17

(474, 634, 654)

(14, 51, 306)

2

ODS-FER

17

(574, 654, 764)

(14, 51, 170)

1

ODS-BER

21

(464, 564, 674)

(15, 84, 210)

2

ODS-BER

22

(474, 564, 664)

(15, 66, 154)

2

ODS-BER

TABLE 12

NEW ODS FEEDFORWARD TBCC WITH RATE 1/3 AND

CONSTRAINT LENGTH V = 7

# permutation

equivalent

K

G

WS

codes

Note

4

(2, 6, 406)

(6, 12, 24)

200704

ODS-FER/BER

5

(2, 16, 422)

(7, 15, 35)

49000

ODS-FER/BER

6

(2, 16, 452)

(8, 45, 120)

10584

ODS-FER/BER

7

(2, 16, 534)

(8, 21, 56)

6318

ODS-FER/BER

8

(2, 56, 432)

(8, 1, 8)

1224

ODS-FER/BER

9

(2, 36, 466)

(10, 99, 306)

736

ODS-FER/BER

10

(2, 216, 566)

(10, 21, 70)

128

ODS-FER/BER

11

(2, 456, 722)

(11, 33, 121)

8

ODS-FER/BER

12

(26, 126, 646)

(12, 178, 948)

48

ODS-FER

12

(2, 336, 516)

(12, 186, 732)

32

ODS-BER

13

(126, 232, 532)

(12, 39, 208)

20

ODS-FER

13

(276, 442, 776)

(12, 39, 130)

4

ODS-BER

14

(226, 422, 476)

(13, 112, 672)

4

ODS-FER

14

(566, 716, 736)

(13, 112, 616)

2

ODS-BER

15

(156, 332, 452)

(14, 330, 2535)

12

ODS-FER

15

(146, 316, 722)

(14, 375, 2280)

12

ODS-BER

16

(316, 336, 452)

(14, 64, 480)

8

ODS-FER/BER

17

(266, 512, 746)

(15, 238, 1700)

4

ODS-FER/BER

18

(256, 662, 746)

(16, 837, 7146)

4

ODS-FER/BER

19

(232, 632, 766)

(16, 342, 2090)

4

ODS-FER/BER

20

(452, 476, 756)

(16, 130, 1120)

2

ODS-FER

20

(456, 476, 666)

(16, 180, 920)

2

ODS-BER

21

(526, 572, 636)

(16, 63, 378)

2

ODS-FER

21

(422, 726, 736)

(16, 84, 273)

2

ODS-BER

22

(456, 626, 772)

(16, 22, 44)

2

ODS-FER

22

(476, 572, 632)

(16, 22, 44)

2

ODS-BER

24

(472, 562, 676)

(16, 24, 48)

2

ODS-FER

24

(462, 532, 736)

(16, 27, 48)

2

ODS-BER

25

(462, 532, 736)

(16, 25, 25)

2

ODS-FER/BER

26

(462, 532, 736)

(16, 26, 26)

2

ODS-FER/BER

TABLE 13

NEW ODS FEEDFORWARD TBCC WITH RATE 1/2 AND

CONSTRAINT LENGTH V = 2

# permutation

equivalent

K

G

WS

codes

Note

2

(1, 4)

(2, 2, 2)

5

ODS-BER

5

(1, 7)

(4, 15, 30)

3

ODS-BER

7

(3, 7)

(4, 7, 14)

2

ODS-FER/BER

TABLE 14

NEW ODS FEEDFORWARD TBCC WITH RATE 1/2 AND

CONSTRAINT LENGTH V = 3

# permutation

equivalent

K

G

WS

codes

Note

2

(4, 40)

(2, 2, 2)

19

ODS-BER

5

(4, 74)

(4, 10, 20)

4

ODS-FER/BER

6

(14, 70)

(4, 9, 24)

2

ODS-BER

7

(4, 74)

(4, 7, 14)

4

ODS-FER/BER

12

(34, 54)

(6, 64, 192)

4

ODS-BER

TABLE 15

NEW ODS FEEDFORWARD TBCC WITH RATE 1/2 AND

CONSTRAINT LENGTH V = 4

# permutation

equivalent

K

G

WS

codes

Note

2

(2, 40)

(2, 2, 2)

74

ODS-BER

5

(2, 56)

(4, 10, 20)

17

ODS-FER/BER

6

(2, 56)

(4, 6, 12)

10

ODS-FER/BER

7

(2, 66)

(4, 7, 14)

7

ODS-FER/BER

8

(2, 56)

(5, 24, 56)

10

ODS-FER/BER

9

(16, 54)

(6, 102, 450)

4

ODS-FER/BER

10

(16, 54)

(6, 90, 390)

4

ODS-FER/BER

16

(46, 66)

(7, 64, 256)

2

ODS-BER

18

(46, 56)

(7, 54, 126)

2

ODS-FER/BER

19

(46, 66)

(7, 38, 76)

2

ODS-BER

20

(46, 66)

(7, 40, 80)

2

ODS-BER

22

(46, 66)

(7, 44, 88)

2

ODS-BER

23

(46, 66)

(7, 46, 92)

2

ODS-BER

TABLE 16

NEW ODS FEEDFORWARD TBCC WITH RATE 1/2 AND

CONSTRAINT LENGTH V = 5

# permutation

equivalent

K

G

WS

codes

Note

2

(1, 40)

(2, 2, 2)

292

ODS-BER

6

(1, 53)

(4, 6, 12)

16

ODS-FER/BER

7

(1, 53)

(4, 7, 14)

28

ODS-FER/BER

8

(1, 53)

(5, 24, 56)

16

ODS-FER/BER

9

(7, 54)

(6, 102, 450)

16

ODS-FER/BER

10

(13, 53)

(6, 40, 180)

6

ODS-FER/BER

12

(23, 47)

(6, 20, 120)

4

ODS-FER/BER

18

(37, 53)

(8, 117, 684)

4

ODS-BER

20

(43, 73)

(8, 100, 340)

2

ODS-BER

21

(23, 67)

(8, 84, 189)

4

ODS-BER

22

(57, 63)

(8, 44, 132)

2

ODS-FER

23

(45, 77)

(8, 46, 92)

2

ODS-FER/BER

TABLE 17

NEW ODS FEEDFORWARD TBCC WITH RATE 1/2 AND

CONSTRAINT LENGTH V = 6

# permutation

equivalent

K

G

WS

codes

Note

5

(4, 464)

(4, 10, 20)

225

ODS-FER/BER

6

(4, 530)

(4, 6, 12)

82

ODS-FER/BER

7

(4, 434)

(4, 7, 14)

54

ODS-FER/BER

8

(4, 434)

(5, 24, 56)

50

ODS-FER/BER

9

(4, 474)

(6, 102, 306)

28

ODS-FER/BER

11

(274, 574)

(7, 176, 880)

4

ODS-FER/BER

(474, 674)

2

13

(134, 670)

(7, 117, 611)

4

ODS-FER/BER

15

(114, 714)

(8, 450, 3120)

6

ODS-FER/BER

17

(374, 444)

(8, 187, 1156)

2

ODS-BER

19

(464, 744)

(8, 19, 190)

2

ODS-FER

19

(634, 734)

(8, 38, 190)

2

ODS-BER

TABLE 18

NEW ODS FEEDFORWARD TBCC WITH RATE 1/2 AND

CONSTRAINT LENGTH V = 7

# permutation

equivalent

K

G

WS

codes

Note

2

(2, 400)

(2, 2, 2)

4624

ODS-BER

6

(2, 452)

(4, 6, 12)

324

ODS-FER/BER

7

(2, 434)

(4, 7, 14)

348

ODS-FER/BER

8

(2, 426)

(5, 24, 56)

68

ODS-FER/BER

9

(2, 456)

(6, 102, 306)

40

ODS-FER/BER

10

(2, 476)

(6, 40, 120)

16

ODS-FER/BER

11

(2, 556)

(7, 176, 616)

16

ODS-FER/BER

13

(56, 670)

(7, 117, 611)

6

ODS-FER/BER

14

(76, 654)

(8, 546, 3640)

2

ODS-FER/BER

(112, 472)

6

(256, 626)

4

(266, 602)

4

(316, 412)

4

15

(376, 412)

(8, 450, 2955)

4

ODS-FER/BER

16

(36, 564)

(8, 238, 1776)

2

ODS-FER/BER

17

(146, 534)

(8, 153, 1190)

4

ODS-FER

17

(176, 444)

(8, 187, 1156)

2

ODS-BER

18

(336, 646)

(8, 54, 468)

4

ODS-FER

18

(336, 676)

(8, 81, 432)

4

ODS-FER

19

(556, 736)

(8, 19, 152)

2

ODS-FER

21

(326, 576)

(10, 1722,

4

ODS-BER

15771)

22

(236, 626)

(10, 1298,

4

ODS-FER

13112)

22

(272, 634)

(10, 1364,

4

ODS-BER

12914)

24

(236, 652)

(10, 744, 6624)

4

ODS-BER

26

(276, 722)

(10, 143, 1118)

4

ODS-BER

27

(316, 466)

(10, 162, 567)

4

ODS-BER

28

(506, 772)

(10, 84, 224)

2

ODS-BER

31

(532, 746)

(10, 31, 124)

2

ODS-FER

31

(446, 756)

(10, 31, 62)

2

ODS-BER

32

(532, 746)

(10, 32, 128)

2

ODS-FER

33

(532, 746)

(10, 33, 132)

2

ODS-FER

33

(452, 766)

(10, 33, 66)

2

ODS-BER

34

(532, 746)

(10, 34, 136)

2

ODS-FER

35

(532, 746)

(10, 35, 140)

2

ODS-FER

35

(452, 766)

(10, 35, 70)

2

ODS-BER

36

(532, 746)

(10, 36, 144)

2

ODS-FER

36

(452, 766)

(10, 36, 72)

2

ODS-BER

37

(532, 746)

(10, 37, 148)

2

ODS-FER

38

(532, 746)

(10, 38, 152)

2

ODS-FER

TABLE 19

NEW ODS FEEDFORWARD TBCC WITH RATE 1/2 AND

CONSTRAINT LENGTH V = 8

# permutation

equivalent

K

G

WS

codes

Note

5

(1, 407)

(4, 10, 20)

3600

ODS-FER/BER

6

(1, 423)

(4, 6, 12)

1296

ODS-FER/BER

7

(1, 415)

(4, 7, 14)

1323

ODS-FER/BER

8

(1, 426)

(5, 24, 56)

624

ODS-FER/BER

9

(1, 447)

(6, 102, 306)

79

ODS-FER/BER

10

(1, 476)

(6, 40, 120)

4

ODS-FER/BER

11

(1, 556)

(7, 176, 616)

4

ODS-FER/BER

12

(1, 573)

(8, 759, 3036)

18

ODS-FER/BER

14

(1, 727)

(8, 546, 2184)

9

ODS-FER/BER

15

(177, 412)

(8, 450, 2955)

4

ODS-FER/BER

16

(55, 727)

(8, 238, 1744)

4

ODS-FER

16

(1, 557)

(8, 372, 1456)

18

ODS-BER

17

(433, 473)

(8, 153, 952)

2

ODS-FER/BER

18

(647, 657)

(8, 54, 324)

2

ODS-FER

18

(537, 737)

(8, 63, 324)

2

ODS-BER

19

(357, 737)

(8, 19, 38)

4

ODS-FER/BER

20

(303, 433)

(9, 240, 2160)

4

ODS-FER/BER

21

(227, 615)

(10, 1680,

4

ODS-FER/BER

15729)

22

(133, 463)

(10, 1298,

6

ODS-BER

11704)

24

(475, 507)

(10, 456, 4320)

2

ODS-BER

27

(67, 745)

(10, 54, 162)

8

ODS-BER

28

(233, 635)

(11, 644, 7308)

4

ODS-BER

29

(233, 565)

(11, 319, 3277)

4

ODS-FER/BER

32

(235, 557)

(12, 1568,

4

ODS-BER

15840)

38

(457, 755)

(12, 380, 1520)

2

ODS-FER/BER

39

(463, 755)

(12, 429, 1482)

2

ODS-BER

40

(463, 755)

(12, 440, 1520)

2

ODS-BER

TABLE 20

NEW ODS FEEDFORWARD TBCC WITH RATE 1/5 AND

VARIOUS CONSTRAINT LENGTHS.

# permutation

equivalent

K

V

G

WS

codes

Note

12

2

(5, 5, 7, 7,7)

(13, 12, 12)

1

ODS-FER/BER

12

3

(54, 54, 64,

(16, 12, 24)

2

ODS-FER/BER

74, 74)

12

4

(52, 56, 66,

(20, 72, 216)

1

ODS-FER/BER

72, 76)

12

5

(37, 47, 55,

(22, 108, 504)

4

ODS-FER/BER

57, 65)

TABLE 21

NEW ODS FEEDFORWARD TBCC WITH RATE ⅖ AND

VARIOUS CONSTRAINT LENGTHS.

# permutation

equivalent

K

V

G

WS

codes

Note

12

3

(54, 64, 74) pl

(8, 51,

1

ODS-FER/BER

192)

12

4

(46, 56, 76) pl

(8, 15,

1

ODS-FER/BER

(62, 72, 76) pl

66)

1

12

5

(43, 57, 64) pl

(9, 78,

1

ODS-FER/BER

(13, 61, 75) p3

456)

3

(32, 43, 57) p3

2

5

(23, 55, 56) p2

(8, 6,

4

ODS-FER if

36)

p2 is used

5

(15, 57, 62) p2

(8, 6, 6)

3

ODS-BER if

p2 is used

12

6

(464, 474, 670) pl

(9, 72,

1

ODS-FER/BER

(544, 730, 744) p2

342)

1

(334, 464, 474) p3

2

12

7

(232, 236, 670) pl

(9, 72,

5

ODS-FER/BER

(232, 334, 474) p2

342)

3

(262, 730, 744) p2

1

(156, 232, 474) p3

6

(354, 362, 544) p3

1

and,

using the optimum tail biting convolutional code to operate on data transmitted over a channel of the communications network.

16. The method of claim 15 , further comprising using the optimum tail biting convolutional code to perform error correction encoding of data transmitted over the channel of the communications network.

Assignments (2)
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded May 10, 2019
From: TELEFONAKTIEBOLAGET LM ERICSSON (PUBL)
To: GUANGDONG OPPO MOBILE TELECOMMUNICATIONS CORP., LTD.
Reel/Frame 049149/0276 →
ASSIGNMENT OF ASSIGNOR'S INTEREST Recorded Feb 12, 2009
From: CHEN, JASON; SHAWN TSAI, SHIAU-HE; ERNSTROM, PER
To: TELEFONAKTIEBOLAGET LM ERICSSON (PUBL)
Reel/Frame 022284/0592 →