Method and apparatus for a parameterized interleaver design process

1. A method, performed by one or more processing devices, of generating an interleaver π(i) of a length N, comprising:

partitioning a primary intermediate interleaver permutation into a number of first subgroups, wherein each of the first subgroups corresponds with a respective predetermined supplemental subpermutation mask;

partitioning each of the first subgroups of the primary intermediate interleaver permutation into a number of second subgroups;

applying each supplemental subpermutation mask to each of the second subgroups of the first subgroup that corresponds to the respective supplemental subpermutation mask, resulting in a corresponding portion of a secondary intermediate interleaver permutation; and

generating the interleaver π(i) based at least in part on the primary intermediate and the secondary intermediate interleaver permutations.

2. The method of claim 1 , wherein each of the second subgroups is of a length 12, and N is a multiple of 12.

3. The method of claim 2 , wherein the supplemental subpermutation masks comprise π 3 =[4, 10, 5, 8, 3, 6, 9, 11, 1, 7, 0, 2], π 4 =[5, 8, 10, 2, 6, 4, 7, 1, 3, 9, 11, 0], π 5 =[10, 0, 9, 1, 11, 7, 3, 5, 8, 6, 2, 4], and π 6 =[9, 7, 2, 4, 10, 8, 3, 6, 11, 1, 5, 0].

4. The method of claim 1 , further comprising:

partitioning an initial interleaver permutation vector into a number of primary subgroups, wherein each of the primary subgroups corresponds with a respective predetermined initial subpermutation mask;

partitioning each of the primary subgroups of the initial interleaver permutation vector into a number of corresponding secondary subgroups;

applying each initial subpermutation mask to each of the secondary subgroups of the primary subgroup that corresponds to the respective initial subpermutation mask, resulting in a corresponding portion of a first intermediate interleaver permutation;

generating a second intermediate interleaver permutation based at least in part on the initial interleaver permutation vector; and

generating the primary intermediate interleaver permutation based at least in part on the first and second intermediate interleaver permutations, wherein the primary intermediate interleaver permutation is of the length N.

5. The method of claim 4 , wherein each of the secondary subgroups is of a length 12, each of the second subgroups is of a length 12, and N is a multiple of 12.

6. The method of claim 5 , wherein:

the initial subpermutation masks comprise π 1 =[9, 11, 8, 6, 10, 2, 4, 0, 7, 5, 1, 3] and π 2 =[8, 11, 6, 4, 0, 7, 3, 10, 1, 5, 9, 2]; and

the supplemental subpermutation masks comprise π 3 =[4, 10, 5, 8, 3, 6, 9, 11, 1, 7, 0, 2], π 4 =[5, 8, 10, 2, 6, 4, 7, 1, 3, 9, 11, 0], π 5 =[10, 0, 9, 1, 11, 7, 3, 5, 8, 6, 2, 4], and π 6 =[9, 7, 2, 4, 10, 8, 3, 6, 11, 1, 5, 0].

7. A method, performed by one or more processing devices, of generating an interleaver π(i) of a length N, comprising:

partitioning an initial interleaver permutation vector π initial into a first initial subgroup π initial 1 of a length N 1 and a second initial subgroup π initial 2 of a length N−N 1 , wherein N 1 is a predetermined parameter;

partitioning π initial 1 into a number of first supplemental subgroups, and applying a predetermined subpermutation mask π 1 to each of the first supplemental subgroups, resulting in a first portion of a first intermediate interleaver permutation π intermediate1 (i), where i=0, 1, . . . , N 1 −1;

partitioning π initial 2 into a number of second supplemental subgroups, and applying a predetermined subpermutation mask π 2 to each of the second supplemental subgroups, resulting in a second portion of the first intermediate interleaver permutation π intermediate1 (i), where i=N 1 , . . . , N−1;

generating a second intermediate interleaver permutation π intermediate2 (i), based at least in part on the initial interleaver permutation vector, where i=0, 1, . . . , N−1;

generating a third intermediate interleaver permutation π intermediate3 (i), based at least in part on the first and second intermediate interleaver permutations, where i=0, 1, . . . , N−1;

partitioning π intermediate3 into four subgroups, π intermediate3 1 , π intermediate3 2 , π intermediate3 3 , and π intermediate3 4 , having K 1 , K 2 , K 3 and K 4 elements, respectively, wherein K 1 , K 2 , K 3 and K 4 comprise predetermined parameters, and K 1 +K 2 +K 3 +K 4 =N;

partitioning π intermediate3 1 into K 1 /12 first intermediate subgroups, and applying a predetermined subpermutation mask π 3 to each of the K 1 /12 first intermediate subgroups, resulting in a first portion of a fourth intermediate interleaver permutation π intermediate4 (i), where i=0, 1, . . . , K 1 −1;

partitioning π intermediate3 2 into K 2 /12 second intermediate subgroups, and applying a predetermined subpermutation mask π 4 to each of the K 2 /12 second intermediate subgroups, resulting in a second portion of the fourth intermediate interleaver permutation π intermediate4 (i), where i=K 1 , . . . , (K 1 +K 2 )−1;

partitioning π intermediate3 3 into K 3 /12 third intermediate subgroups, and applying a predetermined subpermutation mask π 5 to each of the K 3 /12 third intermediate subgroups, resulting in a third portion of the fourth intermediate interleaver permutation π intermediate4 (i), where i=(K 1 +K 2 ), . . . , (K 1 +K 2 +K 3 )−1;

partitioning π intermediate3 4 into K 4 /12 fourth intermediate subgroups, and applying a predetermined subpermutation mask π 6 to each of the K 4 /12 fourth intermediate subgroups, resulting in a fourth portion of the fourth intermediate interleaver permutation π intermediate4 (i), where i=(K 1 +K 2 +K 3 ), . . . , N−1; and

generating the interleaver π(i) based at least in part on the third and fourth intermediate interleaver permutations, where i=0, 1, . . . , N−1.

8. The method of claim 7 , wherein each of the first and second supplemental subgroups is of a length 12, each of the first, second, third and fourth intermediate subgroups is of a length 12, and π 1 =[9, 11, 8, 6, 10, 2, 4, 0, 7, 5, 1, 3], π 2 =[8, 11, 6, 4, 0, 7, 3, 10, 1, 5, 9, 2], π 3 =[4, 10, 5, 8, 3, 6, 9, 11, 1, 7, 0, 2], π 4 =[5, 8, 10, 2, 6, 4, 7, 1, 3, 9, 11, 0], π 5 =[10, 0, 9, 1, 11, 7, 3, 5, 8, 6, 2, 4], and π 6 =[9, 7, 2, 4, 10, 8, 3, 6, 11, 1, 5, 0].

9. The method of claim 8 , wherein:

R z [ ] represents a modulo-Z operator;

s, p, N 1 , K 1 , K 2 , K 3 , K 4 represent a set of interleaver design parameters;

the first portion of the first intermediate interleaver permutation π intermediate1 (i)=π initial 1 ((j−1)×12+π 1 (R 12 [i])), where i=0, 1, . . . , N 1 −1, and where the index i falls within the subgroup j, such that jε{1, 2, . . . , N 1 /12};

the second portion of the first intermediate interleaver permutation π intermediate1 (i)=π initial 2 ((j−1)×12+π 2 (R 12 [i])), where i=N 1 , . . . , N−1, and where the index i falls within the subgroup j, such that jε{1, 2, . . . , (N−N 1 )/12};

the second intermediate interleaver permutation π intermediate2 (i)=π initial (R N [s+p×i]), where i=0, 1, . . . , N−1, where s and p are integers, and p is coprime with N, such that p<N and s<30;

the third intermediate interleaver permutation π intermediate3 (i)=π intermediate2 (π intermediate1 (i)), where i=0, 1, . . . , N−1;

the first portion of the fourth intermediate interleaver permutation π intermediate4 (i)=π intermediate3 1 ((j−1)×12+π 3 (R 12 [i])), where i=0, 1, . . . , K 1 −1, and where the index i falls within the subgroup j, such that jε{1, 2, . . . , K 1 /12};

the second portion of the fourth intermediate interleaver permutation π intermediate4 (i)=π intermediate3 2 ((j−1)×12+π 4 (R 12 [i])), where i=K 1 , . . . , (K 1 +K 2 )−1, and where the index i falls within the subgroup j, such that jε{1, 2, . . . , K 2 /12};

the third portion of the fourth intermediate interleaver permutation π intermediate4 (i)=π intermediate3 3 ((j−1)×12+π 5 (R 12 [i])), where i=(K 1 +K 2 ), . . . , (K 1 +K 2 +K 3 )−1, and where the index i falls within the subgroup j, such that jε{1, 2, . . . , K 3 /12};

the fourth portion of the fourth intermediate interleaver permutation π intermediate4 (i)=π intermediate3 4 ((j−1)×12+π 6 (R 12 [i])), where i=(K 1 +K 2 +K 3 ), . . . , N−1, and where the index i falls within the subgroup j, such that jε{1, 2, . . . , K 4 /12}; and

the interleaver π(i)=π intermediate3 (π intermediate4 (i)), where i=0, 1, . . . , N−1.

10. An apparatus for generating an interleaver π(i) of a length N, comprising a processor configured to:

partition a primary intermediate interleaver permutation into a number of first subgroups, wherein each of the first subgroups corresponds with a respective predetermined supplemental subpermutation mask;

partition each of the first subgroups of the primary intermediate interleaver permutation into a number of second subgroups;

apply each supplemental subpermutation mask to each of the second subgroups of the first subgroup that corresponds to the respective supplemental subpermutation mask, resulting in a corresponding portion of a secondary intermediate interleaver permutation; and

generate the interleaver π(i) based at least in part on the primary intermediate and the secondary intermediate interleaver permutations.

11. The apparatus of claim 10 , wherein each of the second subgroups is of a length 12, and N is a multiple of 12.

12. The apparatus of claim 11 , wherein the supplemental subpermutation masks comprise π 3 =[4, 10, 5, 8, 3, 6, 9, 11, 1, 7, 0, 2], π 4 =[5, 8, 10, 2, 6, 4, 7, 1, 3, 9, 11, 0], π 5 =[10, 0, 9, 1, 11, 7, 3, 5, 8, 6, 2, 4], and π 6 =[9, 7, 2, 4, 10, 8, 3, 6, 11, 1, 5, 0].

13. The apparatus of claim 10 , wherein the processor is further configured to:

partition an initial interleaver permutation vector into a number of primary subgroups, wherein each of the primary subgroups corresponds with a respective predetermined initial subpermutation mask;

partition each of the primary subgroups of the initial interleaver permutation vector into a number of corresponding secondary subgroups;

apply each initial subpermutation mask to each of the secondary subgroups of the primary subgroup that corresponds to the respective initial subpermutation mask, resulting in a corresponding portion of a first intermediate interleaver permutation;

generate a second intermediate interleaver permutation based at least in part on the initial interleaver permutation vector; and

generate the primary intermediate interleaver permutation based at least in part on the first and second intermediate interleaver permutations, wherein the primary intermediate interleaver permutation is of the length N.

14. The apparatus of claim 13 , wherein each of the secondary subgroups is of a length 12, each of the second subgroups is of a length 12, and N is a multiple of 12.

15. The apparatus of claim 14 , wherein:

the initial subpermutation masks comprise π 1 =[9, 11, 8, 6, 10, 2, 4, 0, 7, 5, 1, 3] and π 2 =[8, 11, 6, 4, 0, 7, 3, 10, 1, 5, 9, 2]; and

the supplemental subpermutation masks comprise π 3 =[4, 10, 5, 8, 3, 6, 9, 11, 1, 7, 0, 2], π 4 =[5, 8, 10, 2, 6, 4, 7, 1, 3, 9, 11, 0], π 5 =[10, 0, 9, 1, 11, 7, 3, 5, 8, 6, 2, 4], and π 6 =[9, 7, 2, 4, 10, 8, 3, 6, 11, 1, 5, 0].

16. An apparatus for generating an interleaver π(i) of a length N, comprising a processor configured to:

partition an initial interleaver permutation vector π initial into a first initial subgroup π initial 1 of a length N 1 and a second initial subgroup π initial 2 of a length N−N 1 , wherein N 1 is a predetermined parameter;

partition π initial 1 into a number of first supplemental subgroups, and apply a predetermined subpermutation mask π 1 to each of the first supplemental subgroups, resulting in a first portion of a first intermediate interleaver permutation π intermediate1 (i), where i=0, 1, . . . , N 1 −1;

partition π initial 2 into a number of second supplemental subgroups, and apply a predetermined subpermutation mask π 2 to each of the second supplemental subgroups, resulting in a second portion of the first intermediate interleaver permutation π intermediate1 (i), where i=N 1 , . . . , N−1;

generate a second intermediate interleaver permutation π intermediate2 (i), based at least in part on the initial interleaver permutation vector, where i=0, 1, . . . , N−1;

generate a third intermediate interleaver permutation π intermediate3 (i), based at least in part on the first and second intermediate interleaver permutations, where i=0, 1, . . . , N−1;

partition π intermediate3 into four subgroups, π intermediate3 1 , π intermediate3 2 , π intermediate3 3 , and π intermediate3 4 , having K 1 , K 2 , K 3 and K 4 elements, respectively, wherein K 1 , K 2 , K 3 and K 4 comprise predetermined parameters, and K 1 +K 2 +K 3 +K 4 =N;

partition π intermediate3 1 into K 1 /12 first intermediate subgroups, and apply a predetermined subpermutation mask π 3 to each of the K 1 /12 first intermediate subgroups, resulting in a first portion of a fourth intermediate interleaver permutation π intermediate4 (i), where i=0, 1, . . . , K 1 −1;

partition π intermediate3 2 into K 2 /12 second intermediate subgroups, and apply a predetermined subpermutation mask π 4 to each of the K 2 /12 second intermediate subgroups, resulting in a second portion of the fourth intermediate interleaver permutation π intermediate4 (i), where i=K 1 , . . . , (K 1 +K 2 )−1;

partition π intermediate3 3 into K 3 /12 third intermediate subgroups, and apply a predetermined subpermutation mask π 5 to each of the K 3 /12 third intermediate subgroups, resulting in a third portion of the fourth intermediate interleaver permutation π intermediate4 (i), where i=(K 1 +K 2 ), . . . , (K 1 +K 2 +K 3 )−1;

partition π intermediate3 4 into K 4 /12 fourth intermediate subgroups, and apply a predetermined subpermutation mask π 6 to each of the K 4 /12 fourth intermediate subgroups, resulting in a fourth portion of the fourth intermediate interleaver permutation π intermediate4 (i), where i=(K 1 +K 2 +K 3 ), . . . , N−1; and

generate the interleaver π(i) based at least in part on the third and fourth intermediate interleaver permutations, where i=0, 1, . . . , N−1.

17. The apparatus of claim 16 , wherein each of the first and second supplemental subgroups is of a length 12, each of the first, second, third and fourth intermediate subgroups is of a length 12, and π 1 =[9, 11, 8, 6, 10, 2, 4, 0, 7, 5, 1, 3], π 2 =[8, 11, 6, 4, 0, 7, 3, 10, 1, 5, 9, 2], π 3 =[4, 10, 5, 8, 3, 6, 9, 11, 1, 7, 0, 2], π 4 =[5, 8, 10, 2, 6, 4, 7, 1, 3, 9, 11, 0], π 5 =[10, 0, 9, 1, 11, 7, 3, 5, 8, 6, 2, 4], and π 6 =[9, 7, 2, 4, 10, 8, 3, 6, 11, 1, 5, 0].

18. The apparatus of claim 17 , wherein:

R z [ ] represents a modulo-Z operator;

s, p, N 1 , K 1 , K 2 , K 3 , K 4 represent a set of interleaver design parameters;

the first portion of the first intermediate interleaver permutation π intermediate1 (i)=π initial 1 ((j−1)×12+π 1 (R 12 [i])), where i=0, 1, . . . , N 1 −1, and where the index i falls within the subgroup j, such that jε{1, 2, . . . , N 1 /12};

the second portion of the first intermediate interleaver permutation π intermediate1 (i)=π initial 2 ((j−1)×12+π 2 (R 12 [i])), where i=N 1 , . . . , N−1, and where the index i falls within the subgroup j, such that jε{1, 2, . . . , (N−N 1 )/12};

the second intermediate interleaver permutation π intermediate2 (i)=π initial (R N [s+p×i]), where i=0, 1, . . . , N−1, where s and p are integers, and p is coprime with N, such that p<N and s<30;

the third intermediate interleaver permutation π intermediate3 (i)=π intermediate2 (π intermediate1 (i)), where i=0, 1, . . . , N−1;

the first portion of the fourth intermediate interleaver permutation π intermediate4 (i)=π intermediate3 1 ((j−1)×12+π 3 (R 12 [i])), where i=0, 1, . . . , K 1 −1, and where the index i falls within the subgroup j, such that jε{1, 2, . . . , K 1 /12};

the second portion of the fourth intermediate interleaver permutation π intermediate4 (i)=π intermediate3 2 ((j−1)×12+π 4 (R 12 [i])), where i=K 1 , . . . , (K 1 +K 2 )−1, and where the index i falls within the subgroup j, such that jε{1, 2, . . . , K 2 /12};

the third portion of the fourth intermediate interleaver permutation π intermediate4 (i)=π intermediate3 3 ((j−1)×12+π 5 (R 12 [i])), where i=(K 1 +K 2 ), . . . , (K 1 +K 2 +K 3 )−1, and where the index i falls within the subgroup j, such that jε{1, 2, . . . , K 3 /12};

the fourth portion of the fourth intermediate interleaver permutation π intermediate4 (i)=π intermediate3 4 ((j−1)×12+π 6 (R 12 [i])), where i=(K 1 +K 2 +K 3 ), . . . , N−1, and where the index i falls within the subgroup j, such that jε{1, 2, . . . , K 4 /12}; and

the interleaver π(i)=π intermediate3 (π intermediate4 (i)), where i=0, 1, . . . , N−1.

19. The method of claim 9 , wherein:

the set of interleaver design parameters s, p, N 1 , K 1 , K 2 , K 3 , K 4 comprise a one row from the following table:

N

s

p

N 1

K 1

K 2

K 3

K 4

468

15

229

252

144

132

120

72

720

3

53

516

468

192

36

24

1200

1

277

1080

360

336

384

120

1440

11

277

1068

360

360

360

360

1680

6

593

1620

420

420

420

420

1920

5

167

1716

1668

192

36

24

2160

2

263

2136

1536

408

48

168

2256

8

653

1200

576

576

576

528

2400

11

373

1428

1284

552

432

132

2640

6

13

1572

1212

1032

276

120

2880

11

443

1908

1572

744

456

108

3120

21

709

2052

1908

552

504

156

3360

5

23

2376

2064

360

792

144

3600

11

277

2040

1452

1392

516

240

3840

4

887

2400

1920

720

720

480

4080

7

313

2160

3132

708

132

108

4320

14

563

2160

1080

1080

720

1440

4560

1

313

3684

2268

960

432

900.

20. The apparatus of claim 18 , wherein:

the set of interleaver design parameters s, p, N 1 , K 1 , K 2 , K 3 , K 4 comprise a one row from the following table:

N

s

p

N 1

K 1

K 2

K 3

K 4

468

15

229

252

144

132

120

72

720

3

53

516

468

192

36

24

1200

1

277

1080

360

336

384

120

1440

11

277

1068

360

360

360

360

1680

6

593

1620

420

420

420

420

1920

5

167

1716

1668

192

36

24

2160

2

263

2136

1536

408

48

168

2256

8

653

1200

576

576

576

528

2400

11

373

1428

1284

552

432

132

2640

6

13

1572

1212

1032

276

120

2880

11

443

1908

1572

744

456

108

3120

21

709

2052

1908

552

504

156

3360

5

23

2376

2064

360

792

144

3600

11

277

2040

1452

1392

516

240

3840

4

887

2400

1920

720

720

480

4080

7

313

2160

3132

708

132

108

4320

14

563

2160

1080

1080

720

1440

4560

1

313

3684

2268

960

432

900.