Devices and methods for generating block punctured polar codes
The device and method disclosed herein are configured for generating a polar code of length N and dimension K on the basis of an original polar code being defined by a code sequence S having N max bit indices sorted from least reliable to most reliable sub-channels. The device comprises a processing unit configured to: (a) generate an auxiliary code sequence having N max /2 bit indices by removing bit indices greater than or equal to N max /2 from the code sequence S; (b) remove from the auxiliary code sequence the last N R bit indices to generate a modified auxiliary code sequence; and (c) generate the polar code of length N and dimension K by puncturing the original polar code on the basis of a puncturing set defined by the last p=N max −N bit indices of the modified auxiliary code sequence.
1. A device for generating a polar code of length N and dimension K on the basis of an original polar code being defined by a code sequence S having N max bit indices, wherein the device comprises a processor configured to:
generate an auxiliary code sequence having N max /2 bit indices by removing bit indices greater than or equal to N max /2 from the code sequence S;
remove from the auxiliary code sequence the last N R bit indices to generate a modified auxiliary code sequence, wherein N R denotes the number of removed bits;
determine the number of removed bits N R on the basis of N max , N and a predefined code rate R; and
generate the polar code of length N and dimension K by puncturing the original polar code on the basis of a puncturing set defined by the last p=N max −N bit indices of the modified auxiliary code sequence.
2. The device of claim 1 , wherein the processor is configured to determine the number of removed bits N R on the basis of the following equation:
N R =round( ap+b ),
wherein round( . . . ) denotes a rounding function and a and b denote parameters, which depend on N max and the predefined code rate R.
3. The device of claim 2 , wherein the device further comprises a memory unit and wherein the processor is configured to determine the parameters a and b on the basis of a look-up table stored in the memory.
4. The device of claim 3 , wherein the processor is configured to determine the parameters a and b on the basis of auxiliary parameters a′ and b′ provided in the look-up table and the following equations:
a=f ( R ) a′,
b=f ( R ) b′,
wherein f(R) denotes a function of the predefined code rate R and wherein the auxiliary parameters a′ and b′ depend on N max .
5. The device of claim 4 , wherein the processor is configured to determine the auxiliary parameters a′ and b′ on the basis of the look-up table and the look-up table is:
N max
b′
a′
64
32.455
−0.87273
128
77.319
−1.2332
256
138.56
−1.1028
512
275.89
−1.1111
1024
572.83
−1.1649
6. The device of claim 4 , wherein the processor is configured to determine the parameters a and b on the basis of the auxiliary parameters a′ and b′ provided in the look-up table and the following equations:
a=R 2 a′,
b=R 2 b′.
7. The device of claim 1 , wherein the processor is configured to determine the number of removed bits N R on the basis of the following equation:
N R =max(0,round( ap+b )),
wherein round( . . . ) denotes a rounding function, max( . . . ) denotes the maximum function and a and b denote parameters, which depend on N max and the predefined code rate R.
8. A method for generating a polar code of length N and dimension K on the basis of an original polar code being defined by a code sequence S having N max bit indices, wherein the method comprises:
generating an auxiliary code sequence having N max /2 bit indices by removing bit indices greater than or equal to N max /2 from the code sequence S;
removing from the auxiliary code sequence the last N R bit indices to generate a modified auxiliary code sequence, wherein N R denotes the number of removed bits and wherein the number of removed bits N R is determined on the basis of N max , N and a predefined code rate R; and
generating the polar code of length N and dimension K by puncturing the original polar code on the basis of a puncturing set defined by the last p=N max −N bit indices of the modified auxiliary code sequence.
9. The method of claim 8 , wherein the number of removed bits N R is determined on the basis of the following equation:
N R =round( ap+b ),
wherein round( . . . ) denotes a rounding function and a and b denote parameters, which depend on N max and the predefined code rate R.
10. The method of claim 9 , wherein the parameters a and b are determined on the basis of a look-up table.
11. The method of claim 10 , wherein the parameters a and b are determined on the basis of auxiliary parameters a′ and b′ provided in the look-up table and the following equations:
a=f ( R ) a′,
b=f ( R ) b′,
wherein f(R) denotes a function of the predefined code rate R and wherein the auxiliary parameters a′ and b′ depend on N max .
12. The method of claim 11 , wherein the auxiliary parameters a′ and b′ are determined on the basis of the look-up table and the look-up table is:
N max
b′
a′
64
32.455
−0.87273
128
77.319
−1.2332
256
138.56
−1.1028
512
275.89
−1.1111
1024
572.83
−1.1649
13. The method of claim 11 , wherein the parameters a and b are determined on the basis of the auxiliary parameters a′ and b′ provided in the look-up table and the following equations:
a=R 2 a′,
b=R 2 b′.
14. The method of claim 8 , wherein the number of removed bits N R is determined on the basis of the following equation:
N R =max(0,round( ap+b )),
wherein round( . . . ) denotes a rounding function, max( . . . ) denotes the maximum function and a and b denote parameters, which depend on N max and the predefined code rate R.
15. A non-transitory computer storage medium storing a program code, wherein when the program code is executed by a computer, the program code causes the computer to perform:
generating an auxiliary code sequence having N max /2 bit indices by removing bit indices greater than or equal to N max /2 from the code sequence S;
removing from the auxiliary code sequence the last N R bit indices to generate a modified auxiliary code sequence, wherein N R denotes the number of removed bits and wherein the number of removed bits N R is determined on the basis of N max , N and a predefined code rate R; and
generating the polar code of length N and dimension K by puncturing the original polar code on the basis of a puncturing set defined by the last p=N max −N bit indices of the modified auxiliary code sequence.
16. The computer storage medium of claim 15 , wherein the number of removed bits N R is determined on the basis of the following equation:
N R =round( ap+b ),
wherein round( . . . ) denotes a rounding function and a and b denote parameters, which depend on N max and the predefined code rate R.
17. The computer storage medium of claim 16 , wherein the parameters a and b are determined on the basis of a look-up table.
18. The computer storage medium of claim 17 , wherein the parameters a and b are determined on the basis of auxiliary parameters a′ and b′ provided in the look-up table and the following equations:
a=f ( R ) a′,
b=f ( R ) b′,
wherein f(R) denotes a function of the predefined code rate R and wherein the auxiliary parameters a′ and b′ depend on N max .
19. The computer storage medium of claim 18 , wherein the auxiliary parameters a′ and b′ are determined on the basis of the look-up table and the look-up table is:
N max
b′
a′
64
32.455
−0.87273
128
77.319
−1.2332
256
138.56
−1.1028
512
275.89
−1.1111
1024
572.83
−1.1649
20. The computer storage medium of claim 19 , wherein the parameters a and b are determined on the basis of the auxiliary parameters a′ and b′ provided in the look-up table and the following equations:
a=R 2 a′,
b=R 2 b′.
21. The computer storage medium of claim 15 , wherein the number of removed bits N R is determined on the basis of the following equation:
N R =max(0,round( ap+b )),
wherein round( . . . ) denotes a rounding function, max( . . . ) denotes the maximum function and a and b denote parameters, which depend on N max and the predefined code rate R.