Polar codes and modulation mappings

1. A method for wireless communication, comprising:

performing polar coding to encode a plurality of bits, the polar coding associated with a plurality of component channels associated with a polar code length, wherein the plurality of component channels correspond to two or more pairs of encoded bits, each pair of encoded bits having a same erasure probability, and wherein a quantity of the component channels is based at least in part on the polar code length, and wherein the polar coding is based at least in part on an asymmetry of a generating matrix for encoding the plurality of bits;

interleaving the encoded bits, wherein the interleaving comprises reordering the encoded bits based at least in part on the asymmetry of the generating matrix and an ordering of a reliability of each component channel of the plurality of component channels resulting from the asymmetry of the generating matrix;

mapping the interleaved encoded bits to a modulation symbol, wherein the mapping of each encoded bit is based at least in part on the asymmetry of the generating matrix, and wherein the mapping is configured to polarize the reliability of each component channel of the plurality of component channels; and

transmitting the interleaved encoded bits based at least in part on the mapping.

2. The method of claim 1 , wherein the interleaving comprises:

grouping the encoded bits serially according to the asymmetry of the generating matrix.

3. The method of claim 1 , wherein the mapping is different for different modulation schemes.

4. The method of claim 1 , wherein the interleaving comprises:

matching a first set of encoded bits associated with a first channel reliability to a first portion of the modulation symbol; and

matching a second set of encoded bits associated with a second channel reliability to a second portion of the modulation symbol.

5. The method of claim 1 , wherein the mapping comprises:

using at least one of an anti-Gray mapping or a Gray mapping for a quadrature phase shift keying (QPSK) modulation scheme.

6. The method of claim 1 , wherein the mapping comprises:

using at least one of a natural binary mapping, or a random mapping, or a Gray mapping for a 16 quadrature amplitude modulation (16-QAM) modulation scheme.

7. The method of claim 1 , wherein the mapping comprises:

using a Gray mapping or a random mapping for a 2{circumflex over ( )}2M quadrature amplitude modulation (2{circumflex over ( )}2M-QAM) modulation scheme.

8. The method of claim 1 , wherein performing polar coding comprises:

using a plurality of redundant polar coders to concurrently encode the plurality of bits, wherein each polar coder is associated with a different group of bits from the plurality of bits.

9. The method of claim 1 , wherein each pair of encoded bits is grouped based at least in part on the same erasure probability.

10. An apparatus for wireless communication, comprising:

means for performing polar coding to encode a plurality of bits, the polar coding associated with a plurality of component channels associated with a polar code length, wherein the plurality of component channels correspond to two or more pairs of encoded bits, each pair of encoded bits having a same erasure probability, and wherein a quantity of the component channels is based at least in part on the polar code length, and wherein the polar coding is based at least in part on an asymmetry of a generating matrix for encoding the plurality of bits;

means for interleaving the encoded bits, wherein the interleaving comprises reordering the encoded bits based at least in part on the asymmetry of the generating matrix and an ordering of a reliability of each component channel of the plurality of component channels resulting from the asymmetry of the generating matrix;

means for mapping the interleaved encoded bits to a modulation symbol, wherein the mapping of each encoded bit is based at least in part on the asymmetry of the generating matrix, and wherein the mapping is configured to polarize the reliability of each component channel of the plurality of component channels; and

means for transmitting the interleaved encoded bits based at least in part on the mapping.

11. The apparatus of claim 10 , wherein the means for interleaving comprises:

means for grouping the encoded bits serially according to the asymmetry of the generating matrix.

12. The apparatus of claim 10 , wherein the means for mapping is different for different modulation schemes.

13. The apparatus of claim 10 , wherein the means for interleaving comprises:

means for matching a first set of encoded bits associated with a first channel reliability to a first portion of the modulation symbol; and

means for matching a second set of encoded bits associated with a second channel reliability to a second portion of the modulation symbol.

14. The apparatus of claim 10 , wherein the means for mapping comprises:

means for using at least one of an anti-Gray mapping or a Gray mapping for a quadrature phase shift keying (QPSK) modulation scheme.

15. The apparatus of claim 10 , wherein the means for mapping comprises:

means for using at least one of a natural binary mapping, or a random mapping, or a Gray mapping for a 16 quadrature amplitude modulation (16-QAM) modulation scheme.

16. The apparatus of claim 10 , wherein the means for mapping comprises:

means for using a Gray mapping or a random mapping for a 2{circumflex over ( )}2M quadrature amplitude modulation (2{circumflex over ( )}2M-QAM) modulation scheme.

17. The apparatus of claim 10 , wherein the means for performing polar coding comprises:

means for using a plurality of redundant polar coders to concurrently encode the plurality of bits, wherein each polar coder is associated with a different group of bits from the plurality of bits.

18. An apparatus for wireless communication, in a system comprising:

a processor;

memory in electronic communication with the processor; and

instructions stored in the memory and executable by the processor to cause the apparatus to:

perform polar coding to encode a plurality of bits, the polar coding associated with a plurality of component channels associated with a polar code length, wherein the plurality of component channels correspond to two or more pairs of encoded bits, each pair of encoded bits having a same erasure probability, and wherein a quantity of the component channels is based at least in part on the polar code length, and wherein the polar coding is based at least in part on an asymmetry of a generating matrix for encoding the plurality of bits;

interleave the encoded bits, wherein the instructions executable by the processor to cause the apparatus to interleave comprise instructions executable by the processor to cause the apparatus to reorder the encoded bits based at least in part on the asymmetry of the generating matrix and an ordering of a reliability of each component channel of the plurality of component channels resulting from the asymmetry of the generating matrix;

map the interleaved encoded bits to a modulation symbol, wherein the mapping of each encoded bit is based at least in part on the asymmetry of the generating matrix, and wherein the mapping is configured to polarize the reliability of each component channel of the plurality of component channels; and

transmit the interleaved encoded bits based at least in part on the mapping.

19. The apparatus of claim 18 , wherein the instructions executable by the processor to cause the apparatus to interleave comprise instructions executable by the processor to cause the apparatus to:

group the encoded bits serially according to the asymmetry of the generating matrix.

20. The apparatus of claim 18 , wherein the mapping is different for different modulation schemes.

21. The apparatus of claim 18 , wherein the instructions executable by the processor to cause the apparatus to interleave comprise instructions executable by the processor to cause the apparatus to:

match a first set of encoded bits associated with a first channel reliability to a first portion of the modulation symbol; and

match a second set of encoded bits associated with a second channel reliability to a second portion of the modulation symbol.

22. The apparatus of claim 18 , wherein the instructions executable by the processor to cause the apparatus to map comprise instructions executable by the processor to cause the apparatus to:

use at least one of an anti-Gray mapping or a Gray mapping for a quadrature phase shift keying (QPSK) modulation scheme.

23. The apparatus of claim 18 , wherein the instructions executable by the processor to cause the apparatus to map comprise instructions executable by the processor to cause the apparatus to:

use at least one of a natural binary mapping, or a random mapping, or a Gray mapping for a 16 quadrature amplitude modulation (16-QAM) modulation scheme.

24. The apparatus of claim 18 , wherein the instructions executable by the processor to cause the apparatus to map comprise instructions executable by the processor to cause the apparatus to:

use a Gray mapping or a random mapping for a 2{circumflex over ( )}2M quadrature amplitude modulation (2{circumflex over ( )}2M-QAM) modulation scheme.

25. The apparatus of claim 18 , wherein the instructions executable by the processor to cause the apparatus to perform polar coding comprise instructions executable by the processor to cause the apparatus to:

use a plurality of redundant polar coders to concurrently encode the plurality of bits, wherein each polar coder is associated with a different group of bits from the plurality of bits.

26. A non-transitory computer readable medium storing code for wireless communication, the code comprising instructions executable by a processor to:

perform polar coding to encode a plurality of bits, the polar coding associated with a plurality of component channels associated with a polar code length, wherein the plurality of component channels correspond to two or more pairs of encoded bits, each pair of encoded bits having a same erasure probability, and wherein a quantity of the component channels is based at least in part on the polar code length, and wherein the polar coding is based at least in part on an asymmetry of a generating matrix for encoding the plurality of bits;

interleave the encoded bits, wherein the instructions executable by the processor to interleave comprise instructions executable by the processor to reorder the encoded bits based at least in part on the asymmetry of the generating matrix and an ordering of a reliability of each component channel of the plurality of component channels resulting from the asymmetry of the generating matrix;

map the interleaved encoded bits to a modulation symbol, wherein the mapping of each encoded bit is based at least in part on the asymmetry of the generating matrix, and wherein the mapping is configured to polarize the reliability of each component channel of the plurality of component channels; and

transmit the interleaved encoded bits based at least in part on the mapping.

27. The non-transitory computer readable medium of claim 26 , wherein the instructions executable by the processor to interleave comprise instructions executable by the processor to:

grouping the encoded bits serially according to the asymmetry of the generating matrix.