Enhanced polarization weighting to enable scalability in polar code bit distribution
Methods and devices are described for determining reliabilities of bit positions in a bit sequence for information bit allocation using polar codes. The reliabilities are calculated using a weighted summation over a binary expansion of each bit position, wherein the summation is weighted by an exponential factor that is selected based at least in part on the coding rate of the polar code. Information bits and frozen bits are allocated to the bit positions based on the determined reliabilities, and data is polar encoded as the information bits. The polar encoded data is then transmitted to a remote device.
1. A method for transmitting polar encoded data, the method comprising:
storing data to be polar encoded;
determining a reliability associated with each bit position in a bit sequence by:
calculating a sequence of weighted summations corresponding to each of the bit positions, wherein the reliability of each bit position is determined from its respective weighted summation, wherein the weighted summations are calculated according to the expression w i =Σ j=0 n−1 b j ·β j , wherein w i is the weighted summation for the i th bit position, wherein j is a summation index, wherein n is a total number of bit positions in the bit sequence, wherein b j are elements of a binary expansion over a respective bit position, wherein
β
j
=
2
j
1
m
,
and wherein m is a numerical value different from 4;
rank ordering the bit positions based on their respective reliabilities;
allocating the data as information bits in the most reliable bit positions of a polar code based on the rank ordering;
allocating the remaining portion of bit positions as frozen bits of the polar code;
polar encoding the information bits and the frozen bits; and
transmitting the polar encoded information bits and frozen bits.
2. The method of claim 1 , the method further comprising:
determining a coding rate for polar encoding the data, wherein m is selected based at least in part on the coding rate.
3. The method of claim 1 ,
wherein m comprises an adjustable parameter that is tunable based at least in part on the block size.
4. The method of claim 3 ,
wherein m is selected to spread a distribution of the information bits of the polar code to earlier bit positions relative to a distribution obtained from selecting m=4.
5. The method of claim 1 , wherein m is selected such that the polar code approximates a corresponding polar code, wherein the corresponding polar code implements a coding rate associated with the polar encoding and is constructed using an alternative polar code construction methodology.
6. The method of claim 5 ,
wherein the polar code is constructed according to an enhanced polarization weighting methodology, and wherein the alternative polar code construction methodology comprises a fractally enhanced kernel (FRANK) polar code construction methodology.
7. The method of claim 1 , the method further comprising:
storing second data to be polar encoded;
determining a second coding rate for polar encoding the second data;
determining a second reliability associated with each bit position in the bit sequence by:
calculating a second sequence of second weighted summations corresponding to each of the bit positions, wherein the second reliability of each bit position is determined from its respective second weighted summation, wherein the second weighted summations are calculated according to the expression w 2,i =Σ k=0 n−1 b k ·β 2,k , wherein w 2,i is the weighted summation for the i th bit position, wherein k is a summation index, wherein b k are elements of a binary expansion over a respective bit position, wherein
β
2
,
k
=
2
k
·
1
p
,
and wherein p is a numerical value different from 4, and wherein p is different from m;
performing second rank ordering of the bit positions based on their respective second reliabilities;
allocating the second data as second information bits in the most reliable bit positions of a second polar code based on the second rank ordering;
allocating the remaining portion of bit positions as second frozen bits of the second polar code;
polar encoding the second information bits and the second frozen bits; and
transmitting the polar encoded second information bits and second frozen bits.
8. A user equipment device (UE), comprising:
a radio;
a memory; and
one or more processing elements operably coupled to the radio and the memory;
wherein the radio, the memory, and the one or more processing elements are configured to:
store data to be polar encoded in the memory;
determine a reliability associated with each bit position in a bit sequence, wherein the reliability of each respective bit position is determined by computing a weighted sum over a binary expansion of the respective bit position, wherein the reliability of each bit position is determined from its respective weighted summation, wherein the weighted summations are calculated according to the expression w i =Σ j=0 n−1 b j ·β j , wherein w i is the weighted summation for the i th bit position, wherein j is a summation index, wherein n is a total number of bit positions in the bit sequence, wherein b j are elements of a binary expansion over a respective bit position, wherein
β
j
=
2
j
·
1
m
,
and wherein m is a numerical value different from 4;
rank order the bit positions based on their respective reliabilities; and
allocate the data as information bits in the most reliable bit positions of a polar code based on the rank ordering;
allocate the remaining portion of bit positions as frozen bits of the polar code;
polar encode the information bits and the frozen bits; and
transmit, via the radio, the polar encoded information bits and frozen bits.
9. The UE of claim 8 , wherein the radio, the memory, and the one or more processing elements are further configured to:
determine a coding rate associated with the polar encoding, wherein the sum is weighted further based at least in part on the coding rate.
10. The UE of claim 8 ,
wherein m comprises an adjustable parameter that is tunable based at least in part on a block size of the polar code.
11. The UE of claim 8 ,
wherein m comprises an adjustable parameter that is tunable based at least in part on a coding rate associated with the polar encoding.
12. The UE of claim 8 ,
wherein m is selected to spread a distribution of the information bits of the polar code to earlier bit positions relative to a distribution obtained from selecting m=4.
13. The UE of claim 8 , wherein m is selected such that the polar code approximates a corresponding polar code, wherein the corresponding polar code implements a coding rate associated with the polar encoding and is constructed using an alternative polar code construction methodology.
14. The UE of claim 13 ,
wherein the polar code is constructed according to an enhanced polarization weighting methodology, and wherein the alternative polar code construction methodology comprises a fractally enhanced kernel (FRANK) polar code construction methodology.
15. An apparatus, comprising:
one or more processing elements configured to cause a wireless device to:
store data to be polar encoded;
determine a reliability associated with each bit position in a bit sequence, wherein in determining the reliability associated with each bit position in the bit sequence, the processing element is configured to:
calculate a sequence of weighted summations corresponding to each of the bit positions, wherein the reliability of each bit position is determined from its respective weighted summation, wherein the weighted summations are calculated according to the expression w i =Σ j=0 n−1 b j ·β j , wherein w i is the weighted summation for the i th bit position, wherein j is a summation index, wherein n is a total number of bit positions in the bit sequence, wherein b j are elements of a binary expansion over a respective bit position, wherein
β
j
=
2
j
1
m
,
and wherein m is a numerical value different from 4;
rank order the bit positions based on their respective reliabilities;
allocate the data as information bits in the most reliable bit positions of a polar code based on the rank ordering;
allocate the remaining portion of bit positions as frozen bits of the polar code;
polar encode the information bits and the frozen bits; and
transmit the polar encoded information bits and frozen bits.
16. The apparatus of claim 15 , wherein the one or more processing elements are further configured to cause the wireless device to:
determine a coding rate for polar encoding the data, wherein m is selected based at least in part on the coding rate.
17. The apparatus of claim 15 ,
wherein m comprises an adjustable parameter that is tunable based at least in part on the coding rate.
18. The apparatus of claim 15 ,
wherein m is selected to spread a distribution of the information bits of the polar code to earlier bit positions relative to a distribution obtained from selecting m=4.
19. The apparatus of claim 15 , wherein m is selected such that the polar code approximates a corresponding polar code, wherein the corresponding polar code implements a coding rate associated with the polar encoding and is constructed using an alternative polar code construction methodology.
20. The apparatus of claim 19 ,
wherein the polar code is constructed according to an enhanced polarization weighting methodology, and wherein the alternative polar code construction methodology comprises a fractally enhanced kernel (FRANK) polar code construction methodology.