Methods and apparatus for transmission and reception with polar codes
Method and apparatus for transmission and reception with polar codes are provided to support up to 16 permutations or transformation mappings. For example, 16 versions of copies able to be soft-combined for PBCH or any other data channel or control channel are suggested if the mother code length is 256 or 512 or 1024. With the new design, up to 16 different versions can be used to soft combined to improve the performance. Some sequences are provided as examples to support 16 different permutation patterns. The inverse of these sequences also have the feature to support 16 different permutation patterns.
1. A polar encoding method in a transmitting device, comprising,
obtaining an information bit sequence, wherein the information bit sequence corresponds to a basic ordered sequence with a symmetric property;
making a number of different transformation mappings on the information bit sequence to obtain a transformed sequence, wherein the number of different transformation mappings is dr, and each of the dr mappings is one of d number of transformation patterns, wherein dr and d are integers, d is a maximum number of different transformation patterns for the basic ordered sequence, dr<=d, and a length of the basic ordered sequence N is equal to 2 m ; and
encoding the transformed sequence based on the basic ordered sequence.
2. The polar encoding method in claim 1 , where, the transformation mapping φ satisfies:
∀
j
∈
{
0
,
1
,
…
,
m
-
1
}
φ
(
x
j
)
=
x
j
+
∑
s
=
n
j
+
1
2
m
-
1
r
s
(
j
)
·
m
i
s
wherein x j is a variable, j and m are integers, m i is a m-variate monomial corresponds to g i , g i is the ith row of mth Kronecker power of matrix
[
1
0
1
1
]
,
r s (j) ∈{0,1}, s is from {n j +1, n j +2, . . . , 2 m −1}, n j is specified such that i n j =2 m −1−2 j , and i n j is the n j -th value of the basic ordered sequence.
3. The polar encoding method in claim 2 , wherein if the values of all r s (j) are fixed for the basic ordered sequence, and there are up to d different transformation mapping.
4. The polar encoding method in claim 1 , wherein the information bit sequence includes cyclic redundancy check bits.
5. The polar encoding method in any of claim 1 , wherein
d=16 if the length of the basic ordered sequence is 256 or 512 or 1024; or
d=8 if the length of the basic ordered sequence is 16 or 32 or 64 or 128.
6. The polar encoding method in claim 1 , wherein the information bit sequence includes the information of a primary broadcast channel.
7. A polar encoding method in a transmitting device, comprising,
obtaining an information bit sequence, wherein the information bit sequence corresponds to a basic ordered sequence N with a symmetric property;
encoding the information bit sequence based on the basic ordered sequence, wherein a length of the basic ordered sequence N is equal to 2 m ; and
making dr number of different permutations, wherein each of the dr number of permutations is one of d number of permutation patterns, where dr and d are integers, d is the maximum number of different permutation patterns for the basic ordered sequence, dr<=d.
8. The polar encoding method in claim 7 , where one of the d permutation patterns is calculated from a transformation mapping φ.
9. The polar encoding method in claim 8 , where the i th element of the permutation pattern is
∀i∈{0, 1, . . . , N−1} π(i)=j i , wherein the number j i satisfies that i-th column of M, M is the submatrix of G 2 ⊗m that include all rows with row weight of N/2, G 2 ⊗m is the mth Kronecker power of matrix
[
1
0
1
1
]
,
M φ is constructed based on the transformation map φ.
10. The polar encoding method in claim 8 , where the transformation mapping φ satisfies:
∀
j
∈
{
0
,
1
,
…
,
m
-
1
}
φ
(
x
j
)
=
x
j
+
∑
s
=
n
j
+
1
2
m
-
1
r
s
(
j
)
·
m
i
s
wherein x j is a variable, j and m are integers, m i is a m-variate monomial corresponds to g i , g i is the i-th row of m-th Kronecker power of matrix
[
1
0
1
1
]
,
r s (j) ∈{0,1}, s is from {n j +1, n j +2, . . . , 2 m −1}, n j is specified such that i n j =2 m −1−2 j , and i n j is the n j -th value of the basic ordered sequence.
11. The polar encoding method in claim 7 , wherein if the values of all s are fixed for the basic ordered sequence, there are up to d different permutation patterns.
12. The polar encoding method in claim 7 , wherein the information bit sequence includes cyclic redundancy check bits.
13. The polar encoding method in claim 7 , wherein
d=16 if the length of the basic ordered sequence is 256 or 512 or 1024; or
d=8 if the length of the basic ordered sequence is 16 or 32 or 64 or 128.
14. The polar encoding method in claim 7 , wherein the information bit sequence includes the information of a primary broadcast channel.
15. A polar decoding method in a receiving device, comprising
obtaining a to-be-decoded sequence, wherein the to-be-decoded sequence corresponds to a basic ordered sequence with a symmetric property;
making a number of different de-permutations over the to-be-decoded sequence, wherein the number of different de-permutations is dr and each of the dr de-permutation patterns corresponds to a permutation pattern in a transmitting device, wherein the permutation is one of d permutation patterns, dr and d are integers, d is a maximum number of different permutation patterns for the basic ordered sequence;
decoding the de-permutated to-be-decoded sequence based on a basic ordered sequence, the length of the basic ordered sequence N is equal to 2 m .
16. The polar decoding method in claim 15 , where the permutation pattern is calculated from a transformation mapping φ.
17. The polar decoding method in claim 15 , where the ith element of the permutation pattern is
∀i∈{0, 1, . . . , N−1} π(i)=j i , wherein the number j i satisfies that i-th column of M, M is the submatrix of G 2 ⊗m that include all rows with row weight of N/2, G 2 ⊗m is the m-th Kronecker power of matrix
[
1
0
1
1
]
,
M φ is constructed based on the transformation map φ.
18. The polar decoding method in claim 16 , where the transformation mapping φ satisfies:
∀
j
∈
{
0
,
1
,
…
,
m
-
1
}
φ
(
x
j
)
=
x
j
+
∑
s
=
n
j
+
1
2
m
-
1
r
s
(
j
)
·
m
i
s
where x j is a variable, j and m are integers, m i is a m-variate monomial corresponds to g i , g i is the ith row of mth Kronecker power of matrix
[
1
0
1
1
]
,
r s (j) ∈{0,1}, s is from {n j +1, n j +2, . . . , 2 m −1} n j is specified such that i n j =2 m −1−2 j , and i n j is the n j -th value of the basic ordered sequence.
19. The polar encoding method in claim 15 , wherein if the values of all r s (j) are fixed for the basic ordered sequence, there are up to d different permutation patterns.
20. The polar encoding method in claim 15 , wherein the information bit sequence includes cyclic redundancy check bits.