Decoding method and apparatus of polar code

1. A decoding method of a polar code which is performed by a decoding terminal, comprising:

receiving a receiving sequence which is output on a channel after an input mapping sequence is encoded;

determining a check matrix corresponding to the input mapping sequence;

carrying out Trellis path search according to the receiving sequence and the check matrix, and determining Trellis path likelihood information corresponding to the input mapping sequence;

determining a decision value corresponding to the input mapping sequence according to the Trellis path likelihood information corresponding to the input mapping sequence; and

determining a decoded sequence by de-mapping the decision value corresponding to the input mapping sequence according to a preset mapping relation.

2. The method of claim 1 , wherein the input mapping sequence is a sequence obtained by mapping an input sequence according to the preset mapping relation; and

the determining the Trellis path likelihood information corresponding to the input mapping sequence comprises:

determining the Trellis path likelihood information corresponding to the input mapping sequence according to an encoding sequence, wherein the encoding sequence is a sequence obtained by encoding the input mapping sequence.

3. The method of claim 2 , wherein the input mapping sequence is a symbol set which belongs to a finite field GF(q) and comprises a plurality of input mapping values, wherein q=2 m , and m is a positive integer greater than 1; and

the preset mapping relation comprises: correspondingly mapping every m bits in the input sequence to each input mapping value.

4. The method of claim 3 , wherein the encoding sequence is a sequence obtained by encoding the input mapping sequence through an encoding formula, the encoding formula is: x 1 N =u 1 N G N , the encoding sequence is obtained by x 1 N through an encoding channel, wherein u 1 N refers to the input mapping sequence, G N refers to a preset N-order generator matrix, G N =B N F ⊗n , B N refers to a permutation matrix, F ⊗n refers to a Kronecker power, F ⊗n =F⊗F ⊗(n-1) , N refers to a code length, N=m2 mn , n≥0.

5. The method of claim 4 , wherein the determining the Trellis path likelihood information corresponding to the input mapping sequence comprises:

calculating the Trellis path likelihood information corresponding to the input mapping sequence according to a condition likelihood function formula, and the condition likelihood function formula is:

L (i) ( y 1 N ,û 1 i-1 )=( u i ∈GF ( q ) argmax P u i /U 1 i-1 ,Y 1 N ( u i /û 1 i-1 ,y 1 N ),

wherein, y 1 N refers to the receiving sequence, u 1 N and y 1 N satisfy probability distribution:

P

U

1

N

,

Y

1

N

⁡

(

u

1

N

,

y

1

N

)

=

1

q

N

⁢

W

N

⁡

(

y

1

N

/

u

1

N

⁢

G

N

)

.

6. The method of claim 5 , wherein a parameter of the polar code is (N, K, A, u A C ), A refers to a set of information bit indexes, A C refers to a complementary set of A, K refers to the number of elements in A, and u A C refers to frozen bits with the number of (N−K);

the determining the decision value corresponding to the input mapping sequence according to the Trellis path likelihood information corresponding to the input mapping sequence comprises:

if i⊂A, making û i =L (i) (y 1 N ,û 1 i-1 ); and

if i⊂A C , making û i =u i .

7. The method of claim 3 , wherein when m=2, the input mapping sequence is a sequence composed of elements in (0, 1, α, α 2 ); and the preset N-order generator matrix is: G 4 =B 4 F RS4 ⊗n , wherein,

F

R

⁢

⁢

S

⁢

⁢

4

=

(

1

1

1

0

α

α

2

1

0

α

2

α

1

0

⁢

1

1

1

α

)

.

8. The method of claim 7 , wherein when m=2, the check matrix comprises a first check matrix and a second check matrix, wherein the first check matrix is: H 01 =(1 1 1 α 2 ); and

the second check matrix is:

H

02

=

(

1

1

1

α

2

α

α

2

0

α

2

)

.

9. The method of claim 3 , wherein when m=3, the input mapping sequence is a sequence composed of elements in (0, 1, α, α 2 , α 3 , α 4 , α 5 , α 6 ); and the preset N-order generator matrix is: G 8 =B 8 F RS8 ⊗n , wherein,

F

RS

⁢

⁢

8

=

(

1

1

1

1

1

1

1

0

α

α

2

α

3

α

4

α

5

α

6

1

0

α

2

α

4

α

6

α

1

α

3

α

5

1

0

α

3

α

6

α

2

α

5

α

1

α

4

1

0

α

4

α

1

α

5

α

2

α

6

α

3

1

0

α

5

α

3

α

1

α

6

α

4

α

2

1

0

α

6

α

5

α

4

α

3

α

2

α

1

1

0

1

1

1

1

1

1

1

α

)

.

10. The method of claim 9 , wherein when m=3, the check matrix comprises a third check matrix, a fourth check matrix, a fifth check matrix and a sixth check matrix, wherein the third check matrix is: H 001 =(1 1 1 1 1 1 1 α 6 );

the fourth check matrix is:

H

002

=

(

1

1

1

1

1

1

1

α

6

α

6

α

5

α

4

α

3

α

2

α

1

1

0

)

;

the fifth check matrix is:

H

003

=

(

1

1

1

1

1

1

1

α

6

α

6

α

5

α

4

α

3

α

2

α

1

1

0

α

5

α

3

α

1

α

6

α

4

α

2

1

0

)

;

 and

the sixth check matrix is:

H

004

=

(

1

1

1

1

1

1

1

α

6

α

6

α

5

α

4

α

3

α

2

α

1

1

0

α

5

α

3

α

1

α

6

α

4

α

2

1

0

α

4

α

1

α

5

α

2

α

6

α

3

1

0

)

.

11. A decoding apparatus of a polar code, comprising:

a processor; and

a non-transitory computer-readable medium including computer-executable instructions that, when executed by the processor, facilitate the decoding apparatus carrying out a method comprising:

receiving a receiving sequence which is output on a channel after an input mapping sequence is encoded;

determining a check matrix corresponding to the input mapping sequence;

carrying out Trellis path search according to the receiving sequence and the check matrix, and determining Trellis path likelihood information corresponding to the input mapping sequence;

determining a decision value corresponding to the input mapping sequence according to the Trellis path likelihood information corresponding to the input mapping sequence; and

determining a decoded sequence by de-mapping the decision value corresponding to the input mapping sequence according to a preset mapping relation.

12. The apparatus of claim 11 , wherein the input mapping sequence is a sequence obtained by mapping an input sequence according to the preset mapping relation; and

wherein the determining the Trellis path likelihood information corresponding to the input mapping sequence comprises:

determining the Trellis path likelihood information corresponding to the input mapping sequence according to an encoding sequence, wherein the encoding sequence is a sequence obtained by encoding the input mapping sequence.

13. The apparatus of claim 12 , wherein the input mapping sequence is a symbol set which belongs to a finite field GF(q) and comprises a plurality of input mapping values, wherein q=2 m , and m is a positive integer greater than 1; and

the preset mapping relation comprises: correspondingly mapping every m bits in the input sequence to each input mapping value.

14. The apparatus of claim 13 , wherein the encoding sequence is a sequence obtained by encoding the input mapping sequence through an encoding formula, the encoding formula is: x 1 N =u 1 N G N , the encoding sequence is obtained by x 1 N through an encoding channel, wherein u 1 N refers to the input mapping sequence, G N refers to a preset N-order generator matrix, G N =B N F ⊗n , B N refers to a permutation matrix, F ⊗n refers to a Kronecker power, F ⊗n =F⊗F ⊗(n-1) , N refers to a code length, N=m2 mn , n≥0.

15. The apparatus of claim 14 , wherein the determining the Trellis path likelihood information corresponding to the input mapping sequence comprises:

determining the Trellis path likelihood information corresponding to the input mapping sequence according to a condition likelihood function formula, and the condition likelihood function formula is:

L (i) ( y 1 N ,û 1 i-1 )=( u i ∈GF ( q ) argmax P u i /U 1 i-1 ,Y 1 N ( u i /û 1 i-1 ,y 1 N ),

wherein, y 1 N refers to the receiving sequence, u 1 N and y 1 N satisfy probability distribution:

P

U

1

N

,

Y

1

N

⁡

(

u

1

N

,

y

1

N

)

=

1

q

N

⁢

W

N

⁡

(

y

1

N

/

u

1

N

⁢

G

N

)

.

16. The apparatus of claim 15 , wherein a parameter of the polar code is (N, K, A, u A C ), A refers to a set of information bit indexes, A C refers to a complementary set of A, K refers to the number of elements in A, and u A C refers to frozen bits with the number of (N−K);

wherein the determining the decision value corresponding to the input mapping sequence according to the Trellis path likelihood information corresponding to the input mapping sequence comprises:

if i⊂A, making û i =L (i) (y 1 N ,û 1 i-1 ); and

if i⊂A C , making û i =u i .

17. The apparatus of claim 13 , wherein when m=2, the input mapping sequence is a sequence composed of elements in (0, 1, α, α 2 ); and the preset N-order generator matrix is: G 4 =B 4 F RS4 ⊗n , wherein,

F

RS

⁢

⁢

4

=

(

1

1

1

0

α

α

2

1

0

α

2

α

1

0

1

1

1

α

)

.

18. The apparatus of claim 17 , wherein when m=2, the check matrix comprises a first check matrix and a second check matrix, wherein the first check matrix is: H 01 =(1 1 1 α 2 ); and

the second check matrix is:

H

02

=

(

1

1

1

α

2

α

α

2

0

α

2

)

.

19. The apparatus of claim 13 , wherein when m=3, the input mapping sequence is a sequence composed of elements in (0,1, α, α 2 , α 3 , α 4 , α 5 , α 6 ); and the preset N-order generator matrix is: G 8 =B 8 F RS8 ⊗n , wherein,

F

RS

⁢

⁢

8

=

(

1

1

1

1

1

1

1

0

α

α

2

α

3

α

4

α

5

α

6

1

0

α

2

α

4

α

6

α

1

α

3

α

5

1

0

α

3

α

6

α

2

α

5

α

1

α

4

1

0

α

4

α

1

α

5

α

2

α

6

α

3

1

0

α

5

α

3

α

1

α

6

α

4

α

2

1

0

α

6

α

5

α

4

α

3

α

2

α

1

1

0

1

1

1

1

1

1

1

α

)

.

20. The apparatus of claim 19 , wherein when m=3, the check matrix comprises a third check matrix, a fourth check matrix, a fifth check matrix and a sixth check matrix, wherein the third check matrix is: H 001 =(1 1 1 1 1 1 1 α 6 );

the fourth check matrix is:

H

002

=

(

1

1

1

1

1

1

1

α

6

α

6

α

5

α

4

α

3

α

2

α

1

1

0

)

;

the fifth check matrix is:

H

003

=

(

1

1

⁢

⁢

1

1

⁢

⁢

1

1

⁢

⁢

1

α

6

α

6

α

5

⁢

α

4

α

3

⁢

α

2

α

1

⁢

1

0

α

5

α

3

⁢

α

1

α

6

⁢

α

4

α

2

⁢

1

0

)

;

 and

the sixth check matrix is:

H

001

=

(

1

1

⁢

⁢

1

1

⁢

⁢

1

1

⁢

⁢

1

α

6

α

6

α

5

⁢

α

4

α

3

⁢

α

2

α

1

⁢

1

0

α

5

α

3

⁢

α

1

α

6

⁢

α

4

α

2

⁢

1

0

α

4

α

1

⁢

α

5

α

2

⁢

α

6

α

3

⁢

1

0

)

.