ENCODING METHOD, DECODING METHOD, CODER AND DECODER

• US 20110283162A1
• Filed: 11/12/2010
• Published: 11/17/2011
• Est. Priority Date: 11/13/2009
• Status: Active Grant

• Current Assignee: Panasonic Intellectual Property Corporation of America (Panasonic Holdings Corporation)
• Original Assignee: Panasonic Corporation (Panasonic Holdings Corporation)
• Inventors: Murakami, Yutaka
• Granted Patent: US 8,595,588 B2
• Time in Patent Office: Days
• US Class Current: 714/758
• CPC Class Codes: H03M 13/1105 Decoding
• CPC Class Codes: H03M 13/1111 Soft-decision decoding, e.g. by means of message passing or belief propagation algorithms
• CPC Class Codes: H03M 13/1154 Low-density parity-check convolutional codes [LDPC-CC]
• CPC Class Codes: H03M 13/13 Linear codes
• CPC Class Codes: H03M 13/157 Polynomial evaluation, i.e. determination of a polynomial sum at a given value
• CPC Class Codes: H04L 1/0041 Arrangements at the transmitter end
• CPC Class Codes: H04L 1/0057 Block codes H04L1/0061, H04L1/0064 take precedence

Abstract

An encoding method and encoder of a time-varying LDPC-CC with high error correction performance are provided. In an encoding method of performing low density parity check convolutional coding (LDPC-CC) of a time varying period of q using a parity check polynomial of a coding rate of (n−1)/n (where n is an integer equal to or greater than 2), the time varying period of q is a prime number greater than 3, the method receiving an information sequence as input and encoding the information sequence using equation 1 as a g-th (g=0, 1, . . . q−1) parity check polynomial to satisfy 0:

(D^a#g,1,1+D^a#g,1,2+D^a#g,1,3)X₁(D)+(D^a#g,2,1+D^a#g,2,1+D^a#g,2,2+D^a#g,2,3)X₂(D)+ . . . +(D^a#g,n−1,1+D^a#g,n−1,2+D^a#g,n−1,3)X_n−1(D)+(D^b#g,1+D^b#g,2+1)P(D)=0  (Equation 1)

• • where, in equation 1:
  • “%” represents a modulo and each coefficient satisfies the following with respect to k=1, 2, . . . , n−1:
  • a_#0,k,1%q=a_#1,k,1%q=a_#2,k,1%q=a_#3,k,1%q= . . . =a_#g,k,1%q= . . . =a_#q−2,k,1%q=a_#q−1,k,1%q=v_p=k (v_p=k: fixed value);
  • b_#0,1%q=b_#1,1%q=b_#2,1%q=b_#3,1%q= . . . =b_#g,1%q= . . . =b_#q−2,1%q=b_#q−1,1%q=w (w: fixed value);
  • a_#0,k,2%q=a_#1,k,2%q=a_#2,k,2%q=a_#3,k,2%q= . . . =a_#g,k,2%q= . . . =a_#q−2,k,2%q=a_#q−1,k,2%q=y_p=k (y_p=k: fixed value);
  • b_#0,2%q=b_#1,2%q=b_#2,2%q=b_#3,2%q= . . . =b_#g,2%q= . . . =b_#q−2,2%q=b_#q−1,2%q=z (z: fixed value); and
  • a_#0,k,3%q=a_#1,k,3%q=a_#2,k,3%q=a_#3,k,3%q= . . . =a_#g,k,3%q= . . . =a_#q−2,k,3%q=a_#q−1,k,3%q=s_p=k (s_p=k: fixed value);
  • a_#g,k,1, a_#g,k,2 and a_#g,k,3 are natural numbers equal to or greater than 1 and a_#g,k,1≠a_#g,k,2, a_#g,k,1≠a_#g,k,3 and a_#g,k,2≠a_#g,k,3 hold true;
  • b_#g,1 and b_#g,2 are natural numbers equal to or greater than 1 and b_#g,1≠b_#g,2 holds true; and
  • v_p=k and y_p=k are natural numbers equal to or greater than 1.

Claims

1. An encoding method for performing low density parity check convolutional coding (LDPC-CC) of a time varying period of q using a parity check polynomial of a coding rate of (n−

1)/n (where n is an integer equal to or greater than

     2), the method comprising;

using a prime number greater than 3 as the time varying period of q;

receiving an information sequence as input; and

encoding the information sequence using equation 1 as a g-th (g=0, 1, . . . , q−

1) parity cheek polynomial to satisfy 0;

(D^a#g,1,1+D^a#g,1,2+D^a#g,1,3)X₁(D)+(D^a#g,2,1+D^a#g,2,2+D^a#g,2,3)X₂(D)+ . . . +(D<sup>a#g,n−

1,1</sup>+D<sup>a#g,n−

1,2</sup>+D<sup>a#g,n−

1,3</sup>)X<sub>n−

1</sub>(D)+(D^b#g,1+D^b#g,2+1)P(D)=0 

 

(Equation

     1)

where, in equation 1;

“

%”

represents a modulo and each coefficient satisfies the following with respect to k=1, 2, . . . , n−

1;

a_#0,k,1%q=a_#1,k,1%q=a_#2,k,1%q=a_#3,k,1%q= . . . =a_#g,k,1%q= . . . =a<sub>#q−

2,k,1</sub>%q=a<sub>#q−

1,k,1</sub>%q=v_p=k (v_p=k;

fixed value);

b_#0,1%q=b_#1,1%q=b_#2,1%q=b_#3,1%q= . . . =b_#g,1%q= . . . =b<sub>#q−

2,1</sub>%q=b<sub>#q−

1,1</sub>%q=w (w;

fixed value);

a_#0,k,2%q=a_#1,k,2%q=a_#2,k,2%q=a_#3,k,2%q= . . . =a_#g,k,2%q= . . . =a<sub>#q−

2,k,2</sub>%q=a<sub>#q−

1,k,2</sub>%q=y_p=k (y_p=k;

fixed value);

b_#0,2%q=b_#1,2%q=b_#2,2%q=b_#3,2%q= . . . =b_#g,2%q= . . . =b<sub>#q−

2,2</sub>%q=b<sub>#q−

1,2</sub>%q=z (z;

fixed value); and

a_#0,k,3%q=a_#1,k,3%q=a_#2,k,3%q=a_#3,k,3%q= . . . =a_#g,k,3%q= . . . =a<sub>#q−

2,k,3</sub>%q=a<sub>#q−

1,k,3</sub>%q=s_p=k (s_p=k;

fixed value);

a_#g,k,1, a_#g,k,2 and a_#g,k,3 are natural numbers equal to or greater than 1 and a_#g,k,1≠

a_#g,k,2, a_#g,k,1≠

a_#g,k,3 and a_#g,k,2≠

a_#g,k,3 hold true;

b_#g,1 and b_#g,2 are natural numbers equal to or greater than 1 and b_#g,1≠

b_#g,2 holds true; and

v_p=k and y_p=k are natural numbers equal to or greater than 1.

2. The encoding method according to claim 1, wherein a_#g,k,3=0.

3. The encoding method according to claim 1, wherein:

i and j (i≠

j) are present where equation 2-1 and equation 2-2 hold true, or

i is present where equation 2-3 and equation 2-4 hold true.

(v_p=i,y_p=i)≠

(v_p=j,y_p=j) 

 

(Equation 2-1)

(v_p=i,y_p=i)≠

(y_p=j,v_p=j) 

 

(Equation 2-2)

(v_p=i,y_p=i)≠

(w,z) 

 

(Equation 2-3)

(v_p=i,y_p=i)≠

(z,w) 

 

(Equation 2-4)

where i=1, 2, . . . , n−

1, j=1, 2, . . . , n−

1, and i≠

j hold true.

10. A decoding method corresponding to the encoding method of claim 1 for performing low density parity check convolutional coding (LDPC-CC) of the time varying period of q (prime number greater than 3) using the parity check polynomial of the coding rate of (n−

1)/n (where n is an integer equal to or greater than

     2), the decoding method decoding an encoded information sequence encoded using equation 1 as the g-th (g=0, 1, . . . , q−

1) parity check polynomial to satisfy 0 and comprising;

receiving the encoded information sequence as input; and

decoding the encoded information sequence using belief propagation (BP) based on a parity check matrix generated using equation 1 which is the g-th parity check polynomial to satisfy 0.

11. The decoding method according to claim 10, wherein a_#g,k,3=0.

12. The decoding method according to claim 10, wherein:

i and j (i≠

j) are present where equation 1-1 and equation 1-2 hold true;

or

i is present where equation 1-3 and equation 1-4 hold true.

13. A decoder corresponding to the encoding method of claim 1 for performing low density parity check convolutional coding (LDPC-CC) of the time varying period of q (prime number greater than 3) using the parity check polynomial of the coding rate of (n−

1)/n (where n is an integer equal to or greater than

     2), the decoder decoding an encoded information sequence encoded using equation 1 as the g-th (g=0, 1, . . . , q−

1) parity check polynomial to satisfy 0 and comprising;

a decoding section that receives the encoded information sequence as input and decodes the encoded information sequence using belief propagation (BP) based on a parity check matrix generated using equation 1 which is the g-th parity check polynomial to satisfy 0.

14. The decoder according to claim 13, wherein a_#g,k,3=0.

15. The decoder according to claim 13, wherein:

i and j (i≠

j) are present where equation 1-1 and equation 1-2 hold true;

or

i is present where equation 1-3 and equation 1-4 hold true.

4. An encoding method of performing low density parity check convolutional coding (LDPC-CC) of a time varying period of q using a parity check polynomial of a coding rate of (n−

1)/n (where n is an integer equal to or greater than

     2), the method comprising;

using a prime number greater than 3 as the time varying period of q;

receiving an information sequence as input; and

encoding the information sequence using a g-th (g=0, 1, . . . , q−

1) parity check polynomial to satisfy 0, represented by equation 3;

(D^a#g,1,1+D^a#g,1,2+D^a#g,1,3)X₁(D)+(D^a#g,2,1+D^a#g,2,2+D^a#g,2,3)X₂(D)+ . . . +(D<sup>a#g,n−

1,1</sup>+D<sup>a#g,n−

1,2</sup>+D<sup>a#g,n−

1,3</sup>)X<sub>n−

1</sub>(D)+(D^b#g,1+D^b#g,2+1)P(D)=0 

 

(Equation

     3)

where the g-th parity check polynomial satisfy the following with respect to k=1, 2, . . . , n−

1;

a_#0,k,1%q=a_#1,k,1%q=a_#2,k,1%q=a_#3,k,1%q= . . . =a_#g,k,1%q= . . . =a_#q=2,k,1%q=a<sub>#q−

1,k,1</sub>%q=v_p=k (v_p=k;

fixed-value);

b_#0,1%q=b_#1,1%q=b_#2,1%q=b_#3,1%q= . . . =b_#g,1%q= . . . =b<sub>#q−

2,1</sub>%q=b<sub>#q−

1,1</sub>%q=w (w;

fixed-value);

a_#0,k,2%q=a_#1,k,2%q=a_#2,k,2%q=a_#3,k,2%q= . . . =a_#g,k,2%q= . . . =a<sub>#q−

2,k,2</sub>%q=a<sub>#q−

1,k,2</sub>%q=y_p=k (y_p=k;

fixed-value),

b_#0,2%q=b_#1,2%q=b_#2,2%q=b_#3,2%q= . . . =b_#g,2%q= . . . =b<sub>#q−

2,2</sub>%q=b<sub>#q−

1,2</sub>%q=z (z;

fixed-value); and

a_#0,k,3%q=a_#1,k,3%q=a_#2,k,3%q=a_#3,k,3%q= . . . =a_#g,k,3%q= . . . =a<sub>#q−

2,k,3</sub>%q=a_#1,k,3%q=s_p=k (s_p=k;

fixed-value).

5. The encoding method according to claim 4, wherein a_#g,k,3=0.

6. The encoding method according to claim 4, wherein:

i and j (i≠

j) are present where equation 4-1 and equation 4-2 hold true;

or

i is present where equation 4-3 and equation 4-4 hold true.

(v_p=i,y_p=i)≠

(v_p=j,y_p=j) 

 

(Equation 4-1)

(v_p=i,y_p=i)≠

(y_p=j,v_p=j) 

 

(Equation 4-2)

(v_p=i,y_p=i)≠

(w,z) 

 

(Equation 4-3)

(v_p=i,y_p=i)≠

(z,w) 

 

(Equation 4-4)

where i=1, 2, . . . , n−

1, j=1, 2, . . . , n−

1, and i≠

j hold true.

7. An encoder to perform low density parity check convolutional coding (LDPC-CC) of a time varying period of q using a parity check polynomial of a coding rate of (n−

1)/n (where n is an integer equal to or greater than

     2), using a prime number greater than 3 as the time varying period of q, the encoder comprising;

a generating section that receives information bit X_r[i] (r=1, 2, . . . , n−

1) at point in time i as input, designates an equation equivalent to a g-th (g=0, 1, . . . , q−

1) parity check polynomial to satisfy 0, represented by equation 1, as equation 5, and generates parity bit P[i] at point in time i using an equation with k substituting for g in equation 5 when i%q=k; and

an output section that outputs parity bit P[i];

P[i]=X₁[i]{circle around (+)}X₁└

i−

a_#g,1,1┘

{circle around (+)}X₁└

i−

a_#g,1,2┘

{circle around (+)}X₂[i]{circle around (+)}X₂└

i−

a_#g,2,1┘

{circle around (+)}X₂└

i−

a_#g,2,2┘

{circle around (+)} . . . {circle around (+)}X<sub>n−

1</sub>[i]{circle around (+)}X<sub>n−

1</sub>[i−

a<sub>#g,n−

1,1</sub>]{circle around (+)}X<sub>n−

1</sub>[i−

a<sub>#g,n−

1,2</sub>]{circle around (+)}P[i−

b_#g,1]{circle around (+)}P[i−

b_#g,2] 

 

(Equation

     5)

where {circle around (+)} represents an exclusive OR and g=0, 1, . . . , q−

1.

8. The encoder according to claim 7, wherein a_#g,k,3=0.

9. The encoder according to claim 7, wherein:

i and j (i≠

j) are present where equation 2-1 and equation 2-2 hold true, or

i is present where equation 2-3 and equation 2-4 hold true.