Encoding method, decoding method, coder and decoder
AssigneePanasonic Corporation
InventorYutaka Murakami
Life of this patent
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Abstract
An encoding moihod and encoder of a lime-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 of the attached detailed description as a g-th (g=0, 1, . . . q−1) parity check polynomial to satisfy 0:
Claims15
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 check polynomial to satisfy 0:
- (Da#g,1,1+Da#g,1,2+Da#g,1,3)X1(D)+(Da#g,2,1+Da#g,2,2+Da#g,2,3)X2(D)+ . . . +(Da#g,n−1,1+Da#g,n−1,2+Da#g,n−1,3)Xn−1(D)+(Db#g,1+Db#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=vp=k (vp=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=yp=k (yp=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=sp=k (sp=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
- vp=k and yp=k are natural numbers equal to or greater than 1.
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:
- (Da#g,1,1+Da#g,1,2+Da#g,1,3)X1(D)+(Da#g,2,1+Da#g,2,2+Da#g,2,3)X2(D)+ . . . +(Da#g,n−1,1+Da#g,n−1,2+Da#g,n−1,3)Xn−1(D)+(Db#g,1+Db#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#q−1,k,1%q=vp=k (vp=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=yp=k (yp=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#1,k,3%q=sp=k (sp=k:
- fixed-value).
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 Xr[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]⊕X1└i−a#g,1,1┘⊕X1└i−a#g,1,2┘⊕X2[i]⊕X2└i−a#g,2,1┘⊕X2└i−a#g,2,2┘⊕ . . . {circle around (+)}Xn−1[i]⊕Xn−1[i−a#g,n−1,1]⊕Xn−1[i−a#g,n−1,2]⊕P[i−b#g,1]⊕P[i−b#g,2] (Equation 5)
- where ⊕ represents an exclusive OR and g=0, 1, . . . , q−1.
Dependencies are inferred from the claim text.