Method for encoding multi-mode of BCH codes and encoder thereof

1. An encoder for encoding BCH codes of different modes, comprising:

a combined matrix unit, for providing a plurality of encoding matrices for multiplying elements from the encoding matrices with one input data having p bits, and outputting the results as a calculated data in a first clock cycle;

a linear feedback shift register (LFSR), for linearly shifting the calculated data as an output data, and outputting the output data in a second clock cycle; and

an adder, for adding the output data received from the LFSR and a divided processing data having p bits, and outputting the sum as another input data to the combined matrix unit in the second clock cycle,

wherein an n-bit initial processing data including a k-bit message and being divided per p bits is sequentially inputted to the adder as the divided processing data; an encoded codeword is obtained in [n/p] clock cycles; the second clock cycle is one clock cycle later than the first clock cycle.

2. The encoder according to claim 1 , wherein the encoding matrices with one side aligned form a combined matrix in the combined matrix unit, and the combined matrix unit processes multiplying using elements in one encoding matrix or one encoding matrix with common sub-expressions (CSEs) in another encoding matrix according to corresponding BCH codes.

3. The encoder according to claim 2 , wherein each of the encoding matrices has a form of

F

p

=

[

F

p

-

1

×

[

g

R

-

1

′

g

R

-

2

′

⋮

g

1

′

g

0

′

]

|

⁢

first

⁢

⁢

R

-

1

⁢

⁢

columns

⁢

⁢

of

⁢

⁢

F

p

-

1

]

,

where

F

1

=

[

g

R

-

1

′

1

0

…

0

g

R

-

2

′

0

1

…

0

⋮

⋮

⋮

⋮

⋮

g

1

′

0

0

…

1

g

0

′

0

0

…

0

]

,

wherein for an n-bit initial processing data including a k-bit message and being divided per p bits, R is defined as R=n−k+1; g′ R-1 , g′ R-2 , . . . and g′ 0 are coefficients of a generating polynomial, g(x)=x R +g′ R-1 x R-1 +g′ R-2 x R-2 + . . . +g′ 2 x 2 +g′ 1 x 1 +g′ 0 ; any two encoding matrices have the same or different values of n and/or k.

4. The encoder according to claim 2 , wherein the combined matrix unit further has a logic operation portion to processes the multiplying.

5. The encoder according to claim 1 , wherein space in the combined matrix which is not filled by elements of the encoding matrices is filled with 0.

6. The encoder according to claim 1 , wherein one side of the combined matrix has encoding matrices arranged in sequence.

7. The encoder according to claim 1 , wherein at least one encoding matrix in the combined matrix utilizes CSEs in another encoding matrix in the combined matrix.

8. The encoder according to claim 1 , wherein when a space of the smallest encoding matrix in the combined matrix can be accommodated in a portion of a space of 0 formed adjacent to other encoding matrices, the smallest encoding matrix is located to the space of 0 with two sides adjacent to one encoding matrix, respectively.

9. The encoder according to claim 1 , wherein two adjacent encoding matrices are separated by a plurality of 0.

10. A method for encoding BCH codes of different modes by the encoder according to claim 1 , comprising the steps of:

building a plurality of encoding matrices by the combined matrix unit;

combining the plurality of encoding matrices to form a combined matrix by aligning the plurality of encoding matrices side by side to each other;

seeking common sub-expressions (CSEs) in the combined matrix, and

encoding a message using the combined matrix,

wherein each of the encoding matrix has a form of

F

p

=

[

F

p

-

1

×

[

g

R

-

1

′

g

R

-

2

′

⋮

g

1

′

g

0

′

]

|

⁢

first

⁢

⁢

R

-

1

⁢

⁢

columns

⁢

⁢

of

⁢

⁢

F

p

-

1

]

,

where

F

1

=

[

g

R

-

1

′

1

0

…

0

g

R

-

2

′

0

1

…

0

⋮

⋮

⋮

⋮

⋮

g

1

′

0

0

…

1

g

0

′

0

0

…

0

]

,

wherein for an n-bit initial processing data including a k-bit message and being divided per p bits, R is defined as R=n−k+1;

wherein g′ R-1 , g′ R-2 , . . . and g′ 0 are coefficients of a generating polynomial, g(x)=x R +g′ R-1 x R-1 +g′ R-2 x R-2 + . . . +g′ 2 x 2 +g′ 1 x 1 +g′ 0 ;

wherein any two encoding matrices have the same or different values of n and/or k; and

wherein F is an encoding matrix, p is the amount of data that can be processed in a clock cycle, and R is an equation of the form R=n−k+1, where n is the length of the initial processing data and k is the length of the message; and

wherein n and p are positive integers, and 1<n<p.