Memory system and operating method thereof

1. A memory system comprising:

a memory device; and

a controller including an ECC circuit and coupled with the memory device, wherein the controller is configured to

receive a message in response to a request from a host,

generate a message matrix by the ECC circuit into at least one buffer of the ECC circuit, including predetermined row codes and predetermined column codes symmetrical to the predetermined row codes in accordance with the received message, wherein the message matrix includes a first triangular matrix and a second triangular matrix symmetrical to the first triangular matrix,

encode the message matrix by the ECC circuit using a block-wise concatenated Bose-Chadhuri-Hocquenghem (BCH) code with a symmetrical structure, and

store the encoded message by the ECC circuit into the memory device, and decode the encoded message by the ECC circuit using a block-wise concatenated BCH code with a symmetrical structure.

2. The memory system of claim 1 , wherein the ECC circuit is configured to divide the message into a plurality of message blocks.

3. The memory system of claim 1 , wherein the ECC circuit is configured to divide the encoded message into a plurality of encoded message blocks and a plurality of parity blocks.

4. The memory system of claim 1 , wherein the first triangular matrix is generated using the plurality of message blocks.

5. The memory system of claim 4 , wherein the second triangular matrix is generated using the plurality of message blocks so that the second triangular matrix is symmetrical to the first triangular matrix.

6. The memory system of claim 1 , wherein the first triangular matrix is generated using the plurality of encoded message blocks and the plurality of parity blocks.

7. The memory system of claim 6 , wherein the second triangular matrix is generated using the plurality of encoded message blocks so that the second triangular matrix is symmetrical to the plurality of encoded message blocks of the first triangular matrix.

8. An operation method of a controller in a memory system including a host, the controller and a memory device coupled with the controller, the operation method comprising:

receiving a message from the host into the controller;

dividing the received message into a plurality of message blocks by an ECC circuit of the controller;

generating by the ECC circuit into at least one buffer of the ECC circuit, a first triangular matrix and a second triangular matrix symmetrical to the first triangular matrix using the plurality of message blocks;

generating a message matrix by the ECC circuit by combining the first triangular matrix and the second triangular matrix;

performing an encoding operation to the message matrix by the ECC circuit; and

generating an encoded message by the ECC circuit by obtaining the first triangular matrix and a plurality of parity blocks from the encoded message matrix.

9. The operation method of claim 8 , wherein the message matrix includes a block-wise concatenated Bose-Chadhuri-Hocquenghem (BCH) code, and includes predetermined row codes and predetermined column codes symmetrical to the predetermined row codes.

10. The operation method of claim 8 , wherein the message matrix has an anti-symmetric structure where a plurality of zero padding blocks are included between the first triangular matrix and the second triangular matrix.

11. The operation method of claim 8 , wherein the message matrix has a shortening structure where a plurality of zero padding blocks are not included between the first triangular matrix and the second triangular matrix.

12. The operation method of claim 8 , wherein the encoding operation is performed to respective row codes of the message matrix to generate a parity block corresponding to the respective row codes.

13. The operation method of claim 8 , wherein the second triangular matrix is symmetrical to the first triangular matrix in the encoded message matrix.

14. The operation method of claim 8 , further comprising: storing the encoded message in the memory device.

15. An operation method of a controller in a memory system including a host, the controller and a memory device coupled with the controller, the operation method comprising:

reading an encoded message from the memory device into the controller;

dividing the encoded message into a plurality of encoded message blocks and a plurality of parity blocks by an ECC circuit of the controller;

generating by the ECC circuit into at least one buffer of the ECC circuit, a first triangular matrix and a second triangular matrix symmetrical to the first triangular matrix using the plurality of encoded message blocks and the plurality of parity blocks;

generating a message matrix by the ECC circuit by combining the first triangular matrix and the second triangular matrix;

performing a decoding operation to the message matrix by the ECC circuit; and

generating a decoded message by the ECC circuit by obtaining the first triangular matrix from the decoded message matrix.

16. The operation method of claim 15 , wherein the message matrix includes a block-wise concatenated Bose-Chadhuri-Hocquenghem (BCH) code, and includes predetermined row codes and predetermined column codes symmetrical to the predetermined row codes.

17. The operation method of claim 15 , wherein the message matrix has an anti-symmetric structure where a plurality of zero padding blocks are included between the first triangular matrix and the second triangular matrix.

18. The operation method of claim 15 , wherein the message matrix has a shortening structure where a plurality of zero padding blocks are not included between the first triangular matrix and the second triangular matrix.

19. The operation method of claim 15 , wherein performing the decoding operation to the message matrix includes:

generating a first decoding result by performing the decoding operation to a first row code of the message matrix;

updating a first column code, which is symmetrical to the first row code, by transmitting the first decoding result to the first column code; and

repeating the generating of the first decoding result and the updating the first column code a predetermined number of times until the first row code in the message matrix becomes a last row code.