Low density parity check encoder having length of 16200 and code rate of 3/15, and low density parity check encoding method using the same
A low density parity check (LDPC) encoder, an LDPC decoder, and an LDPC encoding method are disclosed. The LDPC encoder includes first memory, second memory, and a processor. The first memory stores an LDPC codeword having a length of 16200 and a code rate of 3/15. The second memory is initialized to 0. The processor generates the LDPC codeword corresponding to information bits by performing accumulation with respect to the second memory using a sequence corresponding to a parity check matrix (PCM).
1. A low density parity check (LDPC) decoder, comprising:
a receiving unit configured to receive a signal corresponding to an LDPC codeword having a length of 16200 and a code rate of 3/15, the LDPC codeword encoded using a sequence corresponding to a parity check matrix (PCM); and
a decoding unit configured to perform decoding corresponding to the received signal,
wherein the LDPC codeword includes a systematic part corresponding to information bits, a first parity part and a second parity part, and the LDPC codeword is stored in first memory (λ i , i=0, 1, . . . , 16200-1) of a transmitter,
wherein the LDPC codeword is generated by performing accumulation with respect to second memory (p j , j=0, 1, . . . M 1 =M 2 −1) using the sequence,
where M 1 is the size of the first parity part, and M 2 is the size of the second parity part, and
wherein the sequence is represented by the following Sequence Table:
Sequence Table
1st row: 8 372 841 4522 5253 7430 8542 9822 10550 11896 11988
2nd row: 80 255 667 1511 3549 5239 5422 5497 7157 7854 11267
3rd row: 257 406 792 2916 3072 3214 3638 4090 8175 8892 9003
4th row: 80 150 346 1883 6838 7818 9482 10366 10514 11468 12341
5th row: 32 100 978 3493 6751 7787 8496 10170 10318 10451 12561
6th row: 504 803 856 2048 6775 7631 8110 8221 8371 9443 10990
7th row: 152 283 696 1164 4514 4649 7260 7370 11925 11986 12092
8th row: 127 1034 1044 1842 3184 3397 5931 7577 11898 12339 12689
9th row: 107 513 979 3934 4374 4658 7286 7809 8830 10804 10893
10th row: 2045 2499 7197 8887 9420 9922 10132 10540 10816 11876
11st row: 2932 6241 7136 7835 8541 9403 9817 11679 12377 12810
12nd row: 2211 2288 3937 4310 5952 6597 9692 10445 11064 11272
2. The LDPC decoder of claim 1 , wherein the LDPC codeword comprises the systematic part corresponding to the information bits and having a length of 3240, the first parity part corresponding to a dual diagonal matrix included in the PCM and having a length of 1080, and the second parity part corresponding to an identity matrix included in the PCM and having a length of 11880.
3. The LDPC decoder of claim 2 , wherein the sequence has a number of rows equal to a sum of a value obtained by dividing a length of the systematic part, that is, 3240, by a circulant permutation matrix (CPM) size corresponding to the PCM, that is, 360, and a value obtained by dividing a length of the first parity part, that is, 1080, by the CPM size.
4. The LDPC decoder of claim 3 , wherein the accumulation is performed while the rows of the sequence are being repeatedly changed by the CPM size of the PCM.
5. The LDPC decoder of claim 1 , wherein the accumulation for a second information bit, λ 1 , is performed using the following 11 equations:
p
11
=
p
11
⊕
λ
1
p
375
=
p
375
⊕
λ
1
p
844
=
p
844
⊕
λ
1
p
4555
=
p
4555
⊕
λ
1
p
5286
=
p
5286
⊕
λ
1
p
7463
=
p
7463
⊕
λ
1
p
8575
=
p
8575
⊕
λ
1
p
9855
=
p
9855
⊕
λ
1
p
10583
=
p
10583
⊕
λ
1
p
11929
=
p
11929
⊕
λ
1
p
12021
=
p
12021
⊕
λ
1
wherein p j (0≤j≤12959) is the second memory and ⊕ is an addition operator.
6. A low density parity check (LDPC) decoding method, comprising:
receiving a signal corresponding to an LDPC codeword having a length of 16200 and a code rate of 3/15, the LDPC codeword encoded using a sequence corresponding to a parity check matrix (PCM); and
performing decoding corresponding to the received signal,
wherein the LDPC codeword includes a systematic part corresponding to information bits, a first parity part and a second parity part, and the LDPC codeword is stored in first memory (λ i , i=0, 1, . . . , 16200-1) of a transmitter,
wherein the LDPC codeword is generated by performing accumulation with respect to second memory (p j , j=0, 1, . . . M 1 +M 2 −1) using the sequence,
where M 1 is the size of the first parity part, and M 2 is the size of the second parity part, and
wherein the sequence is represented by the following Sequence Table:
Sequence Table
1st row: 8 372 841 4522 5253 7430 8542 9822 10550 11896 11988
2nd row: 80 255 667 1511 3549 5239 5422 5497 7157 7854 11267
3rd row: 257 406 792 2916 3072 3214 3638 4090 8175 8892 9003
4th row: 80 150 346 1883 6838 7818 9482 10366 10514 11468 12341
5th row: 32 100 978 3493 6751 7787 8496 10170 10318 10451 12561
6th row: 504 803 856 2048 6775 7631 8110 8221 8371 9443 10990
7th row: 152 283 696 1164 4514 4649 7260 7370 11925 11986 12092
8th row: 127 1034 1044 1842 3184 3397 5931 7577 11898 12339 12689
9th row: 107 513 979 3934 4374 4658 7286 7809 8830 10804 10893
10th row: 2045 2499 7197 8887 9420 9922 10132 10540 10816 11876
11st row: 2932 6241 7136 7835 8541 9403 9817 11679 12377 12810
12nd row: 2211 2288 3937 4310 5952 6597 9692 10445 11064 11272