# Patent

## Title
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

## Abstract

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).

## Background
CROSS-REFERENCE TO RELATED APPLICATIONS
This application claims the benefit of Korean Patent Application Nos. 10-2014-0106174 and 10-2014-0120009, filed Aug. 14, 2014 and Sep. 11, 2014, respectively, which are hereby incorporated by reference herein in their entirety.
BACKGROUND
1. Technical Field
The present disclosure relates generally to a low density parity check (LDPC) code that is used to correct errors occurring over a wireless channel, and, more particularly, to an LDPC code that is applicable to a digital broadcasting system.
2. Description of the Related Art
Current terrestrial television (TV) broadcasting generates co-channel interference across an area within a distance that is three times a service radius, and thus the same frequency cannot be reused in the area within the distance that is three times the service radius. An area in which the same frequency cannot be reused is called a white space. Spectrum efficiency significantly deteriorates due to the occurrence of a white space.
Accordingly, there arises a need for the development of a transmission technology that facilitates the elimination of a white space and the reuse of a frequency with an emphasis on reception robustness in order to improve spectrum efficiency.
In response to this, the paper “Cloud Transmission: A New Spectrum-Reuse Friendly Digital Terrestrial Broadcasting Transmission System” published on September of 2012 in IEEE Transactions on Broadcasting, Vol. 58, No. 3 proposes a terrestrial cloud transmission technology that facilitates reuse, does not generate a white space, and makes the construction and operation of a single frequency network easy.
Using this terrestrial cloud transmission technology, a broadcasting station can transmit the same nationwide content or locally different content over a single broadcasting channel. However, for this purpose, a receiver should receive one or more terrestrial cloud broadcast signals in an area in which signals transmitted from different transmitters overlap each other, that is, an overlap area, over a single frequency network, and then should distinguish and demodulate the received terrestrial cloud broadcast signals. That is, the receiver should demodulate one or more cloud broadcast signals in a situation in which co-channel interference is present and the timing and frequency synchronization between transmitted signals are not guaranteed.
Meanwhile, Korean Patent Application Publication No. 2013-0135746 entitled “Low Density Parity Check Code for Terrestrial Cloud Transmission” discloses an LDPC code that is optimized for terrestrial cloud transmission and exhibits excellent performance at low code rate (<0.5).
However, Korean Patent Application Publication No. 2013-0135746 is directed to a code length completely different from an LDPC code length used in the DVB broadcast standard, etc., and does not teach a specific LDPC encoding method.
SUMMARY
At least one embodiment of the present invention is directed to the provision of a new LDPC codeword having a length of 16200 and a code rate of 3/15, which is capable of being used for general purposes.
At least one embodiment of the present invention is directed to the provision of an LDPC encoding technique that is capable of efficiently performing LDPC encoding using a sequence having a number of rows equal to a value that is obtained by dividing the sum of the length of the systematic part of an LDPC codeword, that is, 3240, and the length of the first parity part of the LDPC codeword, that is, 1080, by 360.
In accordance with an aspect of the present invention, there is provided an LDPC encoder, including first memory configured to store an LDPC codeword having a length of 16200 and a code rate of 3/15; second memory configured to be initialized to 0; and a processor configured to generate 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).
The accumulation may be performed at parity bit addresses that are updated using the sequence corresponding to the PCM.
The LDPC codeword may include a systematic part corresponding to the information bits and having a length of 3240, a first parity part corresponding to a dual diagonal matrix included in the PCM and having a length of 1080, and a second parity part corresponding to an identity matrix included in the PCM and having a length of 11880.
The sequence may have a number of rows equal to the 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.
The sequence may be 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









The accumulation may be performed while the rows of the sequence are being repeatedly changed by the CPM size of the PCM.
In accordance with an aspect of the present invention, there is provided an LDPC encoding method, including initializing first memory configured to store an LDPC codeword having a length of 16200 and a code rate of 3/15, and second memory; and generating the LDPC codeword corresponding to information bits by performing accumulation with respect to the second memory using a sequence corresponding to a PCM.
The accumulation may be performed at parity bit addresses that are updated using the sequence corresponding to the PCM.
The LDPC codeword may include a systematic part corresponding to the information bits and having a length of 3240, a first parity part corresponding to a dual diagonal matrix included in the PCM and having a length of 1080, and a second parity part corresponding to an identity matrix included in the PCM and having a length of 11880.
The sequence may have a number of rows equal to the 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.
The sequence may be represented by the above Sequence Table.
In accordance with still another aspect of the present invention, there is provided an LDPC decoder, including a receiving unit configured to receive an LDPC codeword encoded using a sequence corresponding to a PCM and is represented by the above Sequence Table; and a decoding unit configured to restore information bits from the received LDPC codeword by performing decoding corresponding to the PCM.



BRIEF DESCRIPTION OF THE DRAWINGS
The above and other objects, features and advantages of the present invention will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings, in which:
FIG. 1 is a block diagram illustrating a broadcast signal transmission and reception system according to an embodiment of the present invention;
FIG. 2 is an operation flowchart illustrating a broadcast signal transmission and reception method according to an embodiment of the present invention;
FIG. 3 is a diagram illustrating the structure of a PCM corresponding to an LDPC code to according to an embodiment of the present invention;
FIG. 4 is a block diagram illustrating an LDPC encoder according to an embodiment of the present invention:
FIG. 5 is a block diagram illustrating an LDPC decoder according to an embodiment of the present invention;
FIG. 6 is an operation flowchart illustrating an LDPC encoding method according to an embodiment of the present invention; and
FIG. 7 is a graph plotting the performance of a QC-LDPC code having a length of 16200 and a code rate of 3/15 according to an embodiment of the present invention against Eb/No.



DETAILED DESCRIPTION
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings. Repeated descriptions and descriptions of well-known functions and configurations that have been deemed to make the gist of the present invention unnecessarily obscure will be omitted below. The embodiments of the present invention are intended to fully describe the present invention to persons having ordinary knowledge in the art to which the present invention pertains. Accordingly, the shapes, sizes, etc. of components in the drawings may be exaggerated to make the description obvious.
Embodiments of the present invention will be described in detail below with reference to the accompanying drawings.
FIG. 1 is a block diagram illustrating a broadcast signal transmission and reception system according to an embodiment of the present invention.
Referring to FIG. 1, it can be seen that a transmitter 10 and a receiver 30 communicate with each other over a wireless channel 20.
The transmitter 10 generates an n-bit codeword by encoding k information bits using an LDPC encoder 13. The codeword is modulated by the modulator 15, and is transmitted via an antenna 17. The signal transmitted via the wireless channel 20 is received via the antenna 31 of the receiver 30, and, in the receiver 30, is subjected to a process reverse to the process in the transmitter 10. That is, the received data is demodulated by a demodulator 33, and is then decoded by an LDPC decoder 35, thereby finally restoring the information bits.
It will be apparent to those skilled in the art that the above-described transmission and reception processes have been described within a minimum range required for a description of the features of the present invention and various processes required for data transmission may be added.
In the following, the specific processes of encoding and decoding that are performed using an LDPC code in the LDPC encoder 13 or LDPC decoder 35 and the specific configurations of encoding and decoding devices, such as the LDPC encoder 13 and the LDPC decoder 35, are described. The LDPC encoder 13 illustrated in FIG. 1 may have a structure illustrated in FIG. 4, and the LDPC decoder 35 may have a structure illustrated in FIG. 5.
FIG. 2 is an operation flowchart illustrating a broadcast signal transmission and reception method according to an embodiment of the present invention.
Referring to FIG. 2, in the broadcast signal transmission and reception method according to this embodiment of the present invention, input bits (information bits) are subjected to LDPC encoding at step S210.
That is, at step S210, an n-bit codeword is generated by encoding k information bits using the LDPC encoder.
In this case, step S210 may be performed as in an LDPC encoding method illustrated in FIG. 6.
Furthermore, in the broadcast signal transmission and reception method, the encoded data is modulated at step S220.
That is, at step S220, the encoded n-bit codeword is modulated using the modulator.
Furthermore, in the broadcast signal transmission and reception method, the modulated data is transmitted at step S230.
That is, at step S230, the modulated codeword is transmitted over a wireless channel via the antenna.
Furthermore, in the broadcast signal transmission and reception method, the received data is demodulated at step S240.
That is, at step S240, the signal transmitted over the wireless channel is received via the antenna of the receiver, and the received data is demodulated using the demodulator.
Furthermore, in the broadcast signal transmission and reception method, the demodulated data is subjected to LDPC decoding at step S250.
That is, at step S250, the information bits are finally restored by performing LDPC decoding using the demodulator of the receiver.
In this case, step S250 corresponds to a process reverse to that of the LDPC encoding method illustrated in FIG. 6, and may correspond to the LDPC decoder of FIG. 5.
An LDPC code is known as a code very close to the Shannon limit for an additive white Gaussian noise (AWGN) channel, and has the advantages of asymptotically excellent performance and parallelizable decoding compared to a turbo code.
Generally, an LDPC code is defined by a low-density parity check matrix (PCM) that is randomly generated. However, a randomly generated LDPC code requires a large amount of memory to store a PCM, and requires a lot of time to access memory. In order to overcome these problems, a quasi-cyclic LDPC (QC-LDPC) code has been proposed. A QC-LDPC code that is composed of a zero matrix or a circulant permutation matrix (CPM) is defined by a PCM that is expressed by the following Equation 1:




  
    
      
        
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In this equation, J is a CPM having a size of L×L, and is given as the following Equation 2. In the following description, L may be 360.




  
    
      
        
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Furthermore, Ji is obtained by shifting an L×L identity matrix I (J0) to the right i (0≦i<L) times, and J∞ is an L×L zero matrix. Accordingly, in the case of a QC-LDPC code, it is sufficient if only index exponent i is stored in order to store Ji, and thus the amount of memory required to store a PCM is considerably reduced.
FIG. 3 is a diagram illustrating the structure of a PCM corresponding to an LDPC code to according to an embodiment of the present invention.
Referring to FIG. 3, the sizes of matrices A and C are g×K and (N−K−g)×(K+g), respectively, and are composed of an L×L zero matrix and a CPM, respectively. Furthermore, matrix Z is a zero matrix having a size of g×(N−K−g), matrix D is an identity matrix having a size of (N−K−g)×(N−K−g), and matrix B is a dual diagonal matrix having a size of g×g. In this case, the matrix B may be a matrix in which all elements except elements along a diagonal line and neighboring elements below the diagonal line are 0, and may be defined as the following Equation 3:




  
    
      
        
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where IL×L is an identity matrix having a size of L×L.

That is, the matrix B may be a bit-wise dual diagonal matrix, or may be a block-wise dual diagonal matrix having identity matrices as its blocks, as indicated by Equation 3. The bit-wise dual diagonal matrix is disclosed in detail in Korean Patent Application Publication No. 2007-0058438, etc.
In particular, it will be apparent to those skilled in the art that when the matrix B is a bit-wise dual diagonal matrix, it is possible to perform conversion into a Quasi-cyclic form by applying row or column permutation to a PCM including the matrix B and having a structure illustrated in FIG. 3.
In this case, N is the length of a codeword, and K is the length of information.
The present invention proposes a newly designed QC-LDPC code in which the code rate thereof is 3/15 and the length of a codeword is 16200, as illustrated in the following Table 1. That is, the present invention proposes an LDPC code that is designed to receive information having a length of 3240 and generate an LDPC codeword having a length of 16200.
Table 1 illustrates the sizes of the matrices A, B, C, D and Z of the QC-LDPC code according to the present invention:









TABLE 1









Sizes













Code rate
Length
A
B
C
D
Z





3/15
16200
1080 ×
1080 ×
11880 ×
11880 ×
1080 ×




3240
1080
4320
11880
11880









The newly designed LDPC code may be represented in the form of a sequence (progression), an equivalent relationship is established between the sequence and matrix (parity bit check matrix), and the sequence may be represented, as follows:










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









An LDPC code that is represented in the form of a sequence is being widely used in the DVB standard.
According to an embodiment of the present invention, an LDPC code presented in the form of a sequence is encoded, as follows. It is assumed that there is an information block S=(s0, s1 . . . , sK−1) having an information size K. The LDPC encoder generates a codeword Λ=(λ0, λ1, λ2, . . . , λN-1) having a size of N=K+M1+M2 using the information block S having a size K. In this case, M1=g, and M2=N−K−g. Furthermore, M1 is the size of parity bits corresponding to the dual diagonal matrix B, and M2 is the size of parity bits corresponding to the identity matrix D. The encoding process is performed, as follows:
Initialization:

λi=si for i=0,1, . . . ,K−1

pj=0 for j=0,1, . . . ,M1+M2−1  (4)

First information bit λ0 is accumulated at parity bit addresses specified in the 1st row of the sequence of the Sequence Table. For example, in an LDPC code having a length of 16200 and a code rate of 3/15, an accumulation process is as follows:
p8=p8⊕λ0 p372=p372⊕λ0 p841=p841⊕λ0 p4522=p4522⊕λ0 p5253=p5253⊕λ0 p7430=p7430⊕λ0 p8542=p8542⊕λ0 p9822=p9822⊕λ0 p10550=p10550⊕λ0 p11896=p11896⊕λ0 p11988=p11988⊕λ0 
where the addition ⊕ occurs in GF(2).
The subsequent L−1 information bits, that is, λm, m=1, 2, . . . , L−1, are accumulated at parity bit addresses that are calculated by the following Equation 5:

(x+m×Q1)mod M1 if x<M1 

M1+{(x−M1+m×Q2)mod M2} if x≧M1  (5)

where x denotes the addresses of parity bits corresponding to the first information bit λ0, that is, the addresses of the parity bits specified in the first row of the sequence of the Sequence Table, Q1=M1/L, Q2=M2/L, and L=360. Furthermore, Q1 and Q2 are defined in the following Table 2. For example, for an LDPC code having a length of 16200 and a code rate of 3/15, M1=1080, Q1=3, M2=11880, Q2=33 and L=360, and the following operations are performed on the second bit λ1 using Equation 5:

p11=p11⊕λ1 p375=p375⊕λ1 p844=p844⊕λ1 p4555=p4555⊕λ1 p5286=p5286⊕λ1 p7463=p7463⊕λ1 p8575=p8575⊕λ1 p9855=p9855⊕λ1 p10583=p10583⊕λ1 p11929=p11929⊕λ1 p12021=p12021⊕λ1 

Table 2 illustrates the sizes of M1, Q1, M2 and Q2 of the designed QC-LDPC code:









TABLE 2








Sizes















Code rate
Length
M1
M2
Q1
Q2






3/15
16200
1080
11880
3
33









The addresses of parity bit accumulators for new 360 information bits from λL to λ2L-1 are calculated and accumulated from Equation 5 using the second row of the sequence.
In a similar manner, for all groups composed of new L information bits, the addresses of parity bit accumulators are calculated and accumulated from Equation 5 using new rows of the sequence.
After all the information bits from λ0 to λK−1 have been exhausted, the operations of the following Equation 6 are sequentially performed from i=1:

pi=pi⊕pi-1 for i=0,1, . . . ,M1−1  (6)

Thereafter, when a parity interleaving operation, such as that of the following Equation 7, is performed, parity bits corresponding to the dual diagonal matrix B are generated:

λK+L·t+s=pQ1·s+t for 0≦s<L, 0≦t<Q1  (7)

When the parity bits corresponding to the dual diagonal matrix B have been generated using K information bits λ0, λ1, λKK−1, parity bits corresponding to the identity matrix D are generated using the M1 generated parity bits λK, λK+1, . . . , λK+M1−1.
For all groups composed of L information bits from λK to λK+M1−1, the addresses of parity bit accumulators are calculated using the new rows (starting with a row immediately subsequent to the last row used when the parity bits corresponding to the dual diagonal matrix B have been generated) of the sequence and Equation 5, and related operations are performed.
When a parity interleaving operation, such as that of the following Equation 8, is performed after all the information bits from λK to λK+M1−1 have been exhausted, parity bits corresponding to the identity matrix D are generated:

λK+M1+L·t+s=pM1+Q2·s+t for 0≦s<L, 0≦t<Q2  (8)

FIG. 4 is a block diagram illustrating an LDPC encoder according to an embodiment of the present invention.
Referring to FIG. 4, the LDPC encoder according to this embodiment of the present invention includes memory 310 and 320 and a processor 330.
The memory 310 is memory that is used to store an LDPC codeword having a length of 16200 and a code rate of 3/15.
The memory 320 is memory that is initialized to 0.
The memory 310 and the memory 320 may correspond to λi (i=0, 1, . . . , N−1) and pj (j=0, 1, . . . , M1+M2−1), respectively.
The memory 310 and the memory 320 may correspond to various types of hardware for storing sets of bits, and may correspond to data structures, such as an array, a list, a stack and a queue.
The processor 330 generates an LDPC codeword corresponding to information bits by performing accumulation with respect to the memory 320 using a sequence corresponding to a PCM.
In this case, the accumulation may be performed at parity bit addresses that are updated using the sequence of the above Sequence Table.
In this case, the LDPC codeword may include a systematic part λ0, λ1, . . . , λK−1 corresponding to the information bits and having a length of 3240 (=K), a first parity part λK, λK+1, . . . , λK+M1−1 corresponding to a dual diagonal matrix included in the PCM and having a length of 1080 (=M1=g), and a second parity part λK+M1, λK+M1+1, . . . , λK+M1+M2−1 corresponding to an identity matrix included in the PCM and having a length of 11880 (=M2).
In this case, the sequence may have a number of rows equal to the sum (3240/360+1080/360=12) of a value obtained by dividing the length of the systematic part, that is, 3240, by a CPM size L corresponding to the PCM, that is, 360, and a value obtained by dividing the length M1 of the first parity part, that is, 1080, by 360.
As described above, the sequence may be represented by the above Sequence Table.
In this case, the memory 320 may have a size corresponding to the sum M1+M2 of the length M1 of the first parity part and the length M2 of the second parity part.
In this case, the parity bit addresses may be updated based on the results of comparing each x of the previous parity bit addresses specified in respective rows of the sequence with the length M1 of the first parity part.
That is, the parity bit addresses may be updated using Equation 5. In this case, x may be the previous parity bit addresses, m may be an information bit index that is an integer larger than 0 and smaller than L, L may be the CPM size of the PCM, Q1 may be M1/L, M1 may be the size of the first parity part, Q2 may be M2/L, and M2 may be the size of the second parity part.
In this case, it may be possible to perform the accumulation while repeatedly changing the rows of the sequence by the CPM size L (=360) of the PCM, as described above.
In this case, the first parity part λK, λK+1, . . . , λK+M1−1 may be generated by performing parity interleaving using the memory 310 and the memory 320, as described in conjunction with Equation 7.
In this case, the second parity part λK+M1, λK+M1+1, . . . , λK+M1+M2−1 may be generated by performing parity interleaving using the memory 310 and the memory 320 after generating the first parity part λK, λK+1, . . . , λK+M1−1 and then performing the accumulation using the first parity part λK, λK+1, . . . , λK+M1−1 and the sequence, as described in conjunction with Equation 8.
FIG. 5 is a block diagram illustrating an LDPC decoder according to an embodiment of the present invention.
Referring to FIG. 5, the LDPC decoder according to this embodiment of the present invention may include a receiving unit 410 and a decoding unit 420.
The receiving unit 410 receives an LDPC codeword that has been encoded using a sequence that corresponds to a PCM and is represented by the above Sequence Table.
The decoding unit 420 restores information bits from the received LDPC codeword by performing decoding corresponding to the PCM.
In this case, the sequence may be used to update the parity bit addresses of the memory, and the parity bit addresses are used for accumulation that is performed to generate parity bits corresponding to the LDPC codeword.
In this case, the LDPC codeword may include a systematic part λ0, λ1, . . . , λK−1 corresponding to the information bits, a first parity part λK, λK+1, . . . , λK+M1−1 corresponding to a dual diagonal matrix included in the PCM, and a second parity part λK+M, λK+M1+1, . . . , λK+M1+M2−1 corresponding to an identity matrix included in the PCM.
In this case, the parity bit addresses may be updated based on the results of comparing each x of the previous parity bit addresses specified in respective rows of the sequence with the length M1 of the first parity part.
That is, the parity bit addresses may be updated using Equation 5. In this case, x may be the previous parity bit addresses, m may be an information bit index that is an integer larger than 0 and smaller than L, L may be the CPM size of the PCM, Q1 may be M1/L, M1 may be the size of the first parity part, Q2 may be M2/L, and M2 may be the size of the second parity part.
FIG. 6 is an operation flowchart illustrating an LDPC encoding method according to an embodiment of the present invention.
Referring to FIG. 6, the LDPC encoding method according to this embodiment of the present invention initializes the first memory that stores an LDPC codeword having a length of 16200 and a code rate of 3/15, and second memory at step S510.
In this case, step S510 may be performed using Equation 4.
Furthermore, in the LDPC encoding method according to this embodiment of the present invention, an LDPC codeword corresponding to information bits is generated by performing accumulation with respect to the second memory using a sequence corresponding to a PCM at step S520.
In this case, the accumulation may be performed at parity bit addresses that are updated using the sequence corresponding to the PCM.
In this case, the LDPC codeword may include a systematic part λ0, λ1, . . . , λK−1 corresponding to the information bits and having a length of 3240 (=K), a first parity part λK, λK+1, . . . , λK+M1−1 corresponding to a dual diagonal matrix included in the PCM and having a length of 1080 (=M1=g), and a second parity part λK+M, λK+M1+1, . . . , λK+M1+M2−1 corresponding to an identity matrix included in the PCM and having a length of 11880 (=M2).
In this case, the sequence may have a number of rows equal to the sum (3240/360+1080/360=12) of a value obtained by dividing the length of the systematic part, that is, 3240, by a CPM size L corresponding to the PCM, that is, 360, and a value obtained by dividing the length M1 of the first parity part, that is, 1080, by 360.
As described above, the sequence may be represented by the above Sequence Table.
In this case, the parity bit addresses may be updated based on the results of comparing each x of the previous parity bit addresses specified in respective rows of the sequence with the length M1 of the first parity part.
That is, the parity bit addresses may be updated using Equation 5. In this case, x may be the previous parity bit addresses, m may be an information bit index that is an integer larger than 0 and smaller than L, L may be the CPM size of the PCM, Q1 may be M1/L, M1 may be the size of the first parity part, Q2 may be M2/L, and M2 may be the size of the second parity part.
In this case, it may be possible to perform the accumulation while repeatedly changing the rows of the sequence by the CPM size L (=360) of the PCM, as described above.
In this case, the first parity part λK, λK+1, . . . , λK+M1−1 may be generated by performing parity interleaving using the memory 310 and the memory 320, as described in conjunction with Equation 7.
In this case, the second parity part λK+M, λK+M1+1, . . . , λK+M1+M2−1 may be generated by performing parity interleaving using the memory 310 and the memory 320 after generating the first parity part λK, λK+1, . . . , λK+M1−1 and then performing the accumulation using the first parity part λK, λK+1, . . . , λK+M1−1 and the sequence, as described in conjunction with Equation 8.
FIG. 7 is a graph plotting the performance of a QC-LDPC code having a length of 16200 and a code rate of 3/15 according to an embodiment of the present invention against Eb/No.
The graph illustrated in FIG. 7 illustrates results that were obtained on the assumption that a log-likelihood ratio (LLR)-based sum-product algorithm in which binary phase shift keying (BPSK) modulation and 50 rounds of repetitive decoding were performed was used for computational experiments. As illustrated in FIG. 7, it can be seen that the designed code is away from the Shannon limit by about 1.25 dB at BER=10−6.
At least one embodiment of the present invention has the advantage of providing a new LDPC codeword having a length of 16200 and a code rate of 3/15, which is capable of being used for general purposes.
At least one embodiment of the present invention has the advantage of providing an LDPC encoding technique that is capable of efficiently performing LDPC encoding using a sequence having a number of rows equal to a value that is obtained by dividing the sum of the length of the systematic part of an LDPC codeword, that is, 3240, and the length of the first parity part of the LDPC codeword, that is, 1080, by 360.
Although the specific embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions and substitutions are possible without departing from the scope and spirit of the invention as disclosed in the accompanying claims.

## Claims

1. A low density parity check (LDPC) encoder, comprising:
first memory configured to store an LDPC codeword having a length of 16200 and a code rate of 3/15;
second memory configured to be initialized to 0; and
a processor configured to generate 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),
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 encoder of claim 1, wherein the LDPC codeword comprises a systematic part corresponding to the information bits and having a length of 3240, a first parity part corresponding to a dual diagonal matrix included in the PCM and having a length of 1080, and a second parity part corresponding to an identity matrix included in the PCM and having a length of 11880.

3. The LDPC encoder 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 by a circulant permutation matrix (CPM) size corresponding to the PCM, and a value obtained by dividing a length of the first parity part by the CPM size.

4. The LDPC encoder of claim 3, wherein the CPM size is 360.

5. The LDPC encoder of claim 1, wherein the accumulation is performed at parity bit addresses that are updated using the sequence.

6. The LDPC encoder of claim 5, wherein the accumulation is performed while the rows of the sequence are being repeatedly changed by a CPM size of the PCM.