ENCODING METHOD AND DEVICE USING RATE-COMPATIBLE, LOW-DENSITY PARITY-CHECK CODE IN COMMUNICATION SYSTEM

Abstract

A 5th generation (5G) or pre-5G communication system for supporting a data transmission rate higher than that of a 4th generation (4G) communication system such as long term evolution (LTE) is disclosed. The present disclosure relates to a rate compatible low-density parity-check (RC-LDPC) encoding method and device therefor. The encoding method includes using LDPC in a communication system, including the operations of LDPC encoding information bits by a first encoding rate, and performing a concatenated single parity check (SPC) encoding for the encoded bits by at least one second encoding rate lower than the first encoding rate.

Claims

1. A method of encoding using a rate-compatible low density parity check (LDPC) code in a communication system, the method comprising: performing an LDPC encoding on information bits by a first code rate; and performing concatenated single parity check (SPC) encodings by at least one second code rate lower than the first code rate on the encoded information bits.

2. The encoding method of claim 1, wherein the performing of the concatenated SPC encodings by the at least one second code rate is performed using a parity check matrix having a stair-wise lower triangular structure in an extension part.

3. The method of claim 1, wherein the performing of the concatenated SPC encodings by the at least one second code rate is performed using a parity check matrix having a stair-wise diagonal matrix in an extension part, and wherein a location of “1” in the extension part is restrictively set.

4. The method of claim 1, wherein the performing of the concatenated SPC encodings by the at least one second code rate is performed according to each code rate in a unit of modulation and coding schemes (MCSs).

5. An encoding apparatus using a rate-compatible low density parity check (LDPC) code in a communication system, the encoding apparatus comprising: a first encoder configured to perform an LDPC encoding on information bits by a first code rate; and at least one second encoder configured to perform concatenated single parity check (SPC) encodings by at least one second code rate lower than the first code rate on the encoded information bits.

6. The encoding apparatus of claim 5, wherein the at least one second encoder is further configured to perform the concatenated SPC encodings by the at least one second code rate using a parity check matrix having a stair-wise lower triangular structure in an extension part.

7. A method of encoding using a rate-compatible low density parity check (LDPC) code in a communication system, the method comprising: performing an LDPC encoding on information bits by a first code rate; and performing at least one signal parity check (SPC) encoding corresponding to at least one second code rate lower than the first code rate on the encoded information bits.

8. The method of claim 7, wherein the performing of the SPC encoding corresponding to the at least one second code rate is performed using a parity check matrix having a partial dual diagonal structure in an extension part.

9. The method of claim 8, further comprising: performing a partial accumulation on a second diagonal component in the extension part after performing the SPC encoding.

10. The method of claim 7, wherein the SPC encoding corresponding to the at least one second code rate is performed according to each code rate in a unit of modulation and coding schemes (MCSs).

11. An encoding apparatus using a rate-compatible low density parity check (LDPC) code in a communication system, the encoding apparatus comprising: a first encoder configured to perform an LDPC encoding on information bits by a first code rate; and at least one second encoder configured to perform at least one signal parity check (SPC) encoding corresponding to at least one second code rate lower than the first code rate on the encoded information bits.

12. The encoding apparatus of claim 11, wherein the at least one second encoder is further configured to perform the SPC encoding corresponding to the at least one second code rate using a parity check matrix having a partial dual diagonal structure in an extension part.

13. A transmission apparatus in a communication system, the transmission apparatus comprising: a transmitter configured to transmit data; and an encoding apparatus configured to perform an encoding by using a rate-compatible low density parity check (LDPC) code, wherein the encoding apparatus comprises: a first encoder that performs an LDPC encoding on information bits by a first code rate; and at least one second encoder that performs concatenated single parity check (SPC) encodings by at least one second code rate lower than the first code rate on the encoded information bits, and wherein the concatenated SPC encodings by the at least one second code rate are performed using a parity check matrix having a stair-wise lower triangular structure in an extension part.

14. A transmission apparatus in a communication system, the transmission apparatus comprising: a transmitter configured to transmit data; and an encoding apparatus configured to perform an encoding by using a rate-compatible low density parity check (LDPC), wherein the encoding apparatus further comprises: a first encoder that performs an LDPC encoder on information bits by a first code rate; and at least one second encoder that performs at least one single parity check (SPC) encoding corresponding to at least one second code rate lower than the first code rate on the encoded information bits, and wherein the SPC encoding corresponding to the at least one second code rate are performed using a parity check matrix having a partial dual diagonal structure in an extension part.

15. The encoding apparatus of claim 5, wherein the at least one second encoder is further configured to perform the concatenated SPC encodings by the at least one second code rate using a parity check matrix having a stair-wise diagonal matrix in an extension part, and wherein a location of “1” in the extension part is restrictively set.

16. The encoding apparatus of claim 5, wherein the at least one second encoder is further configured to perform the concatenated SPC encodings by the at least one second code rate according to each code rate in a unit of modulation and coding schemes (MCSs).

17. The encoding apparatus of claim 12, wherein the at least one second encoder is further configured to perform a partial accumulation on a second diagonal component in the extension part after performing the SPC encoding.

18. The encoding apparatus of claim 11, wherein the at least one second encoder is further configured to perform the SPC encoding corresponding to the at least one second code rate according to each code rate in a unit of modulation and coding schemes (MCSs).

19. The transmission apparatus of claim 13, wherein the at least one second encoder is further configured to perform the concatenated SPC encodings by the at least one second code rate according to each code rate in a unit of modulation and coding schemes (MCSs).

20. The transmission apparatus of claim 14, wherein the at least one second encoder is further configured to perform the SPC encoding corresponding to the at least one second code rate according to each code rate in a unit of modulation and coding schemes (MCSs).

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0035] The above and other aspects, features, and advantages of certain embodiments of the present disclosure will be more apparent from the following description taken in conjunction with the accompanying drawings, in which:

[0036] FIG. 1 illustrates a structure of a parity check matrix of an rate compatible low-density parity-check (RC-LDPC) code designed through a diagonal extension used in the RC-LDPC encoding scheme according to the related art;

[0037] FIG. 2 illustrates a structure of a parity check matrix designed through a lower triangular extension used in the RC-LDPC encoding scheme according to the related art;

[0038] FIGS. 3 and 4 illustrate various encoding schemes of an RC-LDPC code designed through a general extension according to the related art;

[0039] FIG. 5 illustrates decoding complexity of a parity check matrix of an RC-LDPC code designed through a diagonal extension scheme according to an embodiment of the present disclosure;

[0040] FIG. 6 illustrates encoding complexity of a parity check matrix of an RC-LDPC code designed through a general extension scheme according to an embodiment of the present disclosure;

[0041] FIG. 7 illustrates an example of a structure of a parity check matrix having a stair-wise lower triangular structure in an extension part in the RC-LDPC encoding scheme according to an embodiment of the present disclosure;

[0042] FIG. 8 illustrates an example of a structure of a parity check matrix having a partially dual diagonal structure in an extension part in the RC-LDPC encoding scheme according to an embodiment of the present disclosure;

[0043] FIG. 9 illustrates an RC-LDPC encoding method using a parity check matrix having the stair-wise lower triangular structure according to an embodiment of the present disclosure;

[0044] FIG. 10 illustrates an RC-LDPC encoding method using a parity check matrix having the partial dual diagonal structure according to an embodiment of the present disclosure; and

[0045] FIG. 11 illustrates an error correction performance of the RC-LDPC code designed through the conventional extension scheme, and the stair-wise extension scheme and the partial dual diagonal extension scheme according an embodiment of to the present disclosure.

[0046] Throughout the drawings, it should be noted that like reference numbers are used to depict the same or similar elements, features, and structures.

DETAILED DESCRIPTION

[0047] The following description with reference to the accompanying drawings is provided to assist in a comprehensive understanding of various embodiments of the present disclosure as defined by the claims and their equivalents. It includes various specific details to assist in that understanding but these are to be regarded as merely exemplary. Accordingly, those of ordinary skill in the art will recognize that various changes and modifications of the various embodiments described herein can be made without departing from the scope and spirit of the present disclosure. In addition, descriptions of well-known functions and constructions may be omitted for clarity and conciseness.

[0048] The terms and words used in the following description and claims are not limited to the bibliographical meanings, but, are merely used by the inventor to enable a clear and consistent understanding of the present disclosure. Accordingly, it should be apparent to those skilled in the art that the following description of various embodiments of the present disclosure is provided for illustration purpose only and not for the purpose of limiting the present disclosure as defined by the appended claims and their equivalents.

[0049] It is to be understood that the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a component surface” includes reference to one or more of such surfaces.

[0050] The present disclosure proposes a new structure of a parity check matrix of an rate compatible low-density parity-check (RC-LDPC) code which may reduce complexity while maintaining or improving error correction performance. According to an encoding method and apparatus to which the parity check matrix of the RC-LDPC code is applied according to an embodiment of the present disclosure, it is possible to resolve high complexity of the parity check matrix and a time delay caused when the RC-LDPC code is designed through the diagonal extension scheme or the general extension scheme described in the background art.

[0051] First, a problem of the RC-LDPC code designed through the diagonal extension scheme or the general extension scheme will be described in detail to help understanding of the present disclosure. Recognition of the problem motivates the various proposed embodiments of the present disclosure.

[0052] FIG. 5 illustrates decoding complexity of the parity check matrix of the RC-LDPC code designed through the diagonal extension scheme according to an embodiment of the present disclosure, and a structure of the parity check matrix by the diagonal extension scheme is the same as illustrated in FIG. 1.

[0053] Referring to FIG. 5, through the diagonal extension scheme, an RC-LDPC code supporting a simple encoding may be designed. However, when the RC-LDPC code is designed to be optimized in consideration of the diagonal extension scheme, the density of H.sub.0 in the parity check matrix H.sub.D and 1 in matrix B is significantly higher than the density of 1 of the RC-LDPC code designed in consideration of the general extension scheme as illustrated in a reference numeral 501 of FIG. 5. Decoding complexity of the LDPC code is proportional to the density of 1 in the parity check matrix and, accordingly, using the RC-LDPC code designed through the diagonal extension scheme increases the decoding complexity.

[0054] FIG. 6 illustrates encoding complexity of the parity check matrix of the RC-LDPC code designed through the general extension scheme according to an embodiment of the present disclosure, and a structure of the parity check matrix by the general extension scheme is the same as the structure of the parity check matrix by the lower triangular extension scheme in the example of FIG. 1. In FIG. 6, reference numeral 601 denote a part in which simple encoding is not possible due to the lower triangular structure.

[0055] Referring to FIG. 6, the general extension scheme may reduce the density of H.sub.0 in Equation 1 above and 1 in the matrix B.sub.D compared to the diagonal extension scheme and, accordingly, support a decoding having low complexity. However, when the RC-LDPC code is designed through the general extension scheme, the lower triangular matrix T in Equation 2 is designed without any restriction and, in this case, an operation amount increases according to calculation of an inverse matrix and performance of a matrix-multiplication operation. Accordingly, when the general extension scheme is used, a relatively more complex encoding must be performed. Compared to the concatenated SPC encodings through the diagonal extension scheme, the concatenated LDPC encodings and multiple concatenated SPC encodings through the general extension scheme are more complex and also have a higher delay time.

[0056] As described above, between the diagonal extension scheme and the general extension scheme, there is a trade-off relation between encoding complexity and decoding complexity.

[0057] Accordingly, embodiments of the present disclosure propose a method and an apparatus for overcoming an encoding/decoding complexity increase problem and designing and encoding an excellent RC-LDPC code in terms of performance-complexity trade-off.

[0058] Hereinafter, a structure of a new parity check matrix for the RC-LDPC code and an encoding method using the parity check matrix of the new structure will be described according to an embodiment of the present disclosure.

[0059] First, the parity check matrix for the RC-LDPC code according to the present disclosure has a structure including an extension part stair-wise designed in the unit of modulation and coding schemes (MCSs) to be supported or an extension part designed by a partial dual-diagonal component. Hereinafter, the parity check matrixes of the present disclosure according to the structure will be referred to as a parity check matrix having a stair-wise lower triangular structure and a parity check matrix having a partial dual-diagonal structure. The encoding method of the RC-LDPC code according to the present disclosure corresponds to a phased encoding method of the RC-LDPC code using a new parity check matrix of the two structures.

[0060] The parity check matrix having the lower triangular structure includes stair-wise sub-matrix(matrices) in the extension part for code rate compatibility, and the parity check matrix having the partial dual-diagonal structure includes sub-matrix(matrices) having a partial dual-diagonal component within a diagonal matrix. The form of the parity check matrix according to the present disclosure is fixed and the remaining extension parts of the parity check matrix are designed to be optimized.

[0061] FIG. 7 illustrates an example of a structure of a parity check matrix having a stair-wise lower triangular structure in an extension part in the RC-LDPC encoding scheme according to an embodiment of the present disclosure.

[0062] Referring to FIG. 7, a reference numeral 701 indicates an information area of message bits corresponding to information bits, a reference numeral 703 indicates a first parity bit area of first parity bits for information bits, and a reference numeral 705 indicates a second parity area of second parity bits for information bits and corresponds to an extension area (that is, the extension part) of the parity check matrix. In FIG. 7, “A” indicates a sub-matrix for information bits, and “B” indicates a sub-matrix for the first parity bits. Further, a reference numeral 707 indicates a design free area in which “1” can exist in the parity check matrix. As illustrated in FIG. 7, in the parity check matrix of the RC-LDPC code designed to have the stair-wise lower triangular structure in the extension part, the second parity bit area 705 corresponds to a rate-compatible parity area and is designed by a stair-wise diagonal matrix. In FIG. 7, a reference numeral 711 indicates a part in which “1” is located in the diagonal matrix, and reference numerals 713 and 715 indicate parts in which “0” is filled in the diagonal matrix.

[0063] In FIG. 7, a reference numeral 709 indicates a diagonal extension part having the stair-wise lower triangular structure, and the location of “1” is limited according to an MCS level in the diagonal extension part (reference numeral 709) unlike the design free area (reference numeral 707). Further, in the embodiment of FIG. 7, the parity check matrix may be understood as the parity check matrix having the lower triangular structure in which at least one area having a degree, which is not 1, is stair-wise configured according to a code rate in the extension part.

[0064] In FIG. 7, a stair-wise extension scheme of the parity check matrix is encoded according to each supported MCS unit (level or step). For example, when code rates of the LDPC code in the supported MCS are r.sub.0, r.sub.1, r.sub.2, . . . , and r.sub.min and a parity check matrix of the highest code rate is H.sub.0, a parity check matrix of the code rate r.sub.1 of the next MCS level is configured as Equation 3 below.

[00003]$\begin{array}{cc}{H}_1=\left[\begin{array}{cc}{H}_0& 0\\ B_1& I\end{array}\right]& \mathrm{Equation}.Math..Math.3\end{array}$

[0065] In Equation 3 above, B.sub.1 corresponds to a sub-matrix designed for optimization by the code rate r.sub.1. Further, the parity check matrix of the code rate r.sub.2 of the next MCS level is configured as Equation 4 below.

[00004]$\begin{array}{cc}{H}_2=\left[\begin{array}{cc}{H}_1& 0\\ B_2& I\end{array}\right]=\left[\begin{array}{ccc}{H}_0& 0& 0\\ B_1& I& 0\\ B_{21}& B_{22}& I\end{array}\right]& \mathrm{Equation}.Math..Math.4\end{array}$

[0066] The matrix B.sub.2=[B.sub.21;B.sub.22] corresponds to a sub-matrix designed for optimization by the code rate r.sub.2 when a right side part is fixed. Through such a scheme, the parity check matrix can be extended according to each MCS level.

[0067] FIG. 8 illustrates an example of a structure of a parity check matrix having a partially dual diagonal structure in an extension part in the RC-LDPC encoding scheme according to an embodiment of the present disclosure.

[0068] Referring to FIG. 8, a reference numeral 801 indicates an information area of message bits corresponding to information bits, a reference numeral 803 indicates a first parity bit area of first parity bits for information bits, and a reference numeral 805 indicates a second parity area of second parity bits for information bits and corresponds to an extension area (that is, the extension part) of the parity check matrix. In FIG. 8, “A” indicates a sub-matrix for information bits, and “B” indicates a sub-matrix for the first parity bits. Further, a reference numeral 807 indicates a design free area in which “1” can exist in the parity check matrix. As illustrated in FIG. 8, in the parity check matrix of the RC-LDPC code designed to have the partial dual diagonal structure in the extension part, the second parity bit area 805 corresponds to a rate-compatible parity area and is designed by a partial dual diagonal matrix. In FIG. 8, reference numerals 809 and 811 denote parts in which “1” is located in the dual diagonal matrix, and reference numerals 813 and 815 denote parts in which “0” is filled in the diagonal matrix.

[0069] In FIG. 8, an extension scheme of the parity check matrix is also executed according to each supported MCS unit (level or step). While the rate-compatible parity area of the newly extended part is fixed to the diagonal matrix in the conventional diagonal extension scheme, a dual diagonal component is partially configured in the partial dual diagonal extension scheme. For example, when code rates of the LDPC code in the supported MCS are r.sub.0, r.sub.1, r.sub.2, . . . , and r.sub.min and a parity check matrix of the highest code rate is H.sub.0, a parity check matrix of the code rate r.sub.1 of the next MCS level is configured as Equation 5 below.

[00005]$\begin{array}{cc}{H}_1=\left[\begin{array}{cc}{H}_0& 0\\ B_1& I^{″}\end{array}\right]& \mathrm{Equation}.Math..Math.5\end{array}$

[0070] In Equation 5 above, I″ corresponds to a matrix generated by adding an additional diagonal component to the basic identity matrix, and a matrix B.sub.1 corresponds to a sub-matrix designed for optimization by the code rate r.sub.1. A parity check matrix of the code rate r.sub.2 of the next MCS level is configured as Equation 6 below.

[00006]$\begin{array}{cc}{H}_2=\left[\begin{array}{ccc}{H}_0& 0& 0\\ B_1& I^{″}& 0\\ B_2& 0& I^{″}\end{array}\right]& \mathrm{Equation}.Math..Math.6\end{array}$

[0071] A matrix B.sub.2 corresponds to a sub-matrix designed for optimization when a right side part is fixed in the code rate r.sub.2. Through such a scheme, the parity check matrix can be extended according to each MCS level.

[0072] In the embodiments of FIGS. 7 and 8, although the codes rates according to the MCS levels are illustrated up to r.sub.2 for convenience of the description, lower code rates such as r.sub.0, r.sub.1, r.sub.2, . . . , and r.sub.min may be used.

[0073] In the embodiments of FIGS. 7 and 8, the sub-matrix(matrices) in the rate-compatible area are designed to be fixed to the stair-wise type or the partial dual diagonal type in the parity check matrix of the RC-LDPC code according to the present disclosure. By using the parity check matrix designed according to FIGS. 7 and 8, a density of “1” in the rate-compatible area corresponding to the extension part is higher than the density of “1” in the conventional diagonal extension scheme, but a parity check matrix having a particular structure may be designed unlike the conventional general extension scheme. As described above, when the rate-compatible area is fixed to the particular structure, first, it is possible to improve encoding/decoding complexity by reducing the density of “1” in design free areas (reference numerals 707 and 807) of the parity check matrix compared to the conventional diagonal extension scheme. Second, compared to the conventional general extension scheme, simpler encoders may be used (that is, concatenated SPC encoders in the unit of MCSs may be simply used), so that complexity of the encoding process can be reduced.

[0074] FIG. 9 illustrates an RC-LDPC encoding method using a parity check matrix having a stair-wise lower triangular structure according to an embodiment of the present disclosure.

[0075] Referring to FIG. 9, in the RC-LDPC encoding using the parity check matrix having the stair-wise lower triangular structure in the extension part, SPC encodings corresponding to a number of supported MCS units are concatenated and performed. First, an encoding for the highest code rate is performed on information bits in step 901. For an LDPC code of the highest code rate, a general LDPC encoding is performed. The SPC encoding is performed on a codeword acquired therethrough at a first MCS level in step 903. Since a diagonal extension is performed at each MCS level in a stair-wise extension, the SPC encoding may be performed at the next MCS level in step 905. The next level SPC encoding is sequentially performed on the acquired codeword, and a final codeword may be acquired through repetition of the above process. In FIGS. 9 and 10, x briefly indicates an area including an information area and a first parity area, p.sub.1/3 and p.sub.1/4 indicate second parity areas, A and C briefly indicate sub-matrixes of the parity check matrix, and subscripts 1/2, 1/3, and 1/4 indicate examples of corresponding code rates.

[0076] Similar to the configuration illustrated in FIG. 9, an encoding apparatus that performs the RC-LDPC encoding method of FIG. 9 may include a first encoder that performs an LDPC encoding on information bits by a first code rate and at least one second encoder that performs concatenated single parity check (SPC) encodings on the encoded bits by at least one second code rate lower than the first code rate.

[0077] FIG. 10 illustrates an RC-LDPC encoding method using a parity check matrix having a partial dual diagonal structure according to an embodiment of the present disclosure.

[0078] Referring to FIG. 10, in the RC-LDPC encoding using the parity check matrix having the partial dual diagonal structure in the extension part, SPC encodings corresponding to a number of supported MCS units are performed. First, an encoding for the highest code rate is performed on information bits in step 1001. For an LDPC code of the highest code rate, a general LDPC encoding is performed. A codeword acquired therethrough is encoded at a first MCS level in step 1003. Since a partial dual diagonal extension basically includes a diagonal component, the SPC encoding may be first performed in step 1003-1. Further, in the extension part, a partial accumulation is performed in consideration of a second diagonal component 1007 in step 1003-2. The partial accumulation refers to sequential accumulation of parity bits calculated through the SPC encoding in consideration of the second diagonal component. For example, when temporary parity bits generated based on the first diagonal component are p0′, p1′, p2′, . . . and there is the second diagonal component in parts corresponding to the parity bits, final parity bits may be calculated such as p0=p0′, p1=p1′+p0, and p2=p2′+p1.

[0079] The next level SPC encoding is performed on the acquired codeword, in step 1005, and a final codeword may be acquired through repetition of the above process. Parity bits of each MCS level may be generated in parallel since there is no correlation therebetween. In an encoding process for each MCS level, the partial accumulation is performed when there is the second diagonal component in the corresponding MCS level, and is omitted when there is no second diagonal component in the corresponding MCS level.

[0080] Further, similar to the configuration illustrated in FIG. 10, an encoding apparatus that performs the RC-LDPC encoding method of FIG. 10 may include a first encoder that performs an LDPC encoding on information bits by a first code rate and at least one second encoder that performs at least one single parity check (SPC) encoding corresponding to at least one second code rate lower than the first code rate on the encoded bits. The encoding apparatus includes a partial accumulator that performs partial accumulation on the second diagonal component in the extension part after performing the SPC encoding.

[0081] A transmission apparatus that performs an encoding according to the encoding method of FIGS. 9 and 10 may include a transmitter for data transmission to the encoding apparatus of FIGS. 9 and 10 and further include a controller that controls the encoding operation and the transmission operation.

[0082] Meanwhile, in the above described embodiments of the present disclosure, the parity check matrix having the partial dual diagonal structure in the extension part and the parity check matrix having the dual diagonal structure in the extension may be applied to the RC-LDPC decoding method and apparatus in the same/similar way.

[0083] Table 1 below compares encoding/decoding complexity and performance of the RC-LDPC code between the prior art and the present disclosure.

[0084] As described above, the parity check matrix has a structure in which complexity of one of the encoding and the decoding is relatively high in the prior art. According to the present disclosure, in order to reduce the density of “1” in the parity check matrix, “1” is placed in the rate-compatible parity part of the parity check matrix, which is limited to be implementation-friendly. Accordingly, the encoding complexity and the decoding complexity can be relatively reduced according to the present disclosure.

TABLE-US-00001 TABLE 1 Encoding Decoding Limited length Design complexity complexity performance Division method Encoding method order order order Prior art General (high code rate 4 (perform 1 1 CLPC encoding) + matrix- (low code rate multiplication) LDPC encoding or plurality of SPC encodings) Diagonal (high code rate 1 4 (PCM 4 LDPC encoding) + densification) (implementation (one SPC performance) encoding) Present Stairwise (high code rate 2 1 1 disclosure LDPC encoding) + (phased SPC encodings) Partial High code rate 2 2 3 Dual LDPC encoding + Diagonal (phased SPC encodings + partial accumulation)

[0085] In the present disclosure, it is noted, through an experiment by an applicant of the present disclosure, that the density of “1” in the parity check matrix is lower than that of the conventional diagonal extension. Table 2 below shows measurement results of maximum and average degrees for extension parts of the RC-LDPC code designed through the diagonal extension scheme, the stair-wise extension scheme, and the partial dual diagonal extension scheme. Further, in Table 2 below, it may be noted that the extension schemes are asymptotically optimized at the same level through threshold values showing an asymptotic performance for each code and code rate.

[0086] In addition, according to Table 2 below, when the codes are optimized at the same level, the density of “1” in the parity check matrix designed through the stair-wise and partial dual diagonal extension schemes according to the present disclosure is much lower than that designed through the conventional diagonal extension scheme. Accordingly, it may be noted that not only the decoding complexity but also the encoding complexity can be significantly improved.

TABLE-US-00002 TABLE 2 Diagonal Extension Stair-wise Extension Partial Dual-diagonal Extension Threshold Degrees Threshold Degrees Threshold Degrees 1/3  0.01487 Avg. 7.1667 0.01082 Avg. 6.8333 0.016859 Avg. 6.8333 VNs VNs VNs Max. 14 Max. 12 Max. 12 VNs VNs VNs Avg. 5.3333 Avg. 5 Avg. 5.0833 CNs CNs CNs Max. 6 Max. 5 Max. 6 CNs CNs CNs 1/6  −0.554598 Avg. 13.0833 −0.555868 Avg. 12.5833 −0.548997 Avg. 12.25 VNs VNs VNs Max. 28 Max. 22 Max. 22 VNs VNs VNs Avg. 4.125 Avg. 3.9583 Avg. 3.8333 CNs CNs CNs Max. 5 Max. 4 Max. 4 CNs CNs CNs 1/9  −0.713603 Avg. 18.6667 −0.713603 Avg. 16.75 −0.711302 Avg. 17 VNs VNs VNs Max. 40 Max. 28 Max. 30 VNs VNs VNs Avg. 3.7917 Avg. 3.375 Avg. 3.5 CNs CNs CNs Max. 4 Max. 4 Max. 4 CNs CNs CNs 1/12 −0.804954 Avg. 24.3333 −0.802418 Avg. 20.4167 −0.802095 Avg. 21.3333 VNs VNs VNs Max. 50 Max. 34 Max. 36 VNs VNs VNs Avg. 3.8333 Avg. 3.0417 Avg. 3.25 CNs CNs CNs Max. 4 Max. 4 Max. 4 CNs CNs CNs 1/24 −0.911918 Avg. 45.8333 −0.924799 Avg. 37.75 −0.911918 Avg. 42.6667 VNs VNs VNs Max. 80 Max. 58 Max. 66 VNs VNs VNs Avg. 3.6739 Avg. 3.4479 Avg. 3.7008 CNs CNs CNs Max. 4 Max. 4 Max. 4 CNs CNs CNs 1/48 −1.03253 Avg. 87.1667 −1.006168 Avg. 64.75 −0.993052 Avg. 80 VNs VNs VNs Max. 132 Max. 90 Max. 112 VNs VNs VNs Avg. 3.5833 Avg. 3 Avg. 3.375 CNs CNs CNs Max. 4 Max. 3 Max. 4 CNs CNs CNs

[0087] FIG. 11 illustrates an actual experiment result showing an error correction performance of the RC-LDPC code designed through the conventional extension scheme, and the stair-wise extension scheme and the partial dual diagonal extension scheme according to the present disclosure. Under experiment conditions of FIG. 11, a message length corresponds to 800 bits and a codeword encoded by each code is BPSK-modulated and transmitted to a binary additive white Gaussian noise (AWGN) channel, and it may be noted, through an experiment result, that the RC-LDPC code designed according to the present disclosure is more excellent than the conventional diagonal extension scheme and, particularly, a performance difference becomes larger as a code rate is lower.

[0088] The new structure of the parity check matrix of the RC-LDPC code according to the present disclosure may organically support transmission of various code rates through one code structure like the parity check matrix according to the conventional diagonal extension scheme and general extension scheme. Further, a degree of a parameter node of a message bit part (information bit part) of the parity check matrix according to the present disclosure is reduced compared to the conventional extension scheme and general extension scheme, so that the encoding and decoding complexity can be reduced. In addition, a parity bit part of the parity check matrix according to the present disclosure is designed to have an implementation-friendly structure and thus an efficient encoding is possible.

[0089] While the present disclosure has been shown and described with reference to various embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present disclosure as defined by the appended claims and their equivalents.