WO2011010286A4 - Compact decoding of punctured codes - Google Patents
Compact decoding of punctured codes Download PDFInfo
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- WO2011010286A4 WO2011010286A4 PCT/IB2010/053317 IB2010053317W WO2011010286A4 WO 2011010286 A4 WO2011010286 A4 WO 2011010286A4 IB 2010053317 W IB2010053317 W IB 2010053317W WO 2011010286 A4 WO2011010286 A4 WO 2011010286A4
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- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
- H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
- H03M13/1148—Structural properties of the code parity-check or generator matrix
- H03M13/118—Parity check matrix structured for simplifying encoding, e.g. by having a triangular or an approximate triangular structure
- H03M13/1185—Parity check matrix structured for simplifying encoding, e.g. by having a triangular or an approximate triangular structure wherein the parity-check matrix comprises a part with a double-diagonal
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/03—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words
- H03M13/05—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits
- H03M13/11—Error detection or forward error correction by redundancy in data representation, i.e. code words containing more digits than the source words using block codes, i.e. a predetermined number of check bits joined to a predetermined number of information bits using multiple parity bits
- H03M13/1102—Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes
- H03M13/1105—Decoding
- H03M13/1111—Soft-decision decoding, e.g. by means of message passing or belief propagation algorithms
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/61—Aspects and characteristics of methods and arrangements for error correction or error detection, not provided for otherwise
- H03M13/615—Use of computational or mathematical techniques
- H03M13/616—Matrix operations, especially for generator matrices or check matrices, e.g. column or row permutations
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/63—Joint error correction and other techniques
- H03M13/635—Error control coding in combination with rate matching
- H03M13/6362—Error control coding in combination with rate matching by puncturing
-
- H—ELECTRICITY
- H03—ELECTRONIC CIRCUITRY
- H03M—CODING; DECODING; CODE CONVERSION IN GENERAL
- H03M13/00—Coding, decoding or code conversion, for error detection or error correction; Coding theory basic assumptions; Coding bounds; Error probability evaluation methods; Channel models; Simulation or testing of codes
- H03M13/63—Joint error correction and other techniques
- H03M13/635—Error control coding in combination with rate matching
- H03M13/6362—Error control coding in combination with rate matching by puncturing
- H03M13/6368—Error control coding in combination with rate matching by puncturing using rate compatible puncturing or complementary puncturing
- H03M13/6393—Rate compatible low-density parity check [LDPC] codes
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/0001—Systems modifying transmission characteristics according to link quality, e.g. power backoff
- H04L1/0009—Systems modifying transmission characteristics according to link quality, e.g. power backoff by adapting the channel coding
- H04L1/0013—Rate matching, e.g. puncturing or repetition of code symbols
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0045—Arrangements at the receiver end
- H04L1/0052—Realisations of complexity reduction techniques, e.g. pipelining or use of look-up tables
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0057—Block codes
-
- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L1/00—Arrangements for detecting or preventing errors in the information received
- H04L1/004—Arrangements for detecting or preventing errors in the information received by using forward error control
- H04L1/0056—Systems characterized by the type of code used
- H04L1/0067—Rate matching
- H04L1/0068—Rate matching by puncturing
- H04L1/0069—Puncturing patterns
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- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Probability & Statistics with Applications (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Physics (AREA)
- Computer Networks & Wireless Communication (AREA)
- Signal Processing (AREA)
- General Physics & Mathematics (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Algebra (AREA)
- Computing Systems (AREA)
- Quality & Reliability (AREA)
- Error Detection And Correction (AREA)
Abstract
k input bits are encoded according to a code with which is associated a m x n=m+k parity check matrix H. The resulting codeword is punctured, with n'<n bits. The punctured codeword is exported to a corrupting medium such as a communication channel or a memory. A representation of the punctured codeword is imported from the corrupting medium and is decoded using a matrix H' that is smaller than H. For example, H' is m'=m~(n-n ') x n' and is derived by merging selected rows of H. Alternatively, H has at most m rows and fewer than n columns but more than n' columns. Alternatively, H has fewer than m'=m-(n-n') rows and fewer than n' columns.
Claims
AMENDED CLAIMS
received by the International Bureau on 06 November 201 1 (06.1 1 .201 1 )
1. A method of porting k input bits, comprising;
(a) encoding the input bits according to a first code with which is associated a parity check matrix H that has m rows and n-m+k columns, thereby producing a codeword of n bits;
(b) puncturing the codeword, thereby providing a punctured codeword of n'<n bits;
(c) exporting the punctured codeword to a corrupting medium;
(d) importing a representation of the punctured codeword from the corrupting medium; and
(e) decoding the representation of the punctured codeword using a matrix H' that has at most m rows and a number of columns that is less than n and that is not equal to n', wherein H' is a parity check matrix of a second code and wherein the punctured codeword is a codeword of the second code.
2. The method of claim 1, wherein the first code is a block code.
3. The method of claim 1, wherein the decoding includes exchanging messages between nodes of a Tanner graph that correspond to the rows of H' and nodes of the Tanner graph that correspond to the columns of H'.
4. The method of claim 1 , wherein the corrupting medium is a transmission medium, wherein the exporting includes transmitting the punctured codeword via the transmission medium, and wherein the importing includes receiving the representation of the punctured codeword from the transmission medium.
5. The method of claim 1, wherein the corrupting medium is a storage medium, wherein the exporting includes storing the punctured codeword in the storage medium, and wherein the importing includes reading the representation of the punctured codeword from the storage medium.
6. The method of claim 1, further comprising:
(f) deriving H' from H.
7. The method of claim 6, wherein H' has more than n' columns, wherein the puncturing includes eliminating n-n' selected bits from the codeword, and wherein the deriving of H' from H includes performing Gaussian elimination on H to set equal to zero elements 1 through m-m" of the columns of H that correspond to a number m"<n-n' of the selected bits, thereby producing a matrix H", H' then being m-m" rows of H" without the columns that correspond to the m" of the selected bits.
8. The method of claim 7, wherein the Gaussian elimination is terminated when further Gaussian elimination would produce a matrix H' that fails to satisfy a predetermined criterion of sparseness-
9. The method of claim 8, wherein the predetermined criterion of sparseness is that an average column degree of H' is less than the lesser of 10 and one- quarter of a number of rows of H'.
10. The method of claim 6, wherein H' has fewer than m -m-{n-nr) rows and fewer than n' columns, wherein the puncturing includes eliminating n-n' selected bits from the codeword, and wherein the deriving of H' from H is effected by steps including performing Gaussian elimination on H to set equal to zero elements 1 through m' of the columns of Hthat correspond to the selected bits, thereby producing a matrix H", H' then being selected rows of H" without the columns that correspond to the selected bits and without at least one column that corresponds to another bit that is connected, by H, only to the selected bits.
1 1. A memory device comprising:
(a) a memory; and
(b) a controller for storing k input bits in the memory and for recovering the input bits from the memory, the controller including:
(i) an encoder for:
(A) encoding the input bits according to a first code with which is associated a parity check matrix H that has m
rows and n-m+k columns, thereby producing a codeword of n bits, and
(B) puncturing the codeword, thereby providing a punctured codeword of fewer than n bits, and
(ii) a decoder for decoding a representation of the punctured codeword that has been read from the memory, the decoding being effected using a matrix H' that has at most m rows and a number of columns that is less than n and that is not equal to n', wherein H' is a parity check matrix of a second code and wherein the punctured codeword is a codeword of the second code.
A system comprising:
a first memory, and
a host of the first memory including:
(ii) a second memory having stored therein code for managing the first memory by steps including:
(A) encoding k input bits according to a first code with which is associated a parity check matrix H that has m rows and n=m+k columns, thereby producing a codeword of n bits,
(B) puncturing the codeword, thereby providing a punctured codeword of n'<n bits,
(C) storing the punctured codeword in the first memory,
(D) reading a representation of the punctured codeword from the first memory, and
(E) decoding the representation of the punctured codeword using a matrix H' that has at most m rows and a number of columns that is less than n and that is not equal to n', wherein H' is a parity check matrix of a second code and wherein the punctured codeword is a codeword of the second code, and
(ii) a processor for executing the code.
13. The system of claim 12, wherein the code for managing the first memory also includes code for deriving H' from H.
14. The system of claim 13, wherein H' has more than n' columns, wherein the puncturing includes eliminating n-n' selected bits from the codeword, and wherein the deriving of H' from H includes performing Gaussian elimination on H to set equal to zero elements 1 through m-m" of the columns of H that correspond to a number m"<n-n' of the selected bits, thereby producing a matrix H'\ H' then being m-w" rows of H" without the columns that correspond to the m" of the selected bits.
15. The system of claim 14, wherein the Gaussian elimination is terminated when further Gaussian elimination would produce a matrix H' that fails to satisfy a predetermined criterion of sparseness.
16. The system of claim 15, wherein the predetermined criterion of sparseness is that an average column degree of H' is less than the lesser of 10 and one- quarter of a number of rows of H'.
17. The system of claim 13, wherein H' has fewer than m -m-(n-n') rows and fewer than n' columns, wherein the puncturing includes eliminating n-n' selected bits from the codeword, and wherein the deriving of H' from H is effected by steps including performing Gaussian elimination on H to set equal to zero elements 1 through m' of the columns of H that correspond to the selected bits, thereby producing a matrix H", H' then being selected rows of H" without the columns that correspond to the selected bits and without at least one column that corresponds to another bit that is connected, by H, only to the selected bits.
18. A computer-readable storage medium having embodied thereon computer-readable code for managing a memory, the computer-readable code comprising:
(a) program code for encoding k input bits according to a first code with which is associated a parity check matrix H that has m rows and n=m+k columns, thereby producing a codeword of n bits;
(b) program code for puncturing the codeword, thereby providing a punctured codeword of n'<n bits;
(c) program code for storing the punctured codeword in a memory;
(d) program code for reading a representation of the punctured codeword from the memory; and
(e) program code for decoding the representation of the punctured codeword using a matrix H' that has at most m rows and a number of columns that is less than n and that is not equal to n', wherein H' is a parity check matrix of a second code and wherein the punctured codeword is a codeword of the second code.
19. The computer-readable storage medium of claim 18, wherein the computer-readable code further comprises:
(f) program code for deriving H' from H.
20. The computer-readable storage medium of claim 19, wherein H' has more than n' columns, wherein the puncturing includes eliminating n-n' selected bits from the codeword, and wherein the deriving of W from H includes performing Gaussian elimination on H to set equal to zero elements 1 through m-m" of the columns of H that correspond to a number m"<n-n' of the selected bits, thereby producing a matrix H", H' then being m-m" rows of H" without the columns that correspond to the m" of the selected bits.
21. The computer-readable storage medium of claim 20, wherein the Gaussian elimination is terminated when further Gaussian elimination would produce a matrix H' that fails to satisfy a predetermined criterion of sparseness.
22. The computer-readable storage medium of claim 21 , wherein the predetermined criterion of sparseness is that an average column degree of H' is less than the lesser of 10 and one-quarter of a number of rows of H'.
23. The computer-readable medium of claim 19, wherein H' has fewer than m -m-(n-n') rows and fewer than n' columns, wherein the puncturing includes eliminating n-n' selected bits from the codeword, and wherein the deriving of //' from
H is effected by steps including performing Gaussian elimination on H to set equal to zero elements 1 through m' of the columns of H that correspond to the selected bits, thereby producing a matrix H", H' then being selected rows of H" without the columns that correspond to the selected bits and without at least one column that corresponds to another bit that is connected, by H, only to the selected bits.
24. A communication system comprising:
(a) a transmitter including:
(i) an encoder for:
(A) encoding k input bits according to a first code with which is associated a parity check matrix H that has m rows and n-m+k columns, thereby producing a codeword of n bits, and
(B) puncturing the codeword, thereby providing a punctured codeword of n'<n bits, and
(ii) a modulator for transmitting the punctured codeword via a communication channel as a modulated signal; and
(b) a receiver including:
(i) a demodulator for receiving the modulated signal from the communication channel and for demodulating the modulated signal, thereby providing a representation of the punctured codeword, and
(ii) a decoder for decoding the representation of the punctured codeword using a matrix H that has at most m rows and a number of columns that is less than n and that is not equal to wherein H' is a parity check matrix of a second code and wherein the punctured codeword is a codeword of the second code.
25. A method of recovering k input bits that have been encoded as a codeword of n bits according to a first code with which is associated a parity check matrix H that has m rows and n-m+k columns and that have been exported to a corrupting medium as a punctured codeword produced by eliminating n-n' selected bits from the codeword, the method comprising:
(a) importing a representation of the punctured codeword from the corrupting medium; and
(b) decoding the representation of the punctured codeword using a matrix H' that has at most m rows and a number of columns that is less than n and that is not equal to n', wherein H' is a parity check matrix of a second code and wherein the punctured codeword is a codeword of the second code.
26. The method of claim 25, wherein the first code is a block code.
27. The method of claim 25, wherein the decoding includes exchanging messages between nodes of a Tanner graph that correspond to the rows of H' and nodes of the Tanner graph that correspond to the columns of H'.
28- The method of claim 25 , further comprising:
(c) deriving H' from H.
29. The method of claim 28, wherein H' has more than «' columns, wherein the puncturing includes eliminating n-n' selected bits from the codeword, and wherein the deriving of H' from H includes performing Gaussian elimination on H to set equal to zero elements 1 through m-m" of the columns of H that correspond to a number m"<n-n' of the selected bits, thereby producing a matrix H", H' then being m-m" rows of H" without the columns that correspond to the m" of the selected bits.
30. The method of claim 29, wherein the Gaussian elimination is terminated when further Gaussian elimination would produce a matrix H' that fails to satisfy a predetermined criterion of sparseness.
31. The method of claim 30, wherein the predetermined criterion of sparseness is that an average column degree of H' is less than the lesser of 10 and one- quarter of a number of rows of H'.
32. The method of claim 28, wherein //' has fewer than m'~m-{n-n') rows and fewer than n' columns, wherein the puncturing includes eliminating n-n' selected
bits from the codeword, and wherein the deriving of H' from H is effected by steps including performing Gaussian elimination on H to set equal to zero elements 1 through m' of the columns of H that correspond to the selected bits, thereby producing a matrix H", H' then being selected rows of H" without the columns that correspond to the selected bits and without at least one column that corresponds to another bit that is connected, by H, only to the selected bits.
33. A decoder for decoding a representation of a punctured codeword, the punctured codeword having been produced by eliminating n-n ' selected bits from a codeword of n bits, the codeword having been produced by encoding k input bits according to a first code with which is associated a parity check matrix H that has m rows and n=m+k columns, the decoder comprising:
(a) a decoding module for decoding the representation of the punctured codeword using a matrix H' that has at most m rows and a number of columns that is less than n and that is not equal to n ', wherein H' is a parity check matrix of a second code and wherein the punctured codeword is a codeword of the second code.
34. The decoder of claim 33, further comprising:
(b) a code reduction module for deriving H' from H.
35. The method of claim 34, wherein H' has more than n' columns, wherein the puncturing includes eliminating n-n' selected bits from the codeword, and wherein the deriving of H' from H includes performing Gaussian elimination on H to set equal to zero elements 1 through m-m" of the columns of H that correspond to a number m"<n-n' of the selected bits, thereby producing a matrix H", H' then being m~m" rows of H" without the columns that correspond to the m" of the selected bits.
36. The method of claim 35, wherein the Gaussian elimination is terminated when further Gaussian elimination would produce a matrix H' that fails to satisfy a predetermined criterion of sparseness.
37. The method of claim 36, wherein the predetermined criterion of sparseness is that an average column degree of H' is less than the lesser of 10 and one- quarter of a number of rows of H'.
38. The method of claim 34, wherein H' has fewer than m'-m-(n-nr) rows and fewer than n' columns, wherein the puncturing includes eliminating n-n' selected bits from the codeword, and wherein the deriving of H' from H is effected by steps including performing Gaussian elimination on H to set equal to zero elements 1 through m' of the columns of H that correspond to the selected bits, thereby producing a matrix H", H' then being selected rows of H" without the columns that coirespond to the selected bits and without at least one column that corresponds to another bit that is connected, by H, only to the selected bits.
39- A receiver comprising:
(a) a demodulator for receiving a modulated signal from a communication channel and for demodulating the modulated signal to provide a representation of a punctured codeword that had been produced by eliminating n-n ' selected bits from a codeword of n bits, the codeword having been produced by encoding k input bits according to a first code with which is associated a parity check matrix H that has m rows and n=m+k columns; and
(b) a decoding module for decoding the representation of the punctured codeword using a matrix H' that has at most m rows and a number of columns that is less than n and that is not equal to n ', wherein H' is a parity check matrix of a second code and wherein the punctured codeword is a codeword of the second code.
40. The receiver of claim 39, further comprising:
(c) a code reduction module for deriving H' from H.
41. The method of claim 40, wherein H' has more than ri columns, wherein the puncturing includes eliminating n-n' selected bits from the codeword, and wherein the deriving of H' from H includes performing Gaussian elimination on H to set equal to zero elements 1 through m-m" of the columns of H that correspond to a
number m"<n-n' of the selected bits, thereby producing a matrix H", H' then being m-m" rows of H" without the columns that correspond to the m" of the selected bits.
42. The method of claim 41, wherein the Gaussian elimination is terminated when further Gaussian elimination would produce a matrix H' that fails to satisfy a predetermined criterion of sparseness.
43. The method of claim 42, wherein the predetermined criterion of sparseness is that an average column degree of H' is less than the lesser of 10 and one- quarter of a number of rows of H'.
44. The method of claim 40, wherein H' has fewer than m'=m-{n-nr) rows and fewer than n' columns, wherein the puncturing includes eliminating n-ri selected bits from the codeword, and wherein the deriving of H' from H is effected by steps including performing Gaussian elimination on H to set equal to zero elements 1 through m' of the columns of H that correspond to the selected bits, thereby producing a matrix H", H' then being selected rows of H" without the columns that correspond to the selected bits and without at least one column that corresponds to another bit that is connected, by H, only to the selected bits.
Priority Applications (2)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| EP10747670A EP2457329A2 (en) | 2009-07-21 | 2010-07-21 | Compact decoding of punctured codes |
| KR1020127004322A KR101722798B1 (en) | 2009-07-21 | 2010-07-21 | Compact decoding of punctured codes |
Applications Claiming Priority (6)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| US12/506,342 | 2009-07-21 | ||
| US12/506,327 US8516352B2 (en) | 2009-07-21 | 2009-07-21 | Compact decoding of punctured block codes |
| US12/506,316 | 2009-07-21 | ||
| US12/506,327 | 2009-07-21 | ||
| US12/506,342 US8375278B2 (en) | 2009-07-21 | 2009-07-21 | Compact decoding of punctured block codes |
| US12/506,316 US8516351B2 (en) | 2009-07-21 | 2009-07-21 | Compact decoding of punctured block codes |
Publications (3)
| Publication Number | Publication Date |
|---|---|
| WO2011010286A2 WO2011010286A2 (en) | 2011-01-27 |
| WO2011010286A3 WO2011010286A3 (en) | 2011-11-24 |
| WO2011010286A4 true WO2011010286A4 (en) | 2012-01-19 |
Family
ID=43430611
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| PCT/IB2010/053317 Ceased WO2011010286A2 (en) | 2009-07-21 | 2010-07-21 | Compact decoding of punctured codes |
Country Status (3)
| Country | Link |
|---|---|
| EP (1) | EP2457329A2 (en) |
| KR (1) | KR101722798B1 (en) |
| WO (1) | WO2011010286A2 (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TWI427936B (en) | 2009-05-29 | 2014-02-21 | Sony Corp | Receiving apparatus, receiving method, program, and receiving system |
| US9397699B2 (en) | 2009-07-21 | 2016-07-19 | Ramot At Tel Aviv University Ltd. | Compact decoding of punctured codes |
| US10979072B2 (en) * | 2019-03-19 | 2021-04-13 | Western Digital Technologies, Inc. | Punctured bit estimation and bit error rate estimation |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| KR100834650B1 (en) * | 2006-09-04 | 2008-06-02 | 삼성전자주식회사 | Signal transceiving device and method in communication system |
| TWI427936B (en) * | 2009-05-29 | 2014-02-21 | Sony Corp | Receiving apparatus, receiving method, program, and receiving system |
-
2010
- 2010-07-21 WO PCT/IB2010/053317 patent/WO2011010286A2/en not_active Ceased
- 2010-07-21 KR KR1020127004322A patent/KR101722798B1/en not_active Expired - Fee Related
- 2010-07-21 EP EP10747670A patent/EP2457329A2/en not_active Ceased
Also Published As
| Publication number | Publication date |
|---|---|
| EP2457329A2 (en) | 2012-05-30 |
| WO2011010286A3 (en) | 2011-11-24 |
| KR20120046751A (en) | 2012-05-10 |
| WO2011010286A2 (en) | 2011-01-27 |
| KR101722798B1 (en) | 2017-04-05 |
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