RU2006102662A - Способ кодирования кода разреженного контроля четности - Google Patents

Способ кодирования кода разреженного контроля четности Download PDF

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RU2006102662A
RU2006102662A RU2006102662/09A RU2006102662A RU2006102662A RU 2006102662 A RU2006102662 A RU 2006102662A RU 2006102662/09 A RU2006102662/09 A RU 2006102662/09A RU 2006102662 A RU2006102662 A RU 2006102662A RU 2006102662 A RU2006102662 A RU 2006102662A
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parity
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Нам-йюл ЙЮ (KR)
Нам-йюл ЙЮ
Мин-Гоо КИМ (KR)
Мин-Гоо КИМ
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Самсунг Электроникс Ко., Лтд. (KR)
Самсунг Электроникс Ко., Лтд.
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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
    • H03M13/1191—Codes on graphs other than LDPC codes
    • H03M13/1194—Repeat-accumulate [RA] codes
    • H03M13/1197—Irregular repeat-accumulate [IRA] codes
    • 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
    • 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
    • H03M13/1114—Merged schedule message passing algorithm with storage of sums of check-to-bit node messages or sums of bit-to-check node messages, e.g. in order to increase the memory efficiency
    • 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
    • H03M13/116—Quasi-cyclic LDPC [QC-LDPC] codes, i.e. the parity-check matrix being composed of permutation or circulant sub-matrices
    • H03M13/1162—Array based LDPC codes, e.g. array codes
    • 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
    • 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
    • H03M13/61—Aspects and characteristics of methods and arrangements for error correction or error detection, not provided for otherwise
    • H03M13/611—Specific encoding aspects, e.g. encoding by means of decoding
    • 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
    • H03M13/1131—Scheduling of bit node or check node processing
    • H03M13/1137—Partly parallel processing, i.e. sub-blocks or sub-groups of nodes being processed in parallel

Claims (9)

1. Способ генерирования кода разреженного контроля четности, состоящего из матрицы информационной части и матрицы части четности, при этом способ содержит этапы, на которых изменяют матрицу информационной части на структуру кода массива и назначают последовательность степеней каждому из столбцов подматрицы; расширяют матрицу части четности таким образом, чтобы значение смещения между диагональными линиями имело заранее определенное значение в обобщенной двухдиагональной матрице, которая является матрицей части четности; повышают обобщенную двухдиагональную матрицу; определяют значение смещения для циклического сдвига столбцов в каждой подматрице повышенной обобщенной двухдиагональной матрицы; и выполняют процесс кодирования для определения символа четности, соответствующего столбцу матрицы части четности.
2. Способ по п.1, в котором последовательность степеней формируется в соответствии с уравнением (37)
D = {15, 15, 15, 5, 5, 5, 4, 3, 3, 3, 3, 3, 3, 3, 3} (37)
3. Способ по п.1, в котором значение смещения между диагональными линиями является взаимнопростым в отношении числа столбцов в обобщенной двухдиагональной матрице.
4. Способ по п.1, в котором число строк в подматрице является простым числом.
5. Способ по п.1, в котором разность между суммой значений смещения для циклического сдвига строк подматрицы на диагональной линии в обобщенной двухдиагональной матрице, которая является матрицей части четности, и суммой значений смещения для циклического сдвига строк подматрицы на диагональной линии смещения не равна 0.
6. Способ по п.1, в котором процесс кодирования содержит этапы, на которых
(a) определяют символ четности первой строки в подматрице с индексом 0 столбца подматрицы на диагональной линии матрицы части четности;
(b) задают индекс строки в подматрице символа четности, идентичного определенному символу четности в индексе столбца в подматрице в подматрице на диагональной линии смещения, имеющей такой же индекс столбца подматрицы, что и индекс столбца подматрицы заданного символа четности;
(c) определяют символ четности, имеющий такой же индекс строки в заданной подматрице в подматрице на диагональной линии, имеющей такой же индекс строки подматрицы, что и индекс строки подматрицы на диагональной линии смещения; и
(d) многократно выполняют этапы (b) и (c) до тех пор, пока создание матрицы четности не будет завершено.
7. Способ по п.6, в котором на этапе (a) символ четности определяется суммой информационных символов матрицы информационной части, существующих в той же строке, что и индекс строки в подматрице, символы четности которой определяются.
8. Способ по п.6, в котором на этапе (b) индекс строки в подматрице задается в соответствии с уравнением (38)
Figure 00000001
 (38)
где означает индекс строки в подматрице с индексом i столбца подматрицы на диагональной линии смещения, x(l) i означает индекс столбца в подматрице с индексом i столбца, существующем на диагональной линии, а
Figure 00000003
означает значения смешения для циклического сдвига столбцов подматрицы с индексом i столбца подматрицы на диагональной линии смещения.
9. Способ по п.6, в котором на этапе (c) символ четности определяется в соответствии с уравнением (39):
Figure 00000004
 (39)
где
Figure 00000005
означает символ четности, соответствующий x(1) i+(r-f),
Figure 00000006
означает символ четности, соответствующий индексу столбца x(1) i, а
Figure 00000007
означает сумму информационных символов, существующих в строке с индексом y(2) i+(r-f) строки в подматрице с индексом i+(r-f) столбца подматрицы.
RU2006102662/09A 2003-10-14 2004-10-14 Способ кодирования кода разреженного контроля четности RU2308803C2 (ru)

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