# US 8,543,887 B2 · Coding method and coding device

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- Number: US 8,543,887 B2
- Document ID: US8543887B2
- Status: Granted
- Kind: B2
- Application number: 12/601,046
- Filed: 2008-07-10
- Published: 2010-06-17
- Granted: 2013-09-24
- Earliest claimed: 2007-07-10
- Assignees: Sony Corporation
- Applicants: Makoto Noda
- Inventors: Makoto Noda
- Web page: https://patentgrep.com/patent/US8543887B2

## CPC

- H03M 13/13: Linear codes
- H03M 13/033: {Theoretical methods to calculate these checking codes}
- H03M 13/1102: {Codes on graphs and decoding on graphs, e.g. low-density parity check [LDPC] codes}
- H03M 13/6393: {Rate compatible low-density parity check [LDPC] codes}
- H03M: CODING; DECODING; CODE CONVERSION IN GENERAL (using fluidic means F15C4/00; optical analogue/digital converters G02F7/00; coding, decoding or code conversion, specially adapted for particular applications, see the relevant subclasses, e.g. G01D, G01R, G06F, G06T, G09G, G10L, G11B, G11C, H04B, H04L, H04M, H04N; ciphering or deciphering for cryptography or other purposes involving the need for secrecy G09C)

## Abstract

The present invention relates to coding method and coding device that allow Rate-Compatible LDPC (low-density parity-check) codes to have favorable BER performance both with a low code rate and with a high code rate. In coding of LDPC codes that have plural code rates and whose all parity check matrices are composed of plural cyclic matrices, a coder 121 performs the coding in such a way that 1<w0 and w1<w0 are satisfied when the maximum column weight of the cyclic matrices in the check matrix of a certain code whose code rate is not the minimum value among the LDPC codes is defined as w0 and the maximum column weight of the cyclic matrices in the check matrix of a code having a code rate lower than that of the certain code is defined as w1.

## Claims

### Claim 1

A data encoding method employing a data coding device for coding LDPC (low-density parity-check) code that have a plurality of code rates and whose all parity check matrices are composed of a plurality of cyclic matrices, the data encoding method being implemented by a microprocessor, the method comprising:
Providing a translation of data words into codewords so that the relationships 1<W0 and w1<w0 are satisfied when a maximum column weight of the cyclic matrices in a check matrix of a certain code whose code rate is not a minimum value among the LDPC codes is satisfied as W0 and a maximum column weight of the cyclic matrices in the check matrix of a code having a code rate lower than the code rate of the certain code is defined as w1.

### Claim 2 (depends on 1)

The data encoding method according to claim 1, wherein
when one side of the cyclic matrix in a parity check row is defined as m, based on assumption that a certain row address indicating a position of bit 1 in a certain column in the parity check matrix of a code having a high code rate is b, a row address indicating a position of bit 1 in the column in the parity check matrix of a code having a lower code rate can be represented as b+cm with use of an integer c that is constant for each cyclic matrix and is equal to or larger than 0.

### Claim 3 (depends on 2)

The data encoding method according to claim 2, wherein
a value of b or c is so adjusted that all of positions of parity in the check matrices of the codes are on a right side on the check matrix, or on a left side, or with constant intervals.

### Claim 4 (depends on 3)

The data encoding method according to claim 3, wherein
the number of cyclic matrices in the parity check matrix of a code having a highest code rate is only one in a row direction, and 2<w0 is satisfied.

### Claim 5 (depends on 4)

The data encoding method according to claim 4, wherein a
column weight of the cyclic matrices in the parity check matrix of a code having a lowest code rate is 0 or 1.

### Claim 6 (depends on 5)

The data encoding method according to claim 5, wherein a
column weight of the parity check matrix is constant for the codes of all of the code rates.

### Claim 7 (depends on 6)

The data encoding method according to claim 6, wherein a
column weight of the parity check matrix is 3.

### Claim 8 (depends on 7)

The data encoding method according to claim 7, wherein
all of the codes are self-orthogonal.

### Claim 9 (depends on 8)

The data encoding method according to claim 8, wherein
a minimum hamming distance of all of the codes is at least 6.

### Claim 10 (depends on 4)

The data encoding method according to claim 4, wherein
a data word is translated into a code word that is obtained by changing length m of one side of an identity matrix and has a different code length.

### Claim 11

A data encoding device for coding of LDPC codes that have a plurality of code rates and whose all parity check matrices are composed of a plurality of cyclic matrices, the data encoding device comprising:
circuitry performing coding by converting data words into code words such that
the relationships 1<w0 and w1<w0 are satisfied where a maximum column weight of the cyclic matrices in the certain check matrix whose code rate is not a minimum value among the LDPC codes is defined as w0 and a maximum column weight of the cyclic matrices in the check matrix of a code having a code rate lower than the code rate is defined as w1.

### Claim 12 (depends on 11)

The data encoding device according to claim 11, wherein
when one side of the cyclic matrix in a parity check row is defined as m, based on assumption that a certain row address indicating a position of bit 1 in a certain column in the parity check matrix of a code having a high code rate is b, a row address indicating a position of bit 1 in the column in the parity check matrix of a code having a lower code rate can be represented as b+cm with use of an integer c that is constant for each cyclic matrix and is equal to or larger than 0.

### Claim 13 (depends on 12)

The data encoding device according to claim 12, wherein
a value of b or c is so adjusted that all of positions of parity in the check matrices of the codes are on a right side on the check matrix, or on a left side, or with constant intervals.

### Claim 14 (depends on 13)

The data encoding device according to claim 13, wherein
the number of cyclic matrices in the parity check matrix of a code having a highest code rate is only one in a row direction, and 2<w0 is satisfied.

### Claim 15 (depends on 14)

The data encoding device according to claim 14, wherein
column weight of the cyclic matrices in the parity check matrix of a code having a lowest code rate is 0 or 1.

### Claim 16 (depends on 15)

The data encoding device according to claim 15, wherein
column weight of the parity check matrix is constant for the codes of all of the code rates.

### Claim 17 (depends on 16)

The data encoding device according to claim 16, wherein
a column weight of the parity check matrix is 3.

### Claim 18 (depends on 17)

The data encoding device according to claim 17, wherein
all of the codes are self-orthogonal.

### Claim 19 (depends on 18)

The data encoding device according to claim 18, wherein
a minimum hamming distance of all of the codes is at least 6.

### Claim 20 (depends on 14)

The data encoding device according to claim 14, wherein
coding is performed, including a code that is obtained by changing length m of one side of an identity matrix and has a different code length.