Encoding and decoding methods and apparatuses for recording system

• US 20050062623A1
• Filed: 09/21/2004
• Published: 03/24/2005
• Est. Priority Date: 09/22/2003
• Status: Active Grant

• Current Assignee: Institute For Information Technology Advancement, Samsung Electronics Co. Ltd.
• Original Assignee: Samsung Electronics Co. Ltd.
• Inventors: Lee, Jun, Lee, Kyong-mi
• Granted Patent: US 7,414,551 B2
• Time in Patent Office: Days
• US Class Current: 341/107
• CPC Class Codes: H03M 13/1148 Structural properties of the code parity-check or generator matrix
• CPC Class Codes: H03M 13/1177 Regular LDPC codes with parity-check matrices wherein all rows and columns have the same row weight and column weight, respectively
• CPC Class Codes: H03M 13/2963 Turbo-block codes, i.e. turbo codes based on block codes, e.g. turbo decoding of product codes
• CPC Class Codes: H03M 13/6331 Error control coding in combination with equalisation

Abstract

A method and apparatus for encoding and decoding data for a recording system. The method of encoding data involves encoding input data into a predetermined code and precoding the predetermined code so that output levels of a channel can be detected, the channel being defined by a predetermined channel polynomial.

Claims

1. A method of encoding data comprising:

encoding input data into a predetermined code; and

preceding the predetermined code so that output levels of a channel can be detected, the channel being defined by a predetermined channel polynomial.

2. The method of claim 1, wherein the channel is a partial response channel.

3. The method of claim 2, wherein the predetermined channel polynomial PR(D) is defined as follows:

PR(D)=1+a₁D+ . . . +a_nDⁿ

where each of a₁ . . . a_n indicates an integer, n is an integer and D indicates delay.

4. The method of claim 3, wherein the predetermined code is precoded by using a precoding function P(D) defined as follows:

$P<br><br>\left(D\right)=\frac{1}{1\oplus <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{MOD}<br><br>\left(a_1,2\right)<br><br>D\oplus <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\dots <br><br>}\oplus <br><br>\mathrm{MOD}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(a_n,2\right)<br><br>D^n}$

where MOD(a_n,

     2) indicates a signed remainder of a_n divided by 2, and ⊕

indicates a logical exclusive OR operation.

5. A method of decoding data after receiving, via a predetermined channel, a precoded signal obtained by encoding input data into a predetermined code and precoding the predetermined code with the use of a predetermined channel polynomial so that output levels of the predetermined channel can be detected, the method comprising:

receiving the precoded signal via the predetermined channel and obtaining a channel output for the precoded signal; and

decoding the channel output by using a predetermined decoding algorithm.

6. The method of claim 5, wherein the decoding algorithm is a probability propagation algorithm that uses the channel output as an input.

7. The method of claim 6, wherein the decoding algorithm calculates a probability of the predetermined code outputting the channel output as a-priori information and decodes the channel output by using the a-priori information.

8. The method of claim 7, wherein the probability ƒ

_kⁱ of the predetermined code outputting the channel output is defined as follows;

$f_k^i=P<br><br>\left(b_k=i|e_k^{\mathrm{\prime <br><br>}}\right)=\frac{\underset{j}{\sum <br><br>}<br><br>\left[P<br><br>\left(b_k=i\right)<br><br>P<br><br>\left(e_k^{\mathrm{\prime <br><br>}}|Y=S_j<br><br>\left(i\right)\right)\right]}{\underset{i}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>\left[P<br><br>\left(b_k=i\right)<br><br>P<br><br>\left(e_k^{\mathrm{\prime <br><br>}}|Y=S_j<br><br>\left(i\right)\right)\right]}$

where e′

_k indicates the channel output, S_j(i) indicates a j-th set of noiseless PR channel signals that make b_k equal to i, P(e′

_k|Y=S_j(i)) indicates channel transition probability of a k-th PR signal, P(b_k=i) indicates a-priori probability, i=0 or 1, and 1≦

j≦

L−

1, where L indicates the number of PR channel signals.

9. The method of claim 8, wherein the channel transition probability P(e′

_k|Y=S_j(i)) is defined as follows;

$P<br><br>\left(e_k^{\mathrm{\prime <br><br>}}|Y=S_j<br><br>\left(i\right)\right)=\exp <br><br>\left[-w<br><br>\frac{{\left(e_k^{\mathrm{\prime <br><br>}}-S_j<br><br>\left(i\right)\right)}^2}{2<br><br>{\mathrm{\sigma <br><br>}}^2}\right]$

where w indicates a weight factor, and σ

² indicates a noise variance.

10. A method of encoding and decoding data comprising:

encoding input data into a predetermined code;

precoding the predetermined code so that output levels of a channel can be detected, the channel being defined by a predetermined channel polynomial;

receiving a precoded signal, which is obtained by precoding the predetermined code, via the predetermined channel and obtaining a channel output for the precoded signal; and

decoding the channel output by using a predetermined decoding algorithm.

11. The method of claim 10, wherein the predetermined channel polynomial PR(D) is defined as follows:

PR(D)=1+a₁D+ . . . +a_nDⁿ

where each of a₁ . . . a_n indicates an integer, n is an integer and D indicates delay.

12. The method of claim 11, wherein the predetermined code is precoded by using a precoding function P(D) defined as follows:

$P<br><br>\left(D\right)=\frac{1}{1\oplus <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{MOD}<br><br>\left(a_1,2\right)<br><br>D\oplus <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\dots <br><br>}\oplus <br><br>\mathrm{MOD}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(a_n,2\right)<br><br>D^n}$

where MOD(a_n,

     2) indicates a signed remainder of a_n divided by 2 and ⊕

indicates a logical exclusive OR operation.

13. The method of claim 12, wherein the decoding algorithm is a probability propagation algorithm that uses the channel output as an input.

14. The method of claim 13, wherein the decoding algorithm calculates a probability of the predetermined code outputting the channel output as a-priori information and decodes the channel output by using the a-priori information.

15. The method of claim 14, wherein the probability ƒ

_kⁱ of the predetermined code outputting the channel output is defined as follows;

$f_k^i=P<br><br>\left(b_k=i|e_k^{\mathrm{\prime <br><br>}}\right)=\frac{\underset{j}{\sum <br><br>}<br><br>\left[P<br><br>\left(b_k=i\right)<br><br>P<br><br>\left(e_k^{\mathrm{\prime <br><br>}}|Y=S_j<br><br>\left(i\right)\right)\right]}{\underset{i}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>\left[P<br><br>\left(b_k=i\right)<br><br>P<br><br>\left(e_k^{\mathrm{\prime <br><br>}}|Y=S_j<br><br>\left(i\right)\right)\right]}$

where e′

_k indicates the channel output, S_j(i) indicates a j-th set of noiseless PR channel signals that make b_k equal to i, P(e′

_k|Y=S_j(i)) indicates channel transition probability of a k-th PR signal, P(b_k=i) indicates a-priori probability, i=0 or 1, and 1≦

j≦

L−

1, where L indicates the number of PR channel signals.

16. The method of claim 15, wherein the channel transition probability P(e′

_k|Y=S_j(i)) is defined as follows;

$P<br><br>\left(e_k^{\mathrm{\prime <br><br>}}|Y=S_j<br><br>\left(i\right)\right)=\exp <br><br>\left[-w<br><br>\frac{{\left(e_k^{\mathrm{\prime <br><br>}}-S_j<br><br>\left(i\right)\right)}^2}{2<br><br>{\mathrm{\sigma <br><br>}}^2}\right]$

where w indicates a weight factor and σ

² indicates a noise variance.

17. A method of decoding data after receiving, via a predetermined channel, a precoded signal obtained by encoding input data into a predetermined code and preceding the predetermined code with the use of a predetermined channel polynomial so that output levels of the predetermined channel can be detected, the method comprising:

receiving the precoded signal via the predetermined channel and obtaining a channel output for the precoded signal;

receiving first extrinsic information and the channel output and decoding the channel output for the precoded signal by using a first decoding algorithm; and

receiving the channel output for the precoded signal and second extrinsic information obtained as a result of decoding the channel output for the precoded signal, decoding the channel output for the precoded signal by using a second decoding algorithm, and providing the first extrinsic information.

18. The method of claim 17, wherein the first extrinsic information is determined by a-priori information, the second extrinsic information, and a log-likelihood ratio for the channel transition probability.

19. The method of claim 17, wherein the second extrinsic information is determined by the first extrinsic information and a-priori information obtained by using the first decoding algorithm.

20. A method of encoding and decoding data comprising:

encoding input data into a predetermined code;

preceding the predetermined code so that an output level of a channel can be detected, the channel being defined by a predetermined channel polynomial;

receiving a precoded signal, obtained by precoding the predetermined code, via the predetermined channel and obtaining a channel output for the precoded signal;

receiving first extrinsic information and the channel output for the precoded signal and decoding the channel output for the precoded signal by using a first decoding algorithm; and

receiving second extrinsic information obtained as a result of decoding the channel output for the precoded signal and the channel output for the precoded signal, decoding the channel output for the precoded signal by using a second decoding algorithm, and providing the first extrinsic information.

21. The method of claim 20, wherein the predetermined channel polynomial PR(D) is defined as follows:

PR(D)=1+a₁D+ . . . +a_nDⁿ

where each of a₁ . . . a_n indicates an integer, n is an integer and D indicates delay.

22. The method of claim 21, wherein the predetermined code is precoded by using a preceding function P(D) defined as follows:

$P<br><br>\left(D\right)=\frac{1}{1\oplus <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{MOD}<br><br>\left(a_1,2\right)<br><br>D\oplus <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\dots <br><br>}\oplus <br><br>\mathrm{MOD}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(a_n,2\right)<br><br>D^n}$

where MOD(a_n,

     2) indicates a signed remainder of a_n divided by 2, and ⊕

indicates a logical exclusive OR operation.

23. The method of claim 20, wherein the first extrinsic information is determined by a-priori information, the second extrinsic information, and a log-likelihood ratio for the channel transition probability.

24. The method of claim 20, wherein the second extrinsic information is determined by the first extrinsic information and a-priori information obtained by using the first decoding algorithm.

25. An apparatus for encoding and decoding data comprising:

an encoder which encodes input data into a predetermined code;

a precoder which precodes the predetermined code so that an output level of a channel can be detected, the channel being defined by a predetermined channel polynomial;

a channel equalizer which receives the precoded code via the predetermined channel and obtains an output of the predetermined channel for the precoded code; and

a decoder which decodes the output of the predetermined channel by using a predetermined decoding algorithm.

26. The apparatus of claim 25, wherein the predetermined channel polynomial PR(D) is defined as follows:

PR(D)=1+a₁D+ . . . +a_nDⁿ,

where each of a₁ . . . a_n indicates an integer, n is an integer, D indicates delay, and

the precoder precodes the predetermined code by using a preceding function P(D) defined as follows;

$P<br><br>\left(D\right)=\frac{1}{1\oplus <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{MOD}<br><br>\left(a_1,2\right)<br><br>D\oplus <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\dots <br><br>}\oplus <br><br>\mathrm{MOD}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(a_n,2\right)<br><br>D^n}$

where MOD(a_n,

     2) indicates a signed remainder of a_n divided by 2, and ⊕

indicates a logical exclusive OR operation.

27. The apparatus of claim 26, wherein the decoder receives the channel output and decodes the channel output by using a probability propagation algorithm.

28. The apparatus of claim 27, wherein the decoder calculates, as a-priori information, probability ƒ

_kⁱ of the predetermined code outputting the channel output and decodes the channel output by using the a-priori information, and the probability ƒ

_kⁱ is defined as follows;

$f_k^i=P<br><br>\left(b_k=i|e_k^{\mathrm{\prime <br><br>}}\right)=\frac{\underset{j}{\sum <br><br>}<br><br>\left[P<br><br>\left(b_k=i\right)<br><br>P<br><br>\left(e_k^{\mathrm{\prime <br><br>}}|Y=S_j<br><br>\left(i\right)\right)\right]}{\underset{i}{\sum <br><br>}<br><br>\underset{j}{\sum <br><br>}<br><br>\left[P<br><br>\left(b_k=i\right)<br><br>P<br><br>\left(e_k^{\mathrm{\prime <br><br>}}|Y=S_j<br><br>\left(i\right)\right)\right]}$

where e′

_k indicates the channel output, S_j(i) indicates a j-th set of noiseless PR channel signals making b_k equal to i, P(e′

_k|Y=S_j(i)) indicates channel transition probability of a k-th PR signal, P(b_k=i) indicates a-priori probability, i=0 or 1, and 1≦

j≦

L−

1, where L indicates the number of PR channel signals.

29. The apparatus of claim 28, wherein the decoder defines channel transition probability P(e′

_k|Y=S_j(i)) as follows;

$P<br><br>\left(e_k^{\mathrm{\prime <br><br>}}|Y=S_j<br><br>\left(i\right)\right)=\exp <br><br>\left[-w<br><br>\frac{{\left(e_k^{\mathrm{\prime <br><br>}}-S_j<br><br>\left(i\right)\right)}^2}{2<br><br>{\mathrm{\sigma <br><br>}}^2}\right]$

where w indicates a weight factor and σ

² indicates a noise variance.

30. An apparatus for encoding and decoding data comprising:

an encoder which encodes input data into a predetermined code;

a precoder which precodes the predetermined code so that output levels of a channel can be detected, the channel being defined by a predetermined channel polynomial;

a channel equalizer which receives the precoded signal via the predetermined channel and obtains a channel output for the precoded signal;

a first decoder which receives first extrinsic information and the channel output and decodes the channel output by using a first decoding algorithm; and

a second decoder which receives second extrinsic information obtained as a result of decoding the channel output and the channel output, decodes the channel output by using a second decoding algorithm, and provides the first extrinsic information to the first decoder.

31. The apparatus of claim 30, wherein the predetermined channel polynomial PR(D) is defined as follows:

PR(D)=1+a₁D+ . . . +a_nDⁿ,

where each of a₁ . . . a_n indicates an integer, n is an integer and D indicates delay, and

the precoder precodes the predetermined code by using a precoding function P(D) defined as follows;

$P<br><br>\left(D\right)=\frac{1}{1\oplus <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{MOD}<br><br>\left(a_1,2\right)<br><br>D\oplus <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\dots <br><br>}\oplus <br><br>\mathrm{MOD}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(a_n,2\right)<br><br>D^n}$

where MOD(a_n,

     2) indicates a signed remainder of a_n divided by 2, and ⊕

indicates a logical exclusive OR operation.

32. The apparatus of claim 30, wherein the second decoder determines the first extrinsic information by using a-priori information, obtained with the use of a predetermined decoding algorithm, the second extrinsic information, and a log-likelihood ratio for the channel transition probability.

33. The apparatus of claim 30, wherein the first decoder determines the second extrinsic information by using the first extrinsic information and the a-priori information.

34. An apparatus for encoding and decoding data comprising:

a first encoder which encodes input data into a first code;

a second encoder which encodes the input data into a second code;

a multiplexer which multiplexes the input data and the first and second codes;

a precoder which precodes a code output from the multiplexer so that output levels of a channel can be detected, the channel being defined by a predetermined channel polynomial;

a channel equalizer which receives a precoded signal, which is obtained by precoding the code, via the predetermined channel and obtains a channel output for the precoded code;

a first decoder which receives first extrinsic information and the channel output and decodes the channel output by using a first decoding algorithm; and

a second decoder which receives second extrinsic information obtained as a result of decoding the channel output and the channel output, decodes the channel output by using a second decoding algorithm, and provides the first extrinsic information to the first decoder.

35. The apparatus of claim 34, wherein the predetermined channel polynomial PR(D) is defined as follows:

PR(D)=1+a₁D+ . . . +a_nDⁿ,

where each of a₁ . . . a_n indicates an integer, n is an integer and D indicates delay, and

the precoder precodes the predetermined code by using a preceding function P(D) defined as follows;

$P<br><br>\left(D\right)=\frac{1}{1\oplus <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{MOD}<br><br>\left(a_1,2\right)<br><br>D\oplus <br><br>\text{\hspace{1em}<br><br>}<br><br>\mathrm{\dots <br><br>}\oplus <br><br>\mathrm{MOD}<br><br>\text{\hspace{1em}<br><br>}<br><br>\left(a_n,2\right)<br><br>D^n}$

where MOD(a_n,

     2) indicates a signed remainder of a_n divided by 2, and ⊕

indicates a logical exclusive OR operation.

36. The apparatus of claim 34, wherein the second decoder determines the first extrinsic information by using a-priori information, obtained with the use of a predetermined decoding algorithm, the second extrinsic information, and a log-likelihood ratio for the channel transition probability.

37. The apparatus of claim 34, wherein the first decoder determines the second extrinsic information by using the first extrinsic information, the a-priori information, and a log-likelihood ratio for the channel transition probability.

38. The apparatus of claim 34, wherein the first and second encoders encode the input data using different encoding algorithms so as to make an interleaver unnecessary.