Decoding system and decoding method

1. A decoding system, comprising:

a modulator which modulates user data having a predetermined bit length by using a modulation rule which converts the user data in accordance with characteristics of a transmission path into a modulation pattern having a bit length equivalent to or different from the predetermined bit length so as to disperse information on an arbitrary bit of the user data into plural bits of the modulation pattern;

a regenerator which generates a regenerative signal from a signal obtained by transmitting the user data after modulation by the modulator through the transmission path;

a transmission path decoder which generates signals as generation signals corresponding to the modulation pattern, and calculates distances between the regenerative signal and the generation signals in an interval having a length fixedly or dynamically determined depending on the bit length of the modulation pattern, the signals being generated by taking into account the characteristics of the transmission path with respect to the modulation pattern; and

a demodulator which calculates reliability information for each bit of the user data based on the distances between the regenerative signal and the generation signals in the interval, and estimates each bit of the user data based on the calculated reliability information, wherein

the transmission path has characteristics to disperse an arbitrary element of a signal transmitted through the transmission path into plural components of the regenerative signal,

the transmission path decoder generates k (k is a positive integer) generation signals, and respectively calculates k distances between the regenerative signal and each of the k generation signals in the interval, and

the demodulator uses the k distances calculated by the transmission path decoder to respectively calculate likelihood that each bit of the user data is 1 and likelihood that each bit of the user data is 0 by Formula (A), and calculates the reliability information by Formula (B):

wherein Formula (A) is:

p

j

⁡

(

x

)

=

∑

i

=

0

:

d

ij

=

x

k

-

1

⁢

⁢

p

⁡

(

m

i

)

=

∑

i

=

0

:

d

ij

=

x

k

-

1

⁢

⁢

[

1

2

⁢

πσ

2

⁢

exp

⁢

{

-

m

i

2

2

⁢

σ

2

}

]

(

A

)

wherein Formula (B) is:

λ j ={p j (0)− p j (1)}· Q   (B)

where x is 0 or 1, p j (x) is likelihood that j-th bit of the user data is x, d ij is the j-th bit of the user data corresponding to the modulation pattern of i-th generation signal out of the k generation signals, m i is a distance between the i-th generation signal out of the k generation signals and the regenerative signal, i is an integer in 0 to (k−1) range, λ j is the reliability information of the j-th bit of the user data, j is an integer in 1 to M range, M is a bit length of the user data, and the coefficient Q is a real number that is fixedly or dynamically determined;

wherein a middle part of Formula (A) is:

∑

i

=

0

:

d

ij

=

x

k

-

1

⁢

p

⁡

(

m

i

)

;

and

wherein the middle part of Formula (A) expresses a sum of the probabilities of the modulation patterns where d ij is x, out of k probabilities calculated from k modulation patterns.

2. The decoding system according to claim 1 , wherein

the transmission path decoder generates N (N is an integer greater than k) generation signals, respectively calculates N distances between the regenerative signal and each of the N generation signals, extracts k distances out of the calculated N distances in a shorter distance order, and notifies the demodulator of the extracted k distances.

3. The decoding system according to claim 1 , wherein

the modulator uses the modulation rule, which respectively converts plural pieces of the user data into the modulation patterns different from each other, and

the modulation rule is predetermined so that mutually corresponding bits in the modulation patterns include both 0 and 1 in all of the modulation patterns.

4. The decoding system according to claim 1 , wherein

the modulator uses the modulation rule, which respectively converts plural pieces of the user data into the modulation patterns different from each other, and

the modulation rule is predetermined so that a distance between the modulation patterns after conversion is shorter as a distance between the plural pieces of the user data is shorter.

5. The decoding system according to claim 4 , wherein

the distance between the plural pieces of the user data is a Hamming distance calculated in an interval having a predetermined bit length in the plural pieces of the user data, and

the predetermined bit length is determined by the modulation rule.

6. The decoding system according to claim 1 , further comprising:

an error correction encoder which generates the user data by error-correction encoding input data, based on a predetermined error correction code rule; and

an error correction decoder which error-correction decodes each bit of the user data estimated by the demodulator based on the error correction code rule.

7. The decoding system according to claim 6 , wherein the error correction encoder uses a low density parity check code as the error correction code rule.

8. The decoding system according to claim 7 , wherein the error correction decoder performs error-correction decoding by the Sum-Product decoding method based on the low density parity check code.

9. The decoding system according to claim 6 , further comprising:

a recorder which records the user data after modulation by the modulator on an information recording medium; and

an equalization processor which processes the regenerative signal generated by the regenerator in predetermined equalization processing, wherein

the regenerator generates the regenerative signal from the user data, recorded on the information recording medium by the recorder and after modulation by the modulator, as a signal transmitted through the transmission path, and

the transmission path decoder calculates distances between the generation signals and the regenerative signal processed by the equalization processor in equalization processing.

10. The decoding system according to claim 1 , wherein the transmission path has characteristics to limit bandwidth of a signal transmitted through the transmission path.

11. The decoding system according to claim 1 , wherein the transmission path decoder calculates Euclidean distances as the distances between the regenerative signal and the generation signals.

12. A decoding system, comprising:

a modulator which modulates user data having a predetermined bit length by using a modulation rule which converts the user data in accordance with characteristics of a transmission path into a modulation pattern having a bit length equivalent to or different from the predetermined bit length so as to disperse information on an arbitrary bit of the user data into plural bits of the modulation pattern;

a regenerator which generates a regenerative signal from a signal obtained by transmitting the user data after modulation by the modulator through the transmission path;

a transmission path decoder which generates signals as generation signals corresponding to the modulation pattern, and calculates distances between the regenerative signal and the generation signals in an interval having a length fixedly or dynamically determined depending on the bit length of the modulation pattern, the signals being generated by taking into account the characteristics of the transmission path with respect to the modulation pattern; and

a demodulator which calculates reliability information for each bit of the user data based on the distances between the regenerative signal and the generation signals in the interval, and estimates each bit of the user data based on the calculated reliability information, wherein

the modulation rule is determined to limit at least one of a maximum number of times when a same bit continues in the modulation pattern, a minimum number of times when a same bit continues in the modulation pattern, a maximum number of times and a minimum number of times when a same bit continues in the modulation pattern, and a number of times when a specific pattern repeats in the modulation pattern,

the transmission path has characteristics to disperse an arbitrary element of a signal transmitted through the transmission path into plural components of the regenerative signal,

the transmission path decoder generates k (k is a positive integer) generation signals, and respectively calculates k distances between the regenerative signal and each of the k generation signals in the interval, and

the demodulator uses the k distances calculated by the transmission path decoder to respectively calculate likelihood that each bit of the user data is 1 and likelihood that each bit of the user data is 0 by Formula (A), and calculates the reliability information by Formula (B):

wherein Formula (A) is:

p

j

⁡

(

x

)

=

∑

i

=

0

:

d

ij

=

x

k

-

1

⁢

⁢

p

⁡

(

m

i

)

=

∑

i

=

0

:

d

ij

=

x

k

-

1

⁢

⁢

[

1

2

⁢

πσ

2

⁢

exp

⁢

{

-

m

i

2

2

⁢

σ

2

}

]

(

A

)

wherein Formula (B) is:

λ j ={p j (0)− p j (1)}· Q   (B)

where x is 0 or 1, p j (x) is likelihood that j-th bit of the user data is x, d ij is the j-th bit of the user data corresponding to the modulation pattern of i-th generation signal out of the k generation signals, m i is a distance between the i-th generation signal out of the k generation signals and the regenerative signal, i is an integer in 0 to (k−1) range, λ j is the reliability information of the j-th bit of the user data, j is an integer in 1 to M range, M is a bit length of the user data, and the coefficient Q is a real number that is fixedly or dynamically determined;

wherein a middle part of Formula (A) is:

∑

i

=

0

:

d

ij

=

x

k

-

1

⁢

p

⁡

(

m

i

)

;

and

wherein the middle part of Formula (A) expresses a sum of the probabilities of the modulation patterns where d ij is x, out of k probabilities calculated from k modulation patterns.

13. A decoding system, comprising:

a modulator which modulates user data having a predetermined bit length by using a modulation rule which converts the user data in accordance with characteristics of a transmission path into a modulation pattern having a bit length equivalent to or different from the predetermined bit length so as to disperse information on an arbitrary bit of the user data into plural bits of the modulation pattern;

a regenerator which generates a regenerative signal from a signal obtained by transmitting the user data after modulation by the modulator through the transmission path;

a transmission path decoder which generates signals as generation signals corresponding to the modulation pattern, and calculates distances between the regenerative signal and the generation signals in an interval having a length fixedly or dynamically determined depending on the bit length of the modulation pattern, the signals being generated by taking into account the characteristics of the transmission path with respect to the modulation pattern; and

a demodulator which calculates reliability information for each bit of the user data based on the distances between the regenerative signal and the generation signals in the interval, and estimates each bit of the user data based on the calculated reliability information, wherein

the transmission path has characteristics to disperse an arbitrary element of a signal transmitted through the transmission path into plural components of the regenerative signal,

the transmission path decoder generates k (k is a positive integer) generation signals, and respectively calculates k distances between the regenerative signal and each of the k generation signals in the interval,

the transmission path decoder calculates the distances between the regenerative signal and the generation signals only in a central interval of the interval, the central interval being obtained by removing a predetermined length from both ends of the interval, and

the demodulator uses the k distances calculated by the transmission path decoder to respectively calculate likelihood that each bit of the user data is 1 and likelihood that each bit of the user data is 0 by Formula (A), and calculates the reliability information by Formula (B):

wherein Formula (A) is:

p

j

⁡

(

x

)

=

∑

i

=

0

:

d

ij

=

x

k

-

1

⁢

⁢

p

⁡

(

m

i

)

=

∑

i

=

0

:

d

ij

=

x

k

-

1

⁢

⁢

[

1

2

⁢

πσ

2

⁢

exp

⁢

{

-

m

i

2

2

⁢

σ

2

}

]

(

A

)

wherein Formula (B) is:

λ j ={p j (0)− p j (1)}· Q   (B)

where x is 0 or 1, p j (x) is likelihood that j-th bit of the user data is x, d ij is the j-th bit of the user data corresponding to the modulation pattern of i-th generation signal out of the k generation signals, m i is a distance between the i-th generation signal out of the k generation signals and the regenerative signal, i is an integer in 0 to (k−1) range, λ j is the reliability information of the j-th bit of the user data, j is an integer in 1 to M range, M is a bit length of the user data, and the coefficient Q is a real number that is fixedly or dynamically determined;

wherein a middle part of Formula (A) is:

∑

i

=

0

:

d

ij

=

x

k

-

1

⁢

p

⁡

(

m

i

)

;

and

wherein the middle part of Formula (A) expresses a sum of the probabilities of the modulation patterns where d ij is x, out of k probabilities calculated from k modulation patterns.

14. A decoding method, comprising:

a modulating step of modulating user data having a predetermined bit length by using a modulation rule which converts the user data in accordance with characteristics of a transmission path into a modulation pattern having a bit length equivalent to or different from the predetermined bit length so as to disperse information on an arbitrary bit of the user data into plural bits of the modulation pattern;

a regenerating step of generating a regenerative signal from a signal obtained by transmitting the user data after modulation in the modulating step through the transmission path;

a transmission path decoding step of generating signals as generation signals corresponding to the modulation pattern, and calculating distances between the regenerative signal and the generation signals in an interval having a length fixedly or dynamically determined depending on the bit length of the modulation pattern, the signals being generated by taking into account the characteristics of the transmission path with respect to the modulation pattern; and

a demodulating step of calculating reliability information for each bit of the user data based on the distances between the regenerative signal and the generation signals in the interval, and estimating each bit of the user data based on the calculated reliability information, wherein

the transmission path has characteristics to disperse an arbitrary element of a signal transmitted through the transmission path into plural components of the regenerative signal,

the transmission path decoding step generates k (k is a positive integer) generation signals, and respectively calculates k distances between the regenerative signal and each of the k generation signals in the interval, and

the demodulating step uses the k distances calculated in the transmission path decoding step to respectively calculate likelihood that each bit of the user data is 1 and likelihood that each bit of the user data is 0 by Formula (A), and calculates the reliability information by Formula (B):

wherein Formula (A) is:

p

j

⁡

(

x

)

=

∑

i

=

0

:

d

ij

=

x

k

-

1

⁢

⁢

p

⁡

(

m

i

)

=

∑

i

=

0

:

d

ij

=

x

k

-

1

⁢

⁢

[

1

2

⁢

πσ

2

⁢

exp

⁢

{

-

m

i

2

2

⁢

σ

2

}

]

(

A

)

wherein Formula (B) is:

λ j ={p j (0)− p j (1)}· Q   (B)

where x is 0 or 1, p j (x) is likelihood that j-th bit of the user data is x, d ij is the j-th bit of the user data corresponding to the modulation pattern of i-th generation signal out of the k generation signals, m i is a distance between the i-th generation signal out of the k generation signals and the regenerative signal, i is an integer in 0 to (k−1) range, λ j is the reliability information of the j-th bit of the user data, j is an integer in 1 to M range, M is a bit length of the user data, and the coefficient Q is a real number that is fixedly or dynamically determined;

wherein a middle part of Formula (A) is:

∑

i

=

0

:

d

ij

=

x

k

-

1

⁢

p

⁡

(

m

i

)

;

and

wherein the middle part of Formula (A) expresses a sum of the probabilities of the modulation patterns where d ij is x, out of k probabilities calculated from k modulation patterns.