Decoding method and decoding device
In row calculation, a value which is obtained by subtracting an offset according to a minimum of the absolute values of column LLRs from the minimum of the absolute values of the column LLRs is set as a row LLR corresponding to a column of the column LLRs.
1. A decoding method of decoding a codeword encoded with an LDPC (Low-Density Parity-Check) code, comprising:
calculating a LLR (Log-Likelihood Ratio) for each bit in a check matrix of said LDPC code; and
performing an iterative process comprising:
a) calculating row LLRs (Log-Likelihood Ratios) corresponding to a row weight of said check matrix of said LDPC code;
b) calculating column LLRs corresponding to a column weight of said check matrix from said row LLRs calculated by a) in a current iteration;
c) calculating an estimated bit sequence by estimating each bit on a basis of said column LLRs calculated by b) in the current iteration; and
d) checking whether or not the estimated bit sequence calculated by c) in the current iteration is said codeword, and performing a next iteration of the process if the estimated bit sequence is not said codeword,
wherein, in each iteration following an initial iteration of the process, a) includes:
calculating a minimum of absolute values of the column LLRs, calculated by b) in a previous iteration, from columns c each having a value of 1 in a row which is one of targets of calculating the row LLRs;
calculating a direct product with respect to the columns c by the following equation based on a Sum-Product decoding method:
sg
r
,
c
=
∏
c
′
∈
N
(
r
)
\
{
c
}
sgn
(
z
r
,
c
′
)
,
where (Z r,c′ ) indicates the column LLR;
setting a value, as a row LLR of the current iteration, obtained by multiplying between said minimum and the direct product when said minimum is less than a prescribed constant;
determining whether a result value of subtracting an offset value β from said minimum is greater than zero when said minimum is equal to or greater than the prescribed constant, the offset value β being changed in accordance with said minimum;
setting a value, as a row LLR of the current iteration, obtained by multiplying between the result value of the subtraction and the direct product when a result of the determination indicates affirmation; and
setting a value of zero as a row LLR of the current iteration when a result of the determination indicates negation.
2. The decoding method according to claim 1 , wherein a) further includes:
comparing a constant with a minimum of dyadic values which are a target for a dyadic operation executed in the row calculation using an algorithm based on the Sum-Product decoding method;
recognizing the minimum of the dyadic values as a result of the dyadic operation when said minimum of the dyadic values is less than the constant; and
recognizing, as a result of the dyadic operation, a result of subtracting an offset value D(δ) from the minimum of the dyadic values, the offset value D(δ) being acquired by the following equation:
D
(
δ
)
=
max
{
0.9
-
δ
2
,
0
}
,
where the value δ is a variable indicating a difference between the dyadic values.
3. The decoding method according to claim 1 ,
wherein the offset value β is an offset value D(δ) acquired by the following equation:
D
(
δ
)
=
max
{
0.9
-
δ
2
,
0
}
,
where the value δ is a variable indicating a result value of subtracting the minimum of the absolute values of said column LLRs from a second minimum of the absolute values of said column LLRs.
4. The decoding method according to claim 1 , wherein a) further includes:
calculating a first value, a second value and a third value, where
the first value indicates the result value of subtracting the offset value β from the minimum of absolute values of the column LLRs,
the second value indicates a result value of subtracting the offset value β from a second minimum of absolute values of the column LLRs, and
the third value indicates a result value of subtracting an offset value D(δ) as the offset value β from the minimum of absolute values of the column LLRs, the offset value D(δ) being acquired by the following equation:
D
(
δ
)
=
max
{
0.9
-
δ
2
,
0
}
,
where the value δ is a variable indicating a result value of subtracting the minimum of absolute values of the column LLRs from the second minimum of absolute values of the column LLRs;
comparing the second value with zero in the determination with respect to the column c having the minimum of absolute values of the column LLRs;
comparing the first value with zero in the determination with respect to the column c having the second minimum of absolute values of the column LLRs; and
comparing the third value with zero in the determination with respect to the other column c.
5. A decoding device for decoding a codeword encoded with an LDPC (Low-Density Parity-Check) code, comprising:
an LLR calculating unit for calculating an LLR (Log-Likelihood Ratio) for each bit in a check matrix of said LDPC code;
a combination of components configured to perform an iterative process, including:
a row calculating unit for calculating row LLRs (Log-Likelihood Ratios) corresponding to a row weight of said check matrix of said LDPC code;
a column calculating unit for calculating column LLRs corresponding to a column weight of said check matrix from said row LLRs calculated by said row calculating unit in a current iteration;
a bit estimating unit for calculating an estimated bit sequence by estimating each bit on a basis of said column LLRs calculated by said column calculating unit in the current iteration; and
a checking unit for checking whether or not the estimated bit sequence calculated by said bit estimating unit in the current iteration is said codeword, and causing a next iteration of the process to be performed if the estimated bit sequence is not said codeword,
wherein, in each iteration following an initial iteration of the process, said row calculating unit:
calculates a minimum of absolute values of the column LLRs, calculated by the column calculating unit in a previous iteration, from columns c each having a value of 1 in a row which is one of targets of calculating the row LLRs;
calculates a direct product with respect to the columns c by the following equation based on a Sum-Product decoding method:
sg
r
,
c
=
∏
c
′
∈
N
(
r
)
\
{
c
}
sgn
(
z
r
,
c
′
)
,
where (Z r,c′ ) indicates the column LLR;
sets a value, as a row LLR of the current iteration, obtained by multiplying between said minimum and the direct product when said minimum is less than a prescribed constant;
determines whether a result value of subtracting an offset value β from said minimum is greater than zero when said minimum is equal to or greater than the prescribed constant, the offset value β being changed in accordance with said minimum;
sets a value, as a row LLR of the current iteration, obtained by multiplying between the result value of the subtraction and the direct product when a result of the determination indicates affirmation; and
sets a value of zero as a row LLR of the current iteration when a result of the determination indicates negation.
6. The decoding device according to claim 5 , wherein the row calculating unit is configured to further perform processes of:
comparing a constant with a minimum of dyadic values which are a target for a dyadic operation executed in the row calculation using an algorithm based on the Sum-Product decoding method;
recognizing the minimum of the dyadic values as a result of the dyadic operation when said minimum of the dyadic values is less than the constant; and
recognizing, as a result of the dyadic operation, a result of subtracting an offset value D(δ) from the minimum of the dyadic values, the offset value D(δ) being acquired by the following equation:
D
(
δ
)
=
max
{
0.9
-
δ
2
,
0
}
,
where the value δ is a variable indicating a difference between the dyadic values.
7. The decoding device according to claim 5
wherein the offset value β is an offset value D(δ) acquired by the following equation:
D
(
δ
)
=
max
{
0.9
-
δ
2
,
0
}
,
where the value δ is a variable indicating a result value of subtracting the minimum of the absolute values of said column LLRs from a second minimum of the absolute values of said column LLRs.
8. The decoding device according to claim 5 , wherein the row calculating unit is configured to further perform processes of:
calculating a first value, a second value and a third value, where
the first value indicates the result value of subtracting the offset value β from the minimum of absolute values of the column LLRs,
the second value indicates a result value of subtracting the offset value β from a second minimum of absolute values of the column LLRs, and
the third value indicates a result value of subtracting an offset value D(δ) as the offset value β from the minimum of absolute values of the column LLRs, the offset value D(δ) being acquired by the following equation:
D
(
δ
)
=
max
{
0.9
-
δ
2
,
0
}
,
where the value δ is a variable indicating a result value of subtracting the minimum of absolute values of the column LLRs from the second minimum of absolute values of the column LLRs;
comparing the second value with zero in the determination with respect to the column c having the minimum of absolute values of the column LLRs;
comparing the first value with zero in the determination with respect to the column c having the second minimum of absolute values of the column LLRs; and
comparing the third value with zero in the determination with respect to the other column c.