Encoding method, decoding method
An encoding method generates an encoded sequence by performing encoding of a given coding rate according to a predetermined parity check matrix. The predetermined parity check matrix is a first parity check matrix or a second parity check matrix. The first parity check matrix corresponds to a low-density parity check (LDPC) convolutional code using a plurality of parity check polynomials. The second parity check matrix is generated by performing at least one of row permutation and column permutation with respect to the first parity check matrix. An eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressible by using a predetermined mathematical formula.
1. A transmission method for a wireless network system in which information is transmitted in variable-length packets or variable-length frames, the transmission method comprising
generating an encoded sequence of variable length, the encoded sequence comprising: n−1 information sequences denoted as X 1 through X n−1 ; and a parity sequence denoted as P, by encoding the n−1 information sequences at a (n−1)/n coding rate according to a predetermined parity check matrix having m×z rows and n×m×z columns, n being an integer no less than two, m being an integer no less than two, and z being a natural number; and
modulating the encoded sequence to generate a modulated signal, and transmitting the modulated signal, wherein
the generating the encoded sequence is performed by an encoding device including a shift register in which data of the n−1 information sequences is inputted, the parity sequence being calculated using values held in the shift register and the predetermined parity check matrix,
the predetermined parity check matrix is a first parity check matrix or a second parity check matrix, the first parity check matrix corresponding to a low-density parity check (LDPC) convolutional code using a plurality of parity check polynomials, the second parity check matrix generated by performing at least one of row permutation and column permutation with respect to the first parity check matrix, and
given e denoting an integer no less than zero and no greater than m×z−1, α denoting an integer no less than one and no greater than m×z, and i being a variable denoting an integer that is no less than zero and no greater than m−1 and satisfies i=e % m where % denotes a modulo operator,
when e≠α−1, an eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as
(
D
b
1
,
i
+
1
)
P
(
D
)
+
∑
k
=
1
n
-
1
{
(
1
+
∑
j
=
1
rk
,
i
D
ak
,
i
,
j
)
X
k
(
D
)
}
=
0
(
Math
.
1
)
where b 1,i is a natural number, and
when e=α−1, the eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as
P
(
D
)
+
∑
k
=
1
n
-
1
{
(
1
+
∑
j
=
1
rk
,
i
D
ak
,
(
α
-
1
)
%
m
,
j
)
X
k
(
D
)
}
=
0
(
Math
.
2
)
where, in Math. 1 and Math. 2,
p denotes an integer no less than one and no greater than n−1, q denotes an integer no less than one and no greater than r p,i , and r p,i denotes an integer no less than two,
D denotes a delay operator, X p (D) denotes a polynomial representation of an information sequence X p among the n−1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and
a p,i,q denotes a natural number,
when x and y are integers no less than one and no greater than r p,i and satisfy x≠y, a p,i,x ≠a p,i,y holds true for all x and y, thereby short loops in a Tanner graph of the predetermined parity-check matrix are suppressed,
when e=α−1, the eth parity check polynomial only contains one parity bit which can be uniquely determined based on a value of a bit of a known information sequence, thereby allowing sequential determination of bits of the parity sequence, and
α−1=0.
2. A reception method for a wireless network system in which information is transmitted in variable-length packets or variable-length frames, the reception method comprising:
receiving a modulated signal, and demodulating the modulated signal to obtain an encoded sequence of variable length, the encoded sequence being encoded according to a predetermined transmission method, wherein the predetermined transmission method comprises:
generating an encoded sequence comprising: n−1 information sequences denoted as X 1 through X n−1 ; and a parity sequence denoted as P, by encoding the n−1 information sequences at a (n−1)/n coding rate according to a predetermined parity check matrix having m×z rows and n×m×z columns, n being an integer no less than two, m being an integer no less than two, and z being a natural number; and
modulating the encoded sequence to generate a modulated signal, and transmitting the modulated signal,
the reception method further comprises decoding the encoded sequence according to the predetermined parity check matrix by employing belief propagation (BP), wherein
the generating the encoded sequence is performed by an encoder included in a transmission device, the encoder including a shift register in which data of the n−1 information sequences is inputted, the parity sequence being calculated using values held in the shift register and the predetermined parity check matrix,
the predetermined parity check matrix is a first parity check matrix or a second parity check matrix, the first parity check matrix corresponding to a low-density parity check (LDPC) convolutional code using a plurality of parity check polynomials, the second parity check matrix generated by performing at least one of row permutation and column permutation with respect to the first parity check matrix, and
given e denoting an integer no less than zero and no greater than m×z−1, α denoting an integer no less than one and no greater than m×z, and i being a variable denoting an integer that is no less than zero and no greater than m−1 and satisfies i=e % m where % denotes a modulo operator,
when e≠α−1, an eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as
(
D
b
1
,
i
+
1
)
P
(
D
)
+
∑
k
=
1
n
-
1
{
(
1
+
∑
j
=
1
rk
,
i
D
ak
,
i
,
j
)
X
k
(
D
)
}
=
0
(
Math
.
1
)
where b 1,i is a natural number, and
when e=α−1, the eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as
P
(
D
)
+
∑
k
=
1
n
-
1
{
(
1
+
∑
j
=
1
rk
,
i
D
ak
,
(
α
-
1
)
%
m
,
j
)
X
k
(
D
)
}
=
0
(
Math
.
2
)
where, in Math. 1 and Math. 2,
p denotes an integer no less than one and no greater than n−1, q denotes an integer no less than one and no greater than r p,i , and r p,i denotes an integer no less than two,
D denotes a delay operator, X p (D) denotes a polynomial representation of an information sequence X p among the n−1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and
a p,i,q denotes a natural number,
when x and y are integers no less than one and no greater than r p,i and satisfy x≠y, a p,i,x ≠a p,i,y holds true for all x and y, thereby short loops in a Tanner graph of the predetermined parity-check matrix are suppressed,
when e=α−1, the eth parity check polynomial only contains one parity bit which can be uniquely determined based on a value of a bit of a known information sequence, thereby allowing sequential determination of bits of the parity sequence, and
α−1=0.
3. A transmission device for a wireless network system in which information is transmitted in variable-length packets or variable-length frames, the transmission device comprising:
an encoder generating an encoded sequence of variable length, the encoded sequence comprising: n−1 information sequences denoted as X 1 through X n−1 ; and a parity sequence denoted as P, by encoding the n−1 information sequences at a (n−1)/n coding rate according to a predetermined parity check matrix having m×z rows and n×m×z columns, n being an integer no less than two, m being an integer no less than two, and z being a natural number;
a modulator modulating the encoded sequence to generate a modulated signal; and
a transmitter transmitting the modulated signal, wherein
the encoder includes a shift register in which data of the n−1 information sequences is inputted, the parity sequence being calculated using values held in the shift register and the predetermined parity check matrix,
the predetermined parity check matrix is a first parity check matrix or a second parity check matrix, the first parity check matrix corresponding to a low-density parity check (LDPC) convolutional code using a plurality of parity check polynomials, the second parity check matrix generated by performing at least one of row permutation and column permutation with respect to the first parity check matrix, and
given e denoting an integer no less than zero and no greater than m×z−1, α denoting an integer no less than one and no greater than m×z, and i being a variable denoting an integer that is no less than zero and no greater than m−1 and satisfies i=e % m where % denotes a modulo operator,
when e≠α−1, an eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as
(
D
b
1
,
i
+
1
)
P
(
D
)
+
∑
k
=
1
n
-
1
{
(
1
+
∑
j
=
1
rk
,
i
D
ak
,
i
,
j
)
X
k
(
D
)
}
=
0
(
Math
.
1
)
where b 1,i is a natural number, and
when e=α−1, the eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as
P
(
D
)
+
∑
k
=
1
n
-
1
{
(
1
+
∑
j
=
1
rk
,
i
D
ak
,
(
α
-
1
)
%
m
,
j
)
X
k
(
D
)
}
=
0
(
Math
.
2
)
where, in Math. 1 and Math. 2,
p denotes an integer no less than one and no greater than n−1, q denotes an integer no less than one and no greater than r p,i , and r p,i denotes an integer no less than two,
D denotes a delay operator, X p (D) denotes a polynomial representation of an information sequence X p among the n−1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and
a p,i,q denotes a natural number,
when x and y are integers no less than one and no greater than r p,i and satisfy x≠y, a p,i,x ≠a p,i,y holds true for all x and y, thereby short loops in a Tanner graph of the predetermined parity-check matrix are suppressed,
when e=α−1, the eth parity check polynomial only contains one parity bit which can be uniquely determined based on a value of a bit of a known information sequence, thereby allowing sequential determination of bits of the parity sequence, and
α−1=0.
4. A reception device for a wireless network system in which information is transmitted in variable-length packets or variable-length frames, the transmission method comprising:
a receiver that receives a modulated signal;
a demodulator that demodulates the modulated signal to obtain an encoded sequence of variable length; and
a decoder that decodes the encoded sequence, the encoded sequence being encoded according to a predetermined transmission method, the predetermined transmission method comprising:
generating the encoded sequence comprising: n−1 information sequences denoted as X 1 through X n−1 ; and a parity sequence denoted as P, by encoding the n−1 information sequences at a (n−1)/n coding rate according to a predetermined parity check matrix having m×z rows and n×m×z columns, n being an integer no less than two, m being an integer no less than two, and z being a natural number; and
modulating the encoded sequence to generate a modulated signal, and transmitting the modulated signal,
the decoder decoding the encoded sequence according to the predetermined parity check matrix by employing belief propagation (BP), wherein
the generating the encoded sequence is performed by an encoder included in a transmission device, the encoder including a shift register in which data of the n−1 information sequences is inputted, the parity sequence being calculated using values held in the shift register and the predetermined parity check matrix,
the predetermined parity check matrix is a first parity check matrix or a second parity check matrix, the first parity check matrix corresponding to a variable-length low-density parity check (LDPC) convolutional code using a plurality of parity check polynomials, the second parity check matrix generated by performing at least one of row permutation and column permutation with respect to the first parity check matrix, and
given e denoting an integer no less than zero and no greater than m×z−1, α denoting an integer no less than one and no greater than m×z, and i being a variable denoting an integer that is no less than zero and no greater than m−1 and satisfies i=e % m where % denotes a modulo operator,
when e≠α−1, an eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as
(
D
b
1
,
i
+
1
)
P
(
D
)
+
∑
k
=
1
n
-
1
{
(
1
+
∑
j
=
1
rk
,
i
D
ak
,
i
,
j
)
X
k
(
D
)
}
=
0
(
Math
.
1
)
where b 1,i is a natural number, and
when e=α−1, the eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as
P
(
D
)
+
∑
k
=
1
n
-
1
{
(
1
+
∑
j
=
1
rk
,
i
D
ak
,
(
α
-
1
)
%
m
,
j
)
X
k
(
D
)
}
=
0
(
Math
.
2
)
where, in Math. 1 and Math. 2,
p denotes an integer no less than one and no greater than n−1, q denotes an integer no less than one and no greater than r p,i , and r p,i denotes an integer no less than two,
D denotes a delay operator, X p (D) denotes a polynomial representation of an information sequence X p among the n−1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and
a p,i,q denotes a natural number,
when x and y are integers no less than one and no greater than r p,i and satisfy x≠y, a p,i,x ≠a p,i,y holds true for all x and y, thereby short loops in a Tanner graph of the predetermined parity-check matrix are suppressed,
when e=α−1, the eth parity check polynomial only contains one parity bit which can be uniquely determined based on a value of a bit of a known information sequence, thereby allowing sequential determination of bits of the parity sequence, and
α−1=0.
5. A non-transitory computer-readable storage medium having stored thereon a program, the program to be executed by a computer to cause the computer to perform a predetermined transmission process for a wireless network system in which information is transmitted in variable-length packets or variable-length frames, the predetermined transmission process comprising:
generating an encoded sequence of variable length, the encoded sequence comprising: n−1 information sequences denoted as X 1 through X n−1 ; and a parity sequence denoted as P, by encoding the n−1 information sequences at a (n−1)/n coding rate according to a predetermined parity check matrix having m×z rows and n×m×z columns, n being an integer no less than two, m being an integer no less than two, and z being a natural number; and
modulating the encoded sequence to generate a modulated signal, and transmitting the modulated signal, wherein
the computer includes a shift register in which data of the n−1 information sequences is inputted, the parity sequence being calculated using values held in the shift register and the predetermined parity check matrix,
the predetermined parity check matrix is a first parity check matrix or a second parity check matrix, the first parity check matrix corresponding to a low-density parity check (LDPC) convolutional code using a plurality of parity check polynomials, the second parity check matrix generated by performing at least one of row permutation and column permutation with respect to the first parity check matrix, and
given e denoting an integer no less than zero and no greater than m×z−1, α denoting an integer no less than one and no greater than m×z, and i being a variable denoting an integer that is no less than zero and no greater than m−1 and satisfies i=e % m where % denotes a modulo operator,
when e≠α−1, an eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressed as
(
D
b
1
,
i
+
1
)
P
(
D
)
+
∑
k
=
1
n
-
1
{
(
1
+
∑
j
=
1
rk
,
i
D
ak
,
i
,
j
)
X
k
(
D
)
}
=
0
(
Math
.
1
)
where b 1,i is a natural number, and
when e=α−1, the eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressed as
P
(
D
)
+
∑
k
=
1
n
-
1
{
(
1
+
∑
j
=
1
rk
,
i
D
ak
,
(
α
-
1
)
%
m
,
j
)
X
k
(
D
)
}
=
0
(
Math
.
2
)
where, in Math. 1 and Math. 2,
p denotes an integer no less than one and no greater than n−1, q denotes an integer no less than one and no greater than r p,i , and r p,i denotes an integer no less than two,
D denotes a delay operator, X p (D) denotes a polynomial representation of an information sequence X p among the n−1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and
a p,i,q denotes a natural number,
when x and y are integers no less than one and no greater than r p,i and satisfy x≠y, a p,i,x ≠a p,i,y holds true for all x and y, thereby short loops in a Tanner graph of the predetermined parity-check matrix are suppressed,
when e=α−1, the eth parity check polynomial only contains one parity bit which can be uniquely determined based on a value of a bit of a known information sequence, thereby allowing sequential determination of bits of the parity sequence, and
α−1=0.
6. A non-transitory computer-readable storage medium having stored thereon a program, the program to be executed by a computer to cause the computer to perform a reception process for a wireless network system in which information is transmitted in variable-length packets or variable-length frames, the reception process comprising:
receiving a modulated signal, and demodulating the modulated signal to obtain an encoded sequence of variable length, the encoded sequence being encoded according to a predetermined transmission method, wherein
the predetermined transmission method comprises:
generating the encoded sequence comprising: n−1 information sequences denoted as X 1 through X n−1 ; and a parity sequence denoted as P, by encoding the n−1 information sequences at a (n−1)/n coding rate according to a predetermined parity check matrix having m×z rows and n×m×z columns, n being an integer no less than two, m being an integer no less than two, and z being a natural number; and
modulating the encoded sequence to generate a modulated signal, and transmitting the modulated signal,
the generating the encoded sequence is performed by an encoder included in a transmission device, the encoder including a shift register in which data of the n−1 information sequences is inputted, the parity sequence being calculated using values held in the shift register and the predetermined parity check matrix,
the reception process further comprises decoding the encoded sequence according to the predetermined parity check matrix by employing belief propagation (BP),
the predetermined parity check matrix is a first parity check matrix or a second parity check matrix, the first parity check matrix corresponding to a low-density parity check (LDPC) convolutional code using a plurality of parity check polynomials, the second parity check matrix generated by performing at least one of row permutation and column permutation with respect to the first parity check matrix, and
given e denoting an integer no less than zero and no greater than m×z−1, α denoting an integer no less than one and no greater than m×z, and i being a variable denoting an integer that is no less than zero and no greater than m−1 and satisfies i=e % m where % denotes a modulo operator,
when e≠α−1, an eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressed as
(
D
b
1
,
i
+
1
)
P
(
D
)
+
∑
k
=
1
n
-
1
{
(
1
+
∑
j
=
1
rk
,
i
D
ak
,
i
,
j
)
X
k
(
D
)
}
=
0
(
Math
.
1
)
where b 1,i is a natural number, and
when e=α−1, the eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressed as
P
(
D
)
+
∑
k
=
1
n
-
1
{
(
1
+
∑
j
=
1
rk
,
i
D
ak
,
(
α
-
1
)
%
m
,
j
)
X
k
(
D
)
}
=
0
(
Math
.
2
)
where, in Math. 1 and Math. 2,
p denotes an integer no less than one and no greater than n−1, q denotes an integer no less than one and no greater than r p,i , and r p,i denotes an integer no less than two,
D denotes a delay operator, X p (D) denotes a polynomial representation of an information sequence X p among the n−1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and
a p,i,q denotes a natural number,
when x and y are integers no less than one and no greater than r p,i and satisfy x≠y, a p,i,x ≠a p,i,y holds true for all x and y, thereby short loops in a Tanner graph of the predetermined parity-check matrix are suppressed,
when e=α−1, the eth parity check polynomial only contains one parity bit which can be uniquely determined based on a value of a bit of a known information sequence, thereby allowing sequential determination of bits of the parity sequence, and
α−1=0.