Encoding method, decoding method

Abstract

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.

Claims

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: n1 information sequences denoted as X.sub.1 through X.sub.n1; and a parity sequence denoted as P, by encoding the n1 information sequences at a (n1)/n coding rate according to a predetermined parity check matrix having mz rows and nmz 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 n1 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 mz1, denoting an integer no less than one and no greater than mz, and i being a variable denoting an integer that is no less than zero and no greater than m1 and satisfies i=e % m where % denotes a modulo operator, when e1, an eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as $\begin{array}{cc}\left(D^{b1,i}+1\right)P\left(D\right)+\underset{k=1}{\overset{n-1}{.Math.}}\left\{\left(1+\underset{j=1}{\overset{\mathrm{rk},i}{.Math.}}{D}^{\mathrm{ak},i,j}\right)X_k\left(D\right)\right\}=0& \left(\mathrm{Math}.1\right)\end{array}$ where b.sub.1,i is a natural number, and when e=1, the eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as $\begin{array}{cc}P\left(D\right)+\underset{k=1}{\overset{n-1}{.Math.}}\left\{\left(1+\underset{j=1}{\overset{\mathrm{rk},i}{.Math.}}{D}^{\mathrm{ak},\left(-1\right)\%m,j}\right)X_k\left(D\right)\right\}=0& \left(\mathrm{Math}.2\right)\end{array}$ where, in Math. 1 and Math. 2, p denotes an integer no less than one and no greater than n1, q denotes an integer no less than one and no greater than r.sub.p,i, and r.sub.p,i denotes an integer no less than two, D denotes a delay operator, X.sub.p(D) denotes a polynomial representation of an information sequence X.sub.p among the n1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and a.sub.p,i,q denotes a natural number, when x and y are integers no less than one and no greater than r.sub.p,i and satisfy xy, a.sub.p,i,xa.sub.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=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 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: n1 information sequences denoted as X.sub.1 through X.sub.n1; and a parity sequence denoted as P, by encoding the n1 information sequences at a (n1)/n coding rate according to a predetermined parity check matrix having mz rows and nmz 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 n1 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 mz1, denoting an integer no less than one and no greater than mz, and i being a variable denoting an integer that is no less than zero and no greater than m1 and satisfies i=e % m where % denotes a modulo operator, when e1, an eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as $\begin{array}{cc}\left(D^{b1,i}+1\right)P\left(D\right)+\underset{k=1}{\overset{n-1}{.Math.}}\left\{\left(1+\underset{j=1}{\overset{\mathrm{rk},i}{.Math.}}{D}^{\mathrm{ak},i,j}\right)X_k\left(D\right)\right\}=0& \left(\mathrm{Math}.1\right)\end{array}$ where b.sub.1,i is a natural number, and when e=1, the eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as $\begin{array}{cc}P\left(D\right)+\underset{k=1}{\overset{n-1}{.Math.}}\left\{\left(1+\underset{j=1}{\overset{\mathrm{rk},i}{.Math.}}{D}^{\mathrm{ak},\left(-1\right)\%m,j}\right)X_k\left(D\right)\right\}=0& \left(\mathrm{Math}.2\right)\end{array}$ where, in Math. 1 and Math. 2, p denotes an integer no less than one and no greater than n1, q denotes an integer no less than one and no greater than r.sub.p,i, and r.sub.p,i denotes an integer no less than two, D denotes a delay operator, X.sub.p(D) denotes a polynomial representation of an information sequence X.sub.p among the n1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and a.sub.p,i,q denotes a natural number, when x and y are integers no less than one and no greater than r.sub.p,i and satisfy xy, a.sub.p,i,xa.sub.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=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 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: n1 information sequences denoted as X.sub.1 through X.sub.n1; and a parity sequence denoted as P, by encoding the n1 information sequences at a (n1)/n coding rate according to a predetermined parity check matrix having mz rows and nmz 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 n1 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 mz1, denoting an integer no less than one and no greater than mz, and i being a variable denoting an integer that is no less than zero and no greater than m1 and satisfies i=e % m where % denotes a modulo operator, when e1, an eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as $\begin{array}{cc}\left(D^{b1,i}+1\right)P\left(D\right)+\underset{k=1}{\overset{n-1}{.Math.}}\left\{\left(1+\underset{j=1}{\overset{\mathrm{rk},i}{.Math.}}{D}^{\mathrm{ak},i,j}\right)X_k\left(D\right)\right\}=0& \left(\mathrm{Math}.1\right)\end{array}$ where b.sub.1,i is a natural number, and when e=1, the eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as $\begin{array}{cc}P\left(D\right)+\underset{k=1}{\overset{n-1}{.Math.}}\left\{\left(1+\underset{j=1}{\overset{\mathrm{rk},i}{.Math.}}{D}^{\mathrm{ak},\left(-1\right)\%m,j}\right)X_k\left(D\right)\right\}=0& \left(\mathrm{Math}.2\right)\end{array}$ where, in Math. 1 and Math. 2, p denotes an integer no less than one and no greater than n1, q denotes an integer no less than one and no greater than r.sub.p,i, and r.sub.p,i denotes an integer no less than two, D denotes a delay operator, X.sub.p(D) denotes a polynomial representation of an information sequence X.sub.p among the n1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and a.sub.p,i,q denotes a natural number, when x and y are integers no less than one and no greater than r.sub.p,i and satisfy xy, a.sub.p,i,xa.sub.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=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 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: n1 information sequences denoted as X.sub.1 through X.sub.n1; and a parity sequence denoted as P, by encoding the n1 information sequences at a (n1)/n coding rate according to a predetermined parity check matrix having mz rows and nmz 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 n1 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 mz1, denoting an integer no less than one and no greater than mz, and i being a variable denoting an integer that is no less than zero and no greater than m1 and satisfies i=e % m where % denotes a modulo operator, when e1, an eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as $\begin{array}{cc}\left(D^{b1,i}+1\right)P\left(D\right)+\underset{k=1}{\overset{n-1}{.Math.}}\left\{\left(1+\underset{j=1}{\overset{\mathrm{rk},i}{.Math.}}{D}^{\mathrm{ak},i,j}\right)X_k\left(D\right)\right\}=0& \left(\mathrm{Math}.1\right)\end{array}$ where b.sub.1,i is a natural number, and when e=1, the eth parity check polynomial that satisfies zero, of the variable-length LDPC convolutional code, is expressed as $\begin{array}{cc}P\left(D\right)+\underset{k=1}{\overset{n-1}{.Math.}}\left\{\left(1+\underset{j=1}{\overset{\mathrm{rk},i}{.Math.}}{D}^{\mathrm{ak},\left(-1\right)\%m,j}\right)X_k\left(D\right)\right\}=0& \left(\mathrm{Math}.2\right)\end{array}$ where, in Math. 1 and Math. 2, p denotes an integer no less than one and no greater than n1, q denotes an integer no less than one and no greater than r.sub.p,i, and r.sub.p,i denotes an integer no less than two, D denotes a delay operator, X.sub.p(D) denotes a polynomial representation of an information sequence X.sub.p among the n1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and a.sub.p,i,q denotes a natural number, when x and y are integers no less than one and no greater than r.sub.p,i and satisfy xy, a.sub.p,i,xa.sub.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=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 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: n1 information sequences denoted as X.sub.1 through X.sub.n1; and a parity sequence denoted as P, by encoding the n1 information sequences at a (n1)/n coding rate according to a predetermined parity check matrix having mz rows and nmz 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 n1 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 mz1, denoting an integer no less than one and no greater than mz, and i being a variable denoting an integer that is no less than zero and no greater than m1 and satisfies i=e % m where % denotes a modulo operator, when e1, an eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressed as $\begin{array}{cc}\left(D^{b1,i}+1\right)P\left(D\right)+\underset{k=1}{\overset{n-1}{.Math.}}\left\{\left(1+\underset{j=1}{\overset{\mathrm{rk},i}{.Math.}}{D}^{\mathrm{ak},i,j}\right)X_k\left(D\right)\right\}=0& \left(\mathrm{Math}.1\right)\end{array}$ where b.sub.1,i is a natural number, and when e=1, the eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressed as $\begin{array}{cc}P\left(D\right)+\underset{k=1}{\overset{n-1}{.Math.}}\left\{\left(1+\underset{j=1}{\overset{\mathrm{rk},i}{.Math.}}{D}^{\mathrm{ak},\left(-1\right)\%m,j}\right)X_k\left(D\right)\right\}=0& \left(\mathrm{Math}.2\right)\end{array}$ where, in Math. 1 and Math. 2, p denotes an integer no less than one and no greater than n1, q denotes an integer no less than one and no greater than r.sub.p,i, and r.sub.p,i denotes an integer no less than two, D denotes a delay operator, X.sub.p(D) denotes a polynomial representation of an information sequence X.sub.p among the n1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and a.sub.p,i,q denotes a natural number, when x and y are integers no less than one and no greater than r.sub.p,i and satisfy xy, a.sub.p,i,xa.sub.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=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 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: n1 information sequences denoted as X.sub.1 through X.sub.n1; and a parity sequence denoted as P, by encoding the n1 information sequences at a (n1)/n coding rate according to a predetermined parity check matrix having mz rows and nmz 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 n1 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 mz1, denoting an integer no less than one and no greater than mz, and i being a variable denoting an integer that is no less than zero and no greater than m1 and satisfies i=e % m where % denotes a modulo operator, when e1, an eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressed as $\begin{array}{cc}\left(D^{b1,i}+1\right)P\left(D\right)+\underset{k=1}{\overset{n-1}{.Math.}}\left\{\left(1+\underset{j=1}{\overset{\mathrm{rk},i}{.Math.}}{D}^{\mathrm{ak},i,j}\right)X_k\left(D\right)\right\}=0& \left(\mathrm{Math}.1\right)\end{array}$ where b.sub.1,i is a natural number, and when e=1, the eth parity check polynomial that satisfies zero, of the LDPC convolutional code, is expressed as $\begin{array}{cc}P\left(D\right)+\underset{k=1}{\overset{n-1}{.Math.}}\left\{\left(1+\underset{j=1}{\overset{\mathrm{rk},i}{.Math.}}{D}^{\mathrm{ak},\left(-1\right)\%m,j}\right)X_k\left(D\right)\right\}=0& \left(\mathrm{Math}.2\right)\end{array}$ where, in Math. 1 and Math. 2, p denotes an integer no less than one and no greater than n1, q denotes an integer no less than one and no greater than r.sub.p,i, and r.sub.p,i denotes an integer no less than two, D denotes a delay operator, X.sub.p(D) denotes a polynomial representation of an information sequence X.sub.p among the n1 information sequences, and P(D) denotes a polynomial representation of the parity sequence P, and a.sub.p,i,q denotes a natural number, when x and y are integers no less than one and no greater than r.sub.p,i and satisfy xy, a.sub.p,i,xa.sub.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=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 1=0.

Description

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