Parity check matrix generation method, data transmission system, encoding device, decoding device, and a parity check matrix generation program

A parity check matrix generation method for generating a parity check matrix of m rows and n columns in a low-density parity-check code, wherein:

• row r of a parity check matrix is generated by using period list P={p(1), p(2), . . . , p(PL)} (where p(1)−p(PL) are relatively prime) to:
• set as “1” matrix elements that correspond to columns c that satisfy conditions, using integer i and prescribed value F(j), 1≦c≦n−m and c=p(j)·i+r+F(j) if N(j−1)+1≦r≦N(j), where N(j) is defined as a sum of values from element p(1) to element p(j) of said period list P, and moreover, N(0) is defined as “0”;
• to set as “1” matrix elements that correspond to columns c that satisfy a condition c=n−m+r;
• and to set as “0” matrix elements that do not satisfy any of said conditions.

A parity check matrix generation method for generating a parity check matrix of m rows and n columns in low-density parity-check codes;

• wherein:
• row r of a parity check matrix is generated by using period list P={p(1), p(2), . . . , p(PL)} (where p(1)−p(PL) are relatively prime) to:
• set as “1” matrix elements that correspond to columns c that satisfy conditions, using integer i, 1≦c≦n−m+r and c=p(j)·i+n−m+r if N(j−1)+1≦r≦N(j), where N(j) is defined as a sum of values from element p(1) to element p(j) of said period list P, and moreover, N(0) is defined as “0”;
• and to set as “0” matrix elements that do not satisfy any of said conditions.

A parity check matrix generation method for generating a parity check matrix of m rows and n columns in low-density parity-check codes;

• wherein:
• row r of a parity check matrix is generated by using period list P={p(1), p(2), . . . , p(PL)} (where p(1)−p(PL) are relatively prime) and period list Q={q(1), q(2), . . . , q(QL)} (where q(1)−q(QL) are relatively prime) to:
• set as “1” matrix elements that correspond to columns c that satisfy conditions, using integer i and a prescribed value F(j), 1≦c≦n−m and c=p(j)·i+r+F(j) if N(j−1)+1≦r≦N(j), where N(j) is defined as a sum of values from element p(1) to element p(j) of said period list P, and moreover, N(0) is defined as “0”;
• to set as “1” matrix elements that correspond to columns c that satisfy conditions, using integer i, n−m+1≦c≦n−m+r and c=q(j)·i+n−m+r if M(j−1)+1≦r≦M(j), where M(j) is defined as a sum of values from element q(1) to element q(j) of period list Q, and moreover, M(0) is defined as “0”;
• and to set as “0” matrix elements that do not satisfy any of said conditions.

A parity check matrix generation program for generating a parity check matrix of m rows and n columns in low-density parity-check code, said parity check matrix generation program causing a computer to execute processes of:

• generating row r of a parity check matrix by using period list P={p(1), p(2), . . . , p(PL)} (where p(1)−p(PL) are relatively prime) to:
• set as “1” matrix elements that correspond to columns c that satisfy conditions, using integer i and a prescribed value F(j), 1≦c≦n−m and c=p(j)·i+r+F(j) if N(j−1)+1≦r≦N(j), where N(j) is defined to be a sum of values from element p(1) to element p(j) of said period list P, and moreover, N(0) is defined to be “0”;
• to set as “1” matrix elements that correspond to columns c that satisfy a condition c=n−m+r;
• and to set as “0” matrix elements that do not satisfy any of said conditions.

A parity check matrix generation program for generating a parity check matrix of m rows and n columns in low-density parity-check code, said parity check matrix generation program causing a computer to execute a process of:

• generating row r of a parity check matrix by using period list P={p(1), p(2), . . . , p(PL)} (where p(1)−p(PL) are relatively prime) and period list Q={q(1), q(2), . . . , q(QL)} (where q(1)−q(QL) are relatively prime) to:
• set as “1” matrix elements that correspond to columns c that satisfy conditions, using integer i and a prescribed value F(j), 1≦c≦n−m and c=p(j)·i+r+F(j) if N(j−1)+1≦r≦N(j), where N(j) is defined as a sum of values from element p(1) to element p(j) of said period list P, and moreover, N(0) is defined as “0”;
• to set as “1” matrix elements that correspond to columns c that satisfy conditions, using integer i, n−m+1≦c≦n−m+r and c=q(j)·i+n−m+r if M(j−1)+1≦r≦M(j), where M(j) is defined as a sum of values from element q(1) to element q(j) of said period list Q, and moreover, M(0) is defined as “0”;
• and to set as “0” matrix elements that do not satisfy any of said conditions.