Encoding method, encoding apparatus, and program

An encoding apparatus for encoding by use of a quasi-cyclic code having a code length of n=m n0 and an information word length of k=m k0, said encoding apparatus comprising:

• a section configured to create a systematic code with as many as (n0−k0) parity bits inserted therein in units of an information word k0;
• a section configured to make all combinations of (n0−k0) parity bit positions that may occur in units of n0 bits out of said systematic code;
• a section configured to describe a plurality of m×m cyclic matrices by rearranging the sequence of columns in a parity check matrix in all the combinations of the parity bit positions;
• a section configured to subject said parity check matrix to elementary transformation in such a manner that (n−k)×(n−k) matrices made up of the columns corresponding to the parity bit positions are created as a unit matrix;
• a section configured to regard the matrix having undergone elementary transformation as a first matrix and said first matrix minus said unit matrix as a second matrix;
• and
• a section configured to allocate (n−k) bit positions for the parity bits in such a manner that the number of non-zero elements included in said second matrix is minimized.

A program devised as a computer-readable program for controlling encoding by use of a quasi-cyclic code having a code length of n=m n0 and an information word length of k=m k0, said program causing a computer to execute a procedure comprising the steps of:

• creating a systematic code with as many as (n0−k0) parity bits inserted therein in units of an information word k0;
• making all combinations of (n0−k0) parity bit positions that may occur in units of n0 bits out of said systematic code;
• describing a plurality of m×m cyclic matrices by rearranging the sequence of columns in a parity check matrix in all the combinations of the parity bit positions;
• subjecting said parity check matrix to elementary transformation in such a manner that (n−k)×(n−k) matrices made up of the columns corresponding to the parity bit positions are created as a unit matrix;
• regarding the matrix having undergone elementary transformation as a first matrix and said first matrix minus said unit matrix as a second matrix;
• and
• allocating (n−k) bit positions for the parity bits in such a manner that the number of non-zero elements included in said second matrix is minimized.

An encoding method for encoding by use of a quasi-cyclic code having a code length of n=m n0 and an information word length of k=m k0, said encoding method comprising:

• creating a systematic code with as many as (n0−k0) parity bits inserted therein in units of an information word k0;
• making all combinations of (n0−k0) parity bit positions that may occur in units of n0 bits out of said systematic code;
• describing a plurality of m×m cyclic matrices by rearranging the sequence of columns in a parity check matrix in all the combinations of the parity bit positions;
• subjecting said parity check matrix to elementary transformation in such a manner that (n−k)×(n−k) matrices made up of the columns corresponding to the parity bit positions are created as a unit matrix;
• regarding the matrix having undergone elementary transformation as a first matrix and said first matrix minus said unit matrix as a second matrix;
• and
• allocating (n−k) bit positions for the parity bits in such a manner that the maximum number of non-zero elements included in each row of said second matrix is minimized.

An encoding apparatus for encoding by use of a quasi-cyclic code having a code length of n=m n0 and an information word length of k=m k0, said encoding apparatus comprising:

• a section configured to create a systematic code with as many as (n0−k0) parity bits inserted therein in units of an information word k0;
• a section configured to make all combinations of (n0−k0) parity bit positions that may occur in units of n0 bits out of said systematic code;
• a section configured to describe a plurality of m×m cyclic matrices by rearranging the sequence of columns in a parity check matrix in all the combinations of the parity bit positions;
• a section configured to subject said parity check matrix to elementary transformation in such a manner that (n−k)×(n−k) matrices made up of the columns corresponding to the parity bit positions are created as a unit matrix;
• a section configured to regard the matrix having undergone elementary transformation as a first matrix and said first matrix minus said unit matrix as a second matrix;
• and
• a section configured to allocate (n−k) bit positions for the parity bits in such a manner that the maximum number of non-zero elements included in each row of said second matrix is minimized.

A program devised as a computer-readable program for controlling encoding by use of a quasi-cyclic code having a code length of n=m n0 and an information word length of k=m k0, said program causing a computer to execute a procedure comprising:

• creating a systematic code with as many as (n0−k0) parity bits inserted therein in units of an information word k0;
• making all combinations of (n0−k0) parity bit positions that may occur in units of n0 bits out of said systematic code;
• describing a plurality of m×m cyclic matrices by rearranging the sequence of columns in a parity check matrix in all the combinations of the parity bit positions;
• subjecting said parity check matrix to elementary transformation in such a manner that (n−k)×(n−k) matrices made up of the columns corresponding to the parity bit positions are created as a unit matrix;
• regarding the matrix having undergone elementary transformation as a first matrix and said first matrix minus said unit matrix as a second matrix;
• and
• allocating (n−k) bit positions for the parity bits in such a manner that the maximum number of non-zero elements included in each row of said second matrix is minimized.

An encoding method for encoding by use of a quasi-cyclic code having a code length of n=m n0 and an information word length of k=m k0, said encoding method comprising:

• creating a systematic code with as many as (n0−k0) parity bits inserted therein in units of an information word k0;
• making all combinations of (n0−k0) parity bit positions that may occur in units of n0 bits out of said systematic code;
• describing a plurality of m×m cyclic matrices by rearranging the sequence of columns in a parity check matrix in all the combinations of the parity bit positions;
• subjecting said parity check matrix to elementary transformation in such a manner that (n−k)×(n−k) matrices made up of the columns corresponding to the parity bit positions are created as a unit matrix;
• regarding the matrix having undergone elementary transformation as a first matrix and said first matrix minus said unit matrix as a second matrix;
• and
• allocating (n−k) bit positions for the parity bits in such a manner that the maximum number of non-zero elements among the k0 elements arrayed in units of m columns per row of said second matrix is minimized.

An encoding apparatus for encoding by use of a quasi-cyclic code having a code length of n=m n0 and an information word length of k=m k0, said encoding apparatus comprising:

• a section configured to create a systematic code with as many as (n0−k0) parity bits inserted therein in units of an information word k0;
• a section configured to make all combinations of (n0−k0) parity bit positions that may occur in units of n0 bits out of said systematic code;
• a section configured to describe a plurality of m×m cyclic matrices by rearranging the sequence of columns in a parity check matrix in all the combinations of the parity bit positions;
• a section configured to subject said parity check matrix to elementary transformation in such a manner that (n−k)×(n−k) matrices made up of the columns corresponding to the parity bit positions are created as a unit matrix;
• a section configured to regard the matrix having undergone elementary transformation as a first matrix and said first matrix minus said unit matrix as a second matrix;
• and
• a section configured to allocate (n−k) bit positions for the parity bits in such a manner that the maximum number of non-zero elements among the k0 elements arrayed in units of m columns per row of said second matrix is minimized.

A program devised as a computer-readable program for controlling encoding by use of a quasi-cyclic code having a code length of n=m n0 and an information word length of k=m k0, said program causing a computer to execute a procedure comprising the steps of:

• creating a systematic code with as many as (n0−k0) parity bits inserted therein in units of an information word k0;
• making all combinations of (n0−k0) parity bit positions that may occur in units of n0 bits out of said systematic code;
• describing a plurality of m×m cyclic matrices by rearranging the sequence of columns in a parity check matrix in all the combinations of the parity bit positions;
• subjecting said parity check matrix to elementary transformation in such a manner that (n−k)×(n−k) matrices made up of the columns corresponding to the parity bit positions are created as a unit matrix;
• regarding the matrix having undergone elementary transformation as a first matrix and said first matrix minus said unit matrix as a second matrix;
• and
• allocating (n−k) bit positions for the parity bits in such a manner that the maximum number of non-zero elements among the k0 elements arrayed in units of m columns per row of said second matrix is minimized.