Turbo code designing method, turbo code designing apparatus, and recording medium stored with turbo code designing program

A turbo code designing apparatus configured to design a turbo encoding,

• wherein a turbo encoder configured to execute the turbo encoding comprises:
• a first convolutional encoder configured to generate a parity stream of input data by a predetermined RSC encoding as a first parity stream;
• an interleaver configured to swap an order of series inside the input data based on a first rule to generate swapped data;
• and
• a second convolutional encoder configured to generate a parity stream of the swapped data as a second parity stream by use of the RSC encoding,
• wherein the turbo code designing apparatus comprises:
• an RSC code selecting section configured to select a polynomial that indicates the RSC encoding among elements of a Galois field generated by a generator polynomial;
• a PM designing section configured to design a PM that indicates a correspondence of an order of inside series between the input data and the swapped data, based on a period of the RSC encoding;
• a coset designing section configured to design a second rule for generating a plurality of sets that are prime to each other as a plurality of cosets by splitting the input data, based on the period of the RSC encoding;
• and
• an outputting section configured to output information that indicates the designed turbo encoding outside,
• wherein the polynomial the indicates the RSC encoding includes a feedforward polynomial that indicates a feedforward connection and a feedback polynomial that indicates a feedback connection,
• wherein each of the feedforward polynomial and the feedback polynomial is a polynomial selected among the elements of the Galois field or a multiplied product of a plurality of polynomials selected among the elements of the Galois field, and
• wherein the period of the RSC encoding is a bit length of a circulating part when a predetermined bit and subsequent bits thereafter of an output data of the RSC encoding inputted with an input data of which a first bit is 1 and a second bit and subsequent bits thereafter are 0 circulates at a predetermined period,
• wherein the second convolutional encoder comprises:
• a plurality of delays connected in series;
• a first group of adders configured to connects feedforward an output of a part of the plurality of delays to an output of the second convolutional encoder;
• and
• a second group of adders configured to connect feedback an output of a part of the plurality of delays to an input of the second convolutional encoder,
• wherein the RSC code selecting section is further configured to:
• select a feedback polynomial g(x) that indicates a configuration of the feedback connection so that a hamming weight of a parity stream that the second convolutional encoder outputs is smaller than a predetermined first threshold value only when the swapped data inputted into the second convolutional encoder satisfies a predetermined condition;
• and
• select a feedforward polynomial f(x) that indicates a configuration of the feedforward connection, so that the hamming weight of the parity stream that the second convolutional encoder outputs is larger than a predetermined second threshold value only when the swapped data inputted into the second convolutional encoder satisfies the predetermined condition,
• wherein the predetermined condition includes:
• the swapped data is a value in which a distance between digits of which a value is equal to 1 in a binary notation of the swapped data is an integer multiple of a period of the RSC encoding, or, a sum of a plurality of values in each of which a distance between digits of which a value is equal to 1 in the binary notation of the swapped data is an integer multiple of the period of the RSC encoding;
• and
• the feedback polynomial g(x) is divisible by a predetermined generator polynomial, and no combination of at least three polynomials that are different from each other and of which a sum is zero exists in elements of the Galois field generated by the predetermined generator polynomial.

A recording medium stored with a turbo code designing program that realizes, by making a processor execute, a process for designing a turbo encoding,

• wherein a turbo encoder configured to execute the turbo encoding comprises:
• a first convolutional encoder configured to generate a parity stream of input data as a first parity stream by use of a predetermined RSC encoding;
• an interleaver configured to swap an order of series inside the input data based on a first rule to generate swapped data;
• and
• a second convolutional encoder configured to generate a parity stream of the swapped data as a second parity stream by use of the RSC encoding,
• the process includes:
• selecting a polynomial that indicates the RSC encoding among elements of a Galois field generated by a generator polynomial;
• designing the first rule of the interleaver based on the RSC encoding;
• and
• outputting information that indicates the designed turbo encoding outside,
• wherein the polynomial that indicates the RSC encoding includes a feedforward polynomial that indicates a feedforward connection and a feedback polynomial that indicates a feedback connection, and
• wherein each of the feedforward polynomial and the feedback polynomial is a polynomial selected among the elements of the Galois field or a multiplied product of a plurality of polynomials selected among the elements of the Galois field,
• wherein the second convolutional encoder comprises:
• a plurality of delays connected in series;
• a first group of adders configured to connects feedforward an output of a part of the plurality of delays to an output of the second convolutional encoder;
• and
• a second group of adders configured to connect feedback an output of a part of the plurality of delays to an input of the second convolutional encoder,
• wherein the selecting the polynomial that indicates the RSC encoding includes:
• selecting a feedback polynomial g(x) that indicates a configuration of the feedback connection so that a hamming weight of a parity stream that the second convolutional encoder outputs is smaller than a predetermined first threshold value only when the swapped data inputted into the second convolutional encoder satisfies a predetermined condition;
• and
• selecting a feedforward polynomial f(x) that indicates a configuration of the feedforward connection, so that the hamming weight of the parity stream that the second convolutional encoder outputs is larger than a predetermined second threshold value only when the swapped data inputted into the second convolutional encoder satisfies the predetermined condition,
• wherein the predetermined condition includes:
• the swapped data is a value in which a distance between digits of which a value is equal to 1 in a binary notation of the swapped data is an integer multiple of a period of the RSC encoding, or, a sum of a plurality of values in each of which a distance between digits of which a value is equal to 1 in the binary notation of the swapped data is an integer multiple of the period of the RSC encoding;
• and
• the feedback polynomial g(x) is divisible by a predetermined generator polynomial, and no combination of at least three polynomials that are different from each other and of which a sum is zero exists in elements of the Galois field generated by the predetermined generator polynomial.