Decoding apparatus and decoding method

A method of decoding Reed-Muller code in which information data is encoded by using mask symbols and orthogonal codes, the information data including a first portion and a second portion, the method comprising:

• calculating a first exclusive OR of the Reed-Muller code and an exclusive ORed value of a candidate pattern of the mask symbols and the information data corresponding to the candidate pattern;
• calculating a checksum of the first exclusive OR and majority-judging the checksum to decode a part of the second portion of the information data corresponding to the orthogonal codes;
• calculating a second exclusive OR of the first exclusive OR and a product of the part of the second portion of the information data and the orthogonal codes and majority-judging the second exclusive OR to decode a remaining part of the second portion of the information data corresponding to the orthogonal codes;
• Reed-Muller encoding the decoded second portion of the information data and the first portion of the information data;
• and
• detecting the minimum of a Euclidean distance between the Reed-Muller encoded data and an input Reed-Muller code while a plurality of first exclusive ORs are calculated, whereby the first portion of the information data is decoded based on the mask symbols corresponding to the minimum of the Euclidean distance.

An apparatus for decoding Reed-Muller code in which information data is encoded by using mask symbols and orthogonal codes, the information data including a first portion and a second portion, the apparatus comprising:

• a first arithmetic operation unit configured to calculate an exclusive OR of the Reed-Muller code and an exclusive ORed value of a candidate pattern of the mask symbols and the information data corresponding to the candidate pattern;
• a decoder configured to calculate a checksum of the exclusive OR and majority-decide the checksum to decode a part of the second portion of the information data corresponding to the orthogonal codes;
• a second arithmetic operation unit configured to calculate a first accumulation result of each bit of a product of an output from the decoder and the orthogonal codes and a second accumulation result of each inverted bit of a product of the output from the decoder and the orthogonal codes and detect one of the first accumulation result and the second accumulation result which corresponds to a smaller Euclidean distance between the Reed-Muller code input to the first arithmetic operation unit and encoded data of decoded data;
• a minimum detector configured to detect the minimum of an output from the second arithmetic operation unit while a plurality of candidate patterns of the mask symbols are supplied to the first arithmetic operation unit,
• whereby the first portion of the information data is decoded based on the mask symbols corresponding to the minimum of the output from the second arithmetic operation unit.

A method of decoding Reed-Muller code in which information data is encoded by using mask symbols and orthogonal codes, the information data including a first portion and a second portion, the method comprising:

• calculating an exclusive OR of the Reed-Muller code and an exclusive ORed value of a candidate pattern of the mask symbols and the information data corresponding to the candidate pattern;
• calculating a checksum of the exclusive OR and majority-decide the checksum to decode a part of the second portion of the information data corresponding to the orthogonal codes;
• calculating a first accumulation result of each bit of a product of decoded data and the orthogonal codes and a second accumulation result of each inverted bit of a product of the decoded data and the orthogonal codes and detect one of the first accumulation result and the second accumulation result which corresponds to a smaller Euclidean distance between the input Reed-Muller code and encoded data of the decoded data;
• detecting the minimum of one of the first accumulation result and the second accumulation result which has a smaller Euclidean distance between the input Reed-Muller code and encoded data of the decoded data while calculating the exclusive OR of the Reed-Muller code and an exclusive ORed value of each of a plurality of candidate patterns of the mask symbols and the information data corresponding to the candidate pattern,
• whereby the first portion of the information data is decoded based on the mask symbols corresponding to the minimum of one of the first accumulation result and the second accumulation result which has a smaller Euclidean distance between the input Reed-Muller code and encoded data of the decoded data.

An apparatus for decoding Reed-Muller code in which information data is encoded by using mask symbols and orthogonal codes, the information data including a first portion and a second portion, the apparatus comprising:

• an arithmetic operation unit configured to calculate a first product of the Reed-Muller code and an exclusive ORed value of a candidate pattern of the mask symbols and the information data corresponding to the candidate pattern;
• a first decoder configured to calculate a checksum of the first product and majority-decide the checksum to decode a part of the second portion of the information data corresponding to the orthogonal codes;
• a second decoder configured to calculate a second product of the first product and a product of the part of the second portion of the information data and the orthogonal codes and majority-decides the second product to decode a remaining part of the second portion of the information data corresponding to the orthogonal codes;
• a Reed-Muller encoder configured to Reed-Muller encode the second portion of the information data output from the first decoder and the second decoder and the first portion of the information data;
• a maximum correlation detector configured to detect the maximum of a correlation between an output from the Reed-Muller encoder and the Reed-Muller code supplied to the arithmetic operation unit while a plurality of candidate patterns of the mask symbols are supplied to the arithmetic operation unit,
• whereby the first portion of the information data is decoded based on the mask symbols corresponding to the maximum of the correlation.

A method of decoding Reed-Muller code in which information data is encoded by using mask symbols and orthogonal codes, the information data including a first portion and a second portion, the method comprising:

• calculating a first product of the Reed-Muller code and an exclusive ORed value of a candidate pattern of the mask symbols and the information data corresponding to the candidate pattern;
• calculating a checksum of the first product and majority-decide the checksum to decode a part of the second portion of the information data corresponding to the orthogonal codes;
• calculating a second product of the first product and a product of the part of the second portion of the information data and the orthogonal codes and majority-decides the second product to decode a remaining part of the second portion of the information data corresponding to the orthogonal codes;
• Reed-Muller encoding the second portion of the information data and the first portion of the information data;
• detecting the maximum of a correlation between the Reed-Muller encoded data and an input Reed-Muller code while a plurality of first products are calculated, whereby the first portion of the information data is decoded based on the mask symbols corresponding to the maximum of the correlation.

An apparatus for decoding Reed-Muller code in which information data is encoded by using mask symbols and orthogonal codes, the information data including a first portion and a second portion, the apparatus comprising:

• a first arithmetic operation unit configured to calculate a first product of the Reed-Muller code and an exclusive ORed value of a candidate pattern of the mask symbols and the information data corresponding to the candidate pattern;
• a decoder configured to calculate a checksum of the first product and majority-decide the checksum to decode a part of the second portion of the information data corresponding to the orthogonal codes;
• a second arithmetic operation unit configured to calculate a first accumulation result of each bit of a product of an output from the decoder and the orthogonal codes and a second accumulation result of each inverted bit of a product of the output from the decoder and the orthogonal codes and detect a larger one of the first accumulation result and the second accumulation result;
• a maximum detector configured to detect the maximum of an output from the second arithmetic operation unit while a plurality of candidate patterns of the mask symbols are supplied to the first arithmetic operation unit,
• whereby the first portion of the information data is decoded based on the mask symbols corresponding to the maximum of the output from the second arithmetic operation unit.

A method of decoding Reed-Muller code in which information data is encoded by using mask symbols and orthogonal codes, the information data including a first portion and a second portion, the method comprising:

• calculating a first product of the Reed-Muller code and an exclusive ORed value of a candidate pattern of the mask symbols and the information data corresponding to the candidate pattern;
• calculating a checksum of the first product and majority-decide the checksum to decode a part of the second portion of the information data corresponding to the orthogonal codes;
• calculating a first accumulation result of each bit of a product of decoded data and the orthogonal codes and a second accumulation result of each inverted bit of a product of the decoded data and the orthogonal codes and detect a larger one of the first accumulation result and the second accumulation result;
• detecting the maximum of the first accumulation result and the second accumulation result while calculating the first product of the Reed-Muller code and an exclusive ORed value of each of a plurality of candidate patterns of the mask symbols and the information data corresponding to the candidate pattern,
• whereby the first portion of the information data is decoded based on the mask symbols corresponding to the maximum of the first accumulation result and the second accumulation result.