Patent FR-2847398-A1 (FR)
Title: Two-fold sequi-RS codes and their decoding, comprise more adjustable parameters than the Miura codes, larger minimum distance and decoding with erasings
Inventor: PIRET PHILIPPE
IPC: H03M13/15
Filed: 2002-11-18
Abstract: The proposed codes are relatively easy to decode and have the minimum distance (d) larger than that of the Miura codes of the same length (n) and the same dimensions (k). A product code wherein the component code of row and/or the component code of column is of the proposed type can be decoded. The decoding method with erasings applicable to the proposed codes can also be applied to the Miura codes and to the maximal hyperelliptic codes.  The coding method (claimed) comprises a step of computing the symbols forming the words of length n=2q, or of length n=2(q-1), on the basis of information symbols belonging to a body of Galois (Fq) of primitive element (gamma), and the code is associated with a parity matrix (H) and a channel coding of non-hyperelliptic type. In particular, the couples (X,Y) have the values which are determined by the solution of a hyperelliptic equation. The parity matrix is obtained by removing certain columns from the original parity matrix of the channel code. The product code contains the component code of row and/or the component code of column which is the channel code. The decoding method (claimed) for a channel code defined on a body of Galois (Fq) of primitive element (gamma) and the length n=2(q-1) associated with the parity matrix H, comprises the construction of a word length (q-1) on the basis of a received word where the word components carry an erasing if at least one of the original components carries an erasing, and implementing an algorithm for correcting the constructed word in order to obtain a word making part of the code defined by the parity matrix (H). A word which is an estimate of the code word is obtained by solving a system of equations. A device (claimed) for error correction in decoding a channel code defined on a body of Galois (Fq) of primitive element (gamma) and the length n=2(q-1), implements the method. A device (claimed) for error correction in decoding a product code comprises the device applicable to the row code and/or the column code. The device for error correction comprises means for provisionally attributing an erasing to all elements of such row or column if the tentative correction of the row or column fails. A decoder (claimed) comprises at least one device for error correction, and at least one unit for the redundancy suppression. An apparatus (claimed) for receiving coded digital data comprises the decoder and also means for demodulating the coded digital data. An information system (claimed) comprises the decoder, also a hard disc and means for reading the disc. The data storage means (claimed) which are nonremovable comprise the instructions for the program code for executing the steps of the decoding method. The data storage means (claimed) which are partially or totally removable comprise the instructions of the program code. A computer program (claimed) contains the instructions which make the data processing device implement the decoding method.