Method and device for error correction coding based on high-rate generalized concatenated codes

A decoding device, the decoding device comprising:

• a memory controller configured to perform decoding of a codeword matrix wherein:
• the codeword matrix is constructed from L inner nested binary extended Bose-Chaudhuri-Hocquenghem (BCH) codes and L outer codes;
• the extended BCH code in a lowest nesting-level of the inner nested BCH codes is a mere single parity-check (SPC) code;
• and
• the extended BCH code in at least one higher nesting-level of the inner nested BCH codes has an error correction capability and is a sub-code of the BCH code of the lowest nesting level;
• the decoding comprising:
• a first iteration corresponding to the lowest nesting level of the inner extended BCH codes of the codeword matrix and having the following processes:
• applying SPC-decoding to the lines of the second dimension of the codeword matrix with respect to the lowest nesting level of the inner nested extended BCH codes in which the lines of a second dimension of the codeword matrix are encoded in order to obtain an intermediate decoding data matrix of the first iteration and to determine erasure information characterizing lines of the second dimension of the codeword matrix in which an erasure has been detected based on the SPC-decoding;
• inferring the information bits contained in the lines of the second dimension of the intermediate decoding data matrix of the first iteration in order to retrieve code symbols of the outer codes in which the lines of a first dimension of the codeword matrix are encoded;
• applying outer decoding corresponding to the respective codes used for obtaining the original codeword matrix during encoding, to the retrieved code symbols in the lines of the first dimension of the intermediate decoding data matrix of the first iteration in order to obtain a partial decoding result matrix of the first iteration, wherein the erasure information is used during outer decoding to identify erroneous symbols in the intermediate decoding data matrix of the first iteration;
• re-encoding said partial decoding result matrix of the first iteration by applying SPC-encoding to the second dimension of this matrix to obtain are encoded matrix of the first iteration;
• and
• subtracting there-encoded matrix of the first iteration from the codeword matrix in order to obtain a start matrix for a subsequent further iteration;
• and
• for each of the further nesting levels of the inner extended BCH codes of the codeword matrix, a respective further iteration having the following processes:
• applying extended BCH-decoding to the lines of the second dimension of the start matrix of the present iteration with respect to the present nesting level of the inner nested extended BCH codes in which the lines of a second dimension of the start matrix of the present iteration are encoded in order to obtain an intermediate decoding data matrix of the present iteration;
• inferring the information bits contained in the lines of the second dimension of the intermediate decoding data matrix of the present iteration in order to retrieve code symbols of the outer RS codes in which the lines of a first dimension of the codeword matrix are encoded;
• applying outer RS-decoding corresponding to the respective outer RS codes used for obtaining the original codeword matrix during encoding, to the retrieved code symbols in the lines of the first dimension of the intermediate decoding data matrix of the present iteration in order to obtain a partial decoding result matrix of the present iteration;
• if the present iteration corresponds to the highest nesting level of the inner nested extended BCH codes in the codeword matrix, outputting the partial decoding result matrix of the present iteration as a data matrix resulting from the decoding, and
• otherwise, re-encoding the partial decoding result matrix of the present iteration by applying extended BCH-encoding corresponding to the present nesting level to the second dimension of this matrix to obtain are-encoded matrix of the present iteration, and subtracting the re-encoded matrix of the present iteration from the start matrix of the present iteration in order to obtain a start matrix for a subsequent further iteration.

A decoding system, the decoding system comprising:

• non-transitory computer readable medium storing instructions executable by a processor to decode a codeword matrix wherein:
• the codeword matrix is constructed from L inner nested binary extended Bose-Chaudhuri-Hocquenghem (BCH) codes and L outer codes;
• the extended BCH code in a lowest nesting-level of the inner nested BCH codes is a mere single parity-check (SPC) code;
• and the extended BCH code in at least one higher nesting-level of the inner nested BCH codes has an error correction capability and is a sub-code of the BCH code of the lowest nesting level;
• and wherein decoding the codeword matrix includes:
• a first iteration corresponding to the lowest nesting level of the inner extended BCH codes of the codeword matrix and having the following processes:
• applying SPC-decoding to the lines of the second dimension of the codeword matrix with respect to the lowest nesting level of the inner nested extended BCH codes in which the lines of a second dimension of the codeword matrix are encoded in order to obtain an intermediate decoding data matrix of the first iteration and to determine erasure information characterizing lines of the second dimension of the codeword matrix in which an erasure has been detected based on the SPC-decoding;
• inferring the information bits contained in the lines of the second dimension of the intermediate decoding data matrix of the first iteration in order to retrieve code symbols of the outer codes in which the lines of a first dimension of the codeword matrix are encoded;
• applying outer decoding corresponding to the respective codes used for obtaining the original codeword matrix during encoding, to the retrieved code symbols in the lines of the first dimension of the intermediate decoding data matrix of the first iteration in order to obtain a partial decoding result matrix of the first iteration, wherein the erasure information is used during outer decoding to identify erroneous symbols in the intermediate decoding data matrix of the first iteration;
• re-encoding said partial decoding result matrix of the first iteration by applying SPC-encoding to the second dimension of this matrix to obtain are encoded matrix of the first iteration;
• and
• subtracting there-encoded matrix of the first iteration from the codeword matrix in order to obtain a start matrix for a subsequent further iteration;
• and
• for each of the further nesting levels of the inner extended BCH codes of the codeword matrix, a respective further iteration having the following processes:
• applying extended BCH-decoding to the lines of the second dimension of the start matrix of the present iteration with respect to the present nesting level of the inner nested extended BCH codes in which the lines of a second dimension of the start matrix of the present iteration are encoded in order to obtain an intermediate decoding data matrix of the present iteration;
• inferring the information bits contained in the lines of the second dimension of the intermediate decoding data matrix of the present iteration in order to retrieve code symbols of the outer RS codes in which the lines of a first dimension of the codeword matrix are encoded;
• applying outer RS-decoding corresponding to the respective outer RS codes used for obtaining the original codeword matrix during encoding, to the retrieved code symbols in the lines of the first dimension of the intermediate decoding data matrix of the present iteration in order to obtain a partial decoding result matrix of the present iteration;
• if the present iteration corresponds to the highest nesting level of the inner nested extended BCH codes in the codeword matrix, outputting the partial decoding result matrix of the present iteration as a data matrix resulting from the decoding, and
• otherwise, re-encoding the partial decoding result matrix of the present iteration by applying extended BCH-encoding corresponding to the present nesting level to the second dimension of this matrix to obtain are-encoded matrix of the present iteration, and subtracting the re-encoded matrix of the present iteration from the start matrix of the present iteration in order to obtain a start matrix for a subsequent further iteration.