Abstract: Erroneous column(s) in the matrix of data obtained from a transmission channel are first determined on the basis of column parity violation. An error instance in the matrix is next ascertained by matching the erroneous column(s) with an error event characteristic of the transmission channel. A candidate error row is then located in the matrix with respect to the error instance. Lastly, positions in the matrix specified by an intersection of the candidate error row and the erroneous column(s) of the error instance are corrected. Data reliability values assigned to positions of the matrix are used to determine the candidate error row. In particular, with respect to the erroneous column(s) of the error instance, and for each of plural rows of the matrix, factors (e.g., squares) of the reliability values assigned to positions of the matrix are summed to determine a least reliable row as the candidate error row.

Abstract: In an encoding method which utilizes plural codebooks, certain bits of a user data input sequence are considered as branch selection bit(s) which determine (1) how the remainder of the input sequence is to be divided into plural subsequences and (2) which codebooks are addressed using the plural subsequences in order to generate corresponding plural output sequences. The plural output sequences are then concatentated together to form a codeword. The method reduces the size of the codebooks that otherwise would be employed for the particular code involved in the encoding method. The encoding of the present invention is particularly suitable for a Quadbit Modulo 2 (QM2) code.