A communication system of the present invention comprises a transmission side for transmitting a codeword in which the components of a block encoded codeword are rearranged with a predetermined rule of rearrangement to disperse a redundant portion, and a receiving side for decoding into an original codeword by performing a calculation with a correlation matrix having the row components rearranged with the same rule. This correlation matrix is learned by performing a predetermined calculation using a post-coded codeword and a pre-learned correlation matrix, comparing the components of the calculation result with a preset threshold, and updating the elements of the correlation matrix based on the comparison results to obtain the post-learned correlation matrix. Threshold for learning the correlation matrix is gradually increased as the learning operation proceeds, whereby the optimal threshold to keep the enough margin for bit error is obtained for all of the codewords. Thereby, in transmitting or receiving the block encoded codeword on a radio transmission path, it is possible to reduce the probability that the error correction ability is degraded when a burst bit error (burst error) occurs.