A transmitter, a receiver, and corresponding methods are provided. The transmitter includes encoders configured to encode source bit streams from L information sources into bytes of codewords. Each encoder includes different (n, k) multidimensional turbo-product codes of code rate R=k/n, where k is a number of information bytes, and n is code word length. The encoders operate in at least two phases. A first phase involves operating ky column-encoders in parallel on kx bytes per column to generate the code words for a current dimension. A second phase involves operating nx row-encoders in parallel on ky memory locations per rows to generate the code words for the current dimension. The first and second phases are repeated for remaining layers of the current dimension and layers of other dimensions.