We introduce the concept of "parallel error correcting" codes, the error correcting codes for parallel channels. Here, a parallel channel is a set of channels such that the additive error over a finite field occurs in one of its members at time T if the same error occurs in all members at the same time. The set of codewords of a parallel error correcting code has to be a product set, if the messages transmitted are from independent information sources. We present a simple construction of optimal parallel error correcting codes based on ordinary optimal error correcting codes and a construction of optimal linear parallel codes for independent sources based on optimal ordinary linear error correcting codes. The decoding algorithms for these codes are provided as well.

A very interesting recent development in data compression is the Burrows-Wheeler Transformation. The idea is to permute the input sequence in such a way that characters with a similar context are grouped together. We provide a thorough analysis of the Burrows-Wheeler Transformation from an information theoretic point of view. Based on this analysis, the main part of the paper systematically considers techniques to efficiently implement a practical data compression program based on the transformation. We show that our program achieves a better compression rate than other programs that have similar requirements in space and time.

We improve upon previous results on the Burrows and Wheeler (BW)-algorithm. Based on the context tree model, we consider the specific statistical properties of the data at the output of the BWT. We describe six important properties, three of which have not been described elsewhere. These considerations lead to modifications of the coding method, which in turn improve the coding efficiency. We briefly describe how to compute the BWT with low complexity in time and space, using suffix trees in two different representations. Finally, we present experimental results about the compression rate and running time of our method, and compare these results to previous achievements.