Numerical Linear Algebra methods in Data Encoding and Decoding

In this paper, Numerical Linear Algebra techniques for data encoding and decoding are presented. The algorithms are based on matrix triangularization leading to an efficient coding procedure. Rounding off errors can cause serious problems in the process of coding and thus the decoding may be led to inaccurate results. Techniques for improving the stability of the whole process are proposed. The complexity and the error analysis of the proposed methods are discussed. Examples illustrating the algorithms are presented.