A Simple Error Detection and Correction Based on Pseudo Inverse Transformation and Topology

Single Event Effects (SEEs) becomes an important concern for all types of critical applications, not just spatial ones. The reduction of the size of devices increases the likelihood the impact of a charged particle will affect more than one cell, resulting in a Multiple Cell Upset (MCU). Error-correcting codes are among the techniques applied to provide memory reliability. On the other hand, standard code implementations are no longer suitable for providing information reliability because they cannot correct many bit flips per coded word. In this work, an error detection and correction (EDAC) was developed based on the theoretical concepts of Linear Algebra and Topology, through the concepts of pseudo-inverse transformation and using Whitney's Theorem, which is an unprecedented approach and which has a detection rate of 100<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">%</sup>, regardless of the number of cells that their values have changed. The correction rates surpass those of classic algorithms and state-of-the-art works, with up to 40% more robustness in some cases. The synthesis shows that the proposed codes, in addition to being reliable, result in low implementation costs, and the method can be used alongside any memory.