Sistemnyj Analiz i Prikladnaâ Informatika (Jul 2016)
DECODING OF STRUCTURALLY AND LOGICAL CODES
Abstract
The article deals with the description of the main points of the structural and logical coding and the features of SLC codes. There are shown the basic points of the generalized algorithm of decoding SLC, which is based on the method of perfect matrix arrangement (PMA) of the n-dimensional cube vertices for adequate representation and transformation of boolean functions, which is based on the method of generating sequences of variables for building the maximum coverage of the cube vertices. The structural and logical codes (SLC) use natural logic redundancy of the infimum disjunctive normal forms (IDNF) of boolean functions, which make the basis for building the SLC codes and correcting the errors, that occur during data transfer in real discrete channels, on the channels with independent errors. The main task is to define the basic relations between the implemented SLC codes of the logical redundancy and boundary values of multiplicity of independent errors which are corrected. The principal difference between the SLC codes and the well-known correcting codes is that the redundancy, that is needed to correct the errors in converting the discrete information, is not introduced into an additional code sequence but is defined in a natural way, during the construction of codewords of SLC.
