Cyclic code diagnostic algorithm based on direct calculation of simple polynoms

Abstract

One of the main problems of communication is signal recovery in receiving. It is known that all blocks of the code block are formed according to the same rules and by the same coder. It can be assumed that interrelation between checking and information symbols are the same irrespective of the transmitted data. Thus recovery of the coder structure in the receiving part is possible when diagnosing the received code sequences. When using cyclic codes, diagnostics consists in possibility to reveal interrelations between checking and information symbols of each block. When comparing sufficient number of code blocks it is possible to define a common part. Here identical parts are those parts of code blocks which describe the generating polynom used for coding in the transmitter. Cyclic code diagnostic algorithm based on direct calculation of simple polynoms is described. In this case the length of information part of code blocks and the type of the generating polynom is defined. Also the different number of code blocks in the analyzed set is defined. Information part of blocks is imitated by random sequence of zeros and ones. The studied diagnostic algorithm involves calculation for each code block of simple polynoms set as multipliers into which this block is decomposed. Then information accumulating process follows about the frequency of emerging simple polynoms. Further the analysis of blocks and the choice of simple multipliers set is made. Examples of research results are given for the generating polynom value: g=11₁₀=1011=X³+X+1, number of code blocks N=6, to value of the information sequence length equal to k=5. It is shown that the diagnostic result i.e. the multipliers, general for all blocks, are defined correctly. The probability of the wrong diagnostic is examined.