This paper presents an approach to the construction of block error-correcting code for data transmission systems with short packets. The need for this is driven by the necessity of information interaction between objects of machine-type communication network with a dynamically changing structure and unique system of commands or alerts for each network object. The codewords of a code are permutations with a given minimum pairwise Hamming distance. The purpose of the study is to develop a statistical method for constructing a code, in contrast to known algebraic methods, and to investigate the code size. An algorithm for generating codewords has been developed. It can be implemented both by enumeration of the full set of permutations, and by enumeration of a given number of randomly selected permutations. We have experimentally determined the dependencies of the average and the maximum values of the code size on the size of a subset of permutations used for constructing the code. A technique for computing approximation quadratic polynomials for the determined code size dependencies has been developed. These polynomials and their corresponding curves estimate the size of a code generated from a subset of random permutations of such a size that a statistically significant experiment cannot be performed. The results of implementing the developed technique for constructing a code based on permutations of lengths 7 and 11 have been presented. The prediction relative error of the code size did not exceed the value of 0.72% for permutation length 11, code distance 9, random permutation subset size 50,000, and permutation statistical study range limited by 5040.
This paper aims at implementing the principles of establishing frame synchronism for non-separable factorial codes, as well as applying the operation of interleaving fragments received from the communication channel to increase the efficiency of finding permutation boundaries. We apply the algorithm for establishing frame synchronism with parameters defined for the upper limit of the communication channel bit error probability P0_max = 0,495 for environments with a bit error probability P0 ≤ 0,495. The parameters of the algorithm for establishing frame synchronism with the upper limit of the communication channel bit error probability P0_max = 0,4 are determined. The efficiency of using the interleaving operation of fragments received from the communication channel is evaluated. The efficiency of implementing algorithms for establishing frame synchronism with parameters determined for the upper limit of the communication channel bit error probability P0_max ≤ 0,495 and P0_max = 0,4 is compared, for environments with a bit error probability P0 ≤ 0,4. We give recommendations for selecting the synchronization algorithm parameters for communication channels where the bit error probability upper limit P0 ≤ 0,4 is known, and for channels where this value is variable. These recommendations can be used to improve the efficiency of algorithms for establishing frame synchronism when designing telecommunication systems with non-separable data factorial coding in conditions of natural or artificially created high-level communication channel noise.
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