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An estimation of accuracy of theoretical calculations of characteristics for the data transfer algorithm with errors detection and multidimensional deletions correction

Keywords:

T. S. Philippova – Leading Engineer, Public Corporation “Scientific Production Association “Impuls”, St. Petersburg. E-mail: tatyana.philippova@gmail.com
V. V. Khromov – Ph.D. (Eng.), Associate Professor, Public Corporation “Scientific Production Association “Impuls”, St. Petersburg. E-mail: khromov1936@mail.ru


A data transfer algorithm is considered. It uses an antinoise coding for bit-errors detection in data blocks, a correction of deleted data blocks by iterative code and a query of data block if there is a feedback channel. A message with L bits length is divided into packets with m data bits length. A sequence of these packets is divided into r series of packets in k packets in one series. The service bits and the validation bits for errors detection are added to each packet. After series transfer of k channel blocks there is generated a control packet of the first type. It consists of the validation bits. The first validation bit is equal to a sum modulo 2 of the first data bits of the first k packets. The second validation bit is equal to a sum modulo 2 of the second data bits of the first k packets and so on. The control packets of the first type complete each series of channel blocks. Service bits in it are formed the same way as in the data packets. After r series transfer there is formed series of control packets of the second type. The control packet of the second type consists of the validation bits. The first validation bit of the first control packet of the second type is equal to a sum modulo 2 of the first data bits of the first packets of the series from 1 to r. The second validation bit of the first control packet of the second type is equal to a sum modulo 2 of the second data bits of the first packets of the series from 1 to r and so on. The control packet of the first type completes the series of control packets of the second type. The answering station receives a codogram. It reveals channel blocks with error bits by CRC-code and deletes them. If there was deleted only one block from any series, then it can be corrected by the control packet of the first type. If there was deleted only one block from blocks with the same number, then it can be corrected by the control packet of the second type. If there are no deleted blocks, then the message is corrected, else it must repeat item 2 and 3. One of the most important characteristics of the transmission efficiency is a relative speed. It is defined as , where k is the number of data bits, n is the number of bits that are used for the transmission in the session. There is checked the error of calculation, if the bit stream is a stream with a grouping of errors. The probability of query (or reception failure in the simplex mode of transfer) into the system occurs if deleted four or more blocks and if there is at least one configuration from deleted blocks in the form of a rectangle. To assess the probability of query there is obtained a formula that uses the exact probability of deletion the multiplicity of 4 and 5, and the situation with six and more deletions is considered as uncorrectable. The formula for the estimation is true, if the deletions of blocks are independent. This article is an analysis of errors in calculations of the speed transmission, if the bit stream is a stream with a grouping of errors that obeys to the model of generalized Poisson stream. According to the results of the simulation we can conclude that the assumption of deletions independence is accepted for engineering calculations of transmission speed in the range of deletions 0.02-0.07.
References:

  1. Filippova T. S., Xromov V. V. Analiz sistemy' povy'sheniya dostovernosti s peredachej kontrol'ny'x paketov // Start v budushhee – 2013: Vserossijskaya nauchn.-texnich. konf. Trudy' tret'ej nauchn.-texnich. konf. molody'x ucheny'x i speczialistov. OAO «KBSM». SPb. 2013. S. 266–271.
  2. E'lementy' teorii peredachi diskretnoj informaczii / Pod red. L. P. Purtova. M.: Svyaz'. 1972.
  3. Aksenov B. E., Aleksandrov A. M. Povy'shenie dostovernosti peredachi informaczii v sistemax upravleniya. L.: LPI im. M.I. Kalinina. 1981. 

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