A.V. Rabin – Ph.D.(Eng.), Associate Professor, Department of Aerospace Computer and Program Systems, Saint-Petersburg State University of Aerospace Instrumentation
In modern ways of noise immunity’s increase a channel is fixed as a rule. Thus, transitional probabilities of output signals (with the fixed probabilities of input signals) don’t change. As a result, the number of phases in modulation in such systems doesn’t change also. The feature of signals’ processing in receivers in telecommunication systems are the basis of the offered orthogonal coding: the transmitted signals are chosen according to the decision of developers, and processing of the transmitted signals and noise is made with use of special approach. If in this case orthogonal codes are applied, increase of transmitted signals and decrease of noise are provided. This characteristic exists not only in the channels with additive noise, but also in the fading channels.
For formation of orthogonal codes, it is required to implement the synthesis of square matrices. The product of these matrices is the unitary matrix multiplied by the monomial characterizing the correcting ability of a code.This problem is solved with the condition that elements of the matrices are polynoms of the degree 1. As a result, the class of the matriсes allowing to solve practical problems of noise immunity’s increase was synthesized. Technical realization of orthogonal coding is characterized by low complexity: on each step a decoding process is reduced to calculation of several dot products and comparison with fixed (zero, in this case) threshold. For this reason, the offered way of coding and design of receiving and transmitting devices can be implemented in various communication systems.Thus, the proposed way of orthogonal coding can be considered as a variety of reception of signals of M ary DPSK with an optimum choice of a modulation code. Optimization is reached by averaging of error rate on all digits of the M ary code.
The procedure of harmonization of orthogonal codes’ symbols with DPSK of high frequency rate differs from the existing methods in rules of assignment ofset of phases and way of digital processing in a demodulator.With use of an example of the orthogonal code based onpair of coding and decoding matriсes the solution of a problem of synchronization of signals in combination with orthogonal codes is considered and results of simulation confirming practical applicability of the proposed technical solution are given.
- Kudryashov B. Osnovy' teorii kodirovaniya. SPb.: BXV-Peterburg. 2016. 393 s.
- Sh. Ge, Zh. Wang, P. Luo, M. Karpovsky. Reliable and Secure Memories Based on Algebraic Manipulation Detection Codes and Robust Error Correction // Proc. Int. DependSymp. 2013.
- Rabin A.V., Mironchikov E.T. Ortogonal'noe kodirovanie i ego ispol'zovanie s fazoraznostnoj modulyacziej // Programmny'e produkty' i sistemy' (Tver': MNIIPU). 2007. № 3 (sent). S. 77−80.
- Bezzateev S.V., Shexunova N.A. Sovershenny'e kody' vo vzveshennoj metrike Xe'mminga // Problemy' peredachi informaczii (RAN). 2012. T. 48. № 3. S. 39−42.
- Biglieri E., Caire G., Taricco G. Error Probability over Fading Channels: A Unified Approach // European Transactions on Telecommunications. January 2008.
- Biglieri E., Caire G., Taricco G. Coding for the Fading Channel: A Survey // Signal Processing for Multimedia. Ed. J.S. Byrnes. IOS Press. 2009.
- Jiang A, Schwartz M, Bruck J. Error-correcting Codes for Rank Modulation // Proc. IEEE ISIT. 2008. P. 1736−1740.
- Afanas'ev V.B., Davy'dov A.A., Zigangirov D.K. Postroenie i analiz kodov s rasstoyaniem 4 i 6, minimiziruyushhix veroyatnost' oshibki dekodera // Informaczionny'e proczessy'. 2016. T. 16. № 1. S. 41−60.