Analysis and investigation of algebraic geometric codes properties
DOI:
https://doi.org/10.30837/rt.2018.4.195.08Keywords:
algebraic geometric code, energy gain, orthogonal signal, noise-immune codingAbstract
Linear block noise-proof codes constructed according to algebraic curves (algebraic geometric codes) are considered, their design properties are evaluated, algorithms of construction and decoding are studied. The energy efficiency of the transmission of discrete messages by M-ary orthogonal signals in the application of algebraic geometric codes is studied; the achievable energy gain from the use of noise-immune coding is estimated. It is shown that in discrete channels without memory it is possible to obtain a significant energy gain, which increases with the transition to long algebraic geometric codes constructed by curves with a large number of points with respect to the genus of the curve. It is established that the computational complexity of implementing algebraic geometric codes is comparable to other known noise-resistant codes, for example, Reed-Solomon codes and others. Thus, high energy efficiency in combination with acceptable computational complexity of implementation confirm the prospects of algebraic geometric codes using in modern telecommunication systems and networks to improve the noise immunity of data transmission channels.References
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