title: ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ ÐÐÐ-ÑÐ¾Ð·Ð²ÐµÐ·Ð´Ð¸Ð¹ Ñ Ð´ÑÐ¾Ð±Ð½Ð¾Ð¹ ÑÐ½ÑÑÐ¾Ð¿Ð¸ÐµÐ¹ Ð¿ÑÐ¸ Ð¿ÐµÑÐµÐ´Ð°ÑÐµ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð¿Ð¾ Ð¾Ð¿ÑÐ¾Ð²Ð¾Ð»Ð¾ÐºÐ¾Ð½Ð½ÑÐ¼ Ð»Ð¸Ð½Ð¸ÑÐ¼ ÑÐ²ÑÐ·Ð¸
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Application of QAM constellations with fractional entropy when transmitting information over fiber-optic communication lines
Creators: name: ÐÑÐ¾Ð±ÑÐ¸Ðº, ÐÐ¸ÑÐ°Ð¸Ð»
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: Ð²ÐµÑÐ¾ÑÑÐ½Ð¾ÑÑÐ½ÑÐ¹ ÑÐµÐ¹Ð¿Ð¸Ð½Ð³
Ð´ÑÐ¾Ð±Ð½Ð°Ñ ÑÐ½ÑÑÐ¾Ð¿Ð¸Ñ
Ð¾Ð¿ÑÐ¾Ð²Ð¾Ð»Ð¾ÐºÐ¾Ð½Ð½ÑÐµ Ð»Ð¸Ð½Ð¸Ð¸ ÑÐ²ÑÐ·Ð¸
Ñ ÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ°Ñ Ð´Ð¸ÑÐ¿ÐµÑÑÐ¸Ñ
ÑÐ¸Ð»ÑÑÑ ÐÐµÑÑÐµÐ»Ñ
"Ð¶Ð°Ð´Ð½ÑÐ¹" Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼
probabilistic shaping
fractional entropy
fiber optic communication lines
chromatic dispersion
Bessel filter
"greedy" algorithm

description: Ð¦ÐµÐ»ÑÑ Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ²Ð»ÑÐµÑÑÑ Ð¿Ð¾Ð²ÑÑÐµÐ½Ð¸Ðµ ÑÐºÐ¾ÑÐ¾ÑÑÐ¸ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð¸ ÑÐ½Ð¸Ð¶ÐµÐ½Ð¸Ðµ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ñ Ð·Ð°ÑÑÐ°Ñ Ð¿ÑÐ¸ Ð¿ÐµÑÐµÐ´Ð°ÑÐµ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ ÑÐµÑÐµÐ· ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½ÑÐµ ÑÐ°ÑÑÐ¾ÑÐ½Ð¾-ÑÐµÐ»ÐµÐºÑÐ¸Ð²Ð½ÑÐµ ÐºÐ°Ð½Ð°Ð»Ñ ÑÐ²ÑÐ·Ð¸ Ð¿ÑÑÑÐ¼ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ "Ð¶Ð°Ð´Ð½Ð¾Ð³Ð¾" Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð¼Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð¸ ÑÐ½ÑÑÐ¾Ð¿Ð¸Ð¸ Ð¸ ÐÐÐ-ÑÐ¾Ð·Ð²ÐµÐ·Ð´Ð¸Ð¹ Ñ Ð´ÑÐ¾Ð±Ð½Ð¾Ð¹ ÑÐ½ÑÑÐ¾Ð¿Ð¸ÐµÐ¹ (Ð´ÑÐ¾Ð±Ð½ÑÑ ÐÐÐ-ÑÐ¾Ð·Ð²ÐµÐ·Ð´Ð¸Ð¹).Â  Ð ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð±ÑÐ»Ð¸ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ñ ÑÐ¾ÑÐ¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¸ Ð´ÐµÐ¼Ð¾Ð´ÑÐ»ÑÑÐ¸Ð¸ ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð² Ñ ÐÐÐ-ÑÐ¾Ð·Ð²ÐµÐ·Ð´Ð¸ÑÐ¼Ð¸ Ñ Ð´ÑÐ¾Ð±Ð½Ð¾Ð¹ ÑÐ½ÑÑÐ¾Ð¿Ð¸ÐµÐ¹ Ð¸ "Ð¶Ð°Ð´Ð½ÑÐ¹" Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð¼Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð¸ ÑÐ½ÑÑÐ¾Ð¿Ð¸Ð¸ Ð¿Ð¾ Ð¿Ð¾Ð´Ð½ÐµÑÑÑÐ¸Ð¼. ÐÐ° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð±ÑÐ»Ð° ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð° Ð¸Ð¼Ð¸ÑÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ Ð¼Ð¾Ð´ÐµÐ»Ñ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ ÑÐµÑÐµÐ· ÑÐ°ÑÑÐ¾ÑÐ½Ð¾-ÑÐµÐ»ÐµÐºÑÐ¸Ð²Ð½ÑÐµ ÐºÐ°Ð½Ð°Ð»Ñ Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼ "Ð¶Ð°Ð´Ð½Ð¾Ð³Ð¾" Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° ÑÐ°ÑÐ¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð¼Ð¾ÑÐ½Ð¾ÑÑÐ¸ Ð¸ ÑÐ½ÑÑÐ¾Ð¿Ð¸Ð¸ Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÐÐÐ-ÑÐ¾Ð·Ð²ÐµÐ·Ð´Ð¸Ð¹ Ñ Ð´ÑÐ¾Ð±Ð½Ð¾Ð¹ ÑÐ½ÑÑÐ¾Ð¿Ð¸ÐµÐ¹. Ð¢Ð°ÐºÐ¶Ðµ Ð±ÑÐ»Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð° ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ÑÑÑ Ð¿ÑÐµÐ´Ð»Ð¾Ð¶ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¼ÐµÑÐ¾Ð´Ð°. ÐÐ»Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¹ Ð±ÑÐ»Ð¾ Ð²ÑÐ±ÑÐ°Ð½Ð¾ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ðµ ÑÐµÐ»ÐµÐ²Ð¾Ð¹ Ð²ÐµÑÐ¾ÑÑÐ½Ð¾ÑÑÐ¸ Ð±Ð¸ÑÐ¾Ð²Ð¾Ð¹ Ð¾ÑÐ¸Ð±ÐºÐ¸ BER = 10^{â2}. ÐÐ»Ñ Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ Ð²ÐµÑÐ¾ÑÑÐ½Ð¾ÑÑÐ¸ Ð±Ð¸ÑÐ¾Ð²Ð¾Ð¹ Ð¾ÑÐ¸Ð±ÐºÐ¸ Ð±ÑÐ»Ð¾ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð¿ÑÐ¸ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ð¸ Ð´ÑÐ¾Ð±Ð½ÑÑ ÐÐÐ-ÑÐ¾Ð·Ð²ÐµÐ·Ð´Ð¸Ð¹ Ð² ÐºÐ°Ð½Ð°Ð»Ð°Ñ Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ ÑÐ¸Ð»ÑÑÑÐ° ÐÐµÑÑÐµÐ»Ñ Ð²Ð¾Ð·Ð¼Ð¾Ð¶Ð½Ð¾ Ð¿Ð¾Ð»ÑÑÐ¸ÑÑ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð²ÑÐ¸Ð³ÑÑÑ Ð¿Ð¾ÑÑÐ¸ Ð² 1,6 Ð´Ð, Ð¿Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÑÐ°Ð½Ð´Ð°ÑÑÐ½ÑÑ ÐÐÐ-ÑÐ¾Ð·Ð²ÐµÐ·Ð´Ð¸Ð¹. Ð¢Ð°ÐºÐ¶Ðµ Ð¿Ð¾ÐºÐ°Ð·Ð°Ð½Ð¾, ÑÑÐ¾ Ð´Ð»Ñ ÑÐ°ÐºÐ¾Ð³Ð¾ Ð¶Ðµ ÑÐ¸Ð¿Ð° ÐºÐ°Ð½Ð°Ð»Ð° Ð¼Ð¾Ð¶Ð½Ð¾ ÑÐ²ÐµÐ»Ð¸ÑÐ¸ÑÑ ÑÐºÐ¾ÑÐ¾ÑÑÑ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸ Ð½Ð° 33%. ÐÐ»Ñ ÐºÐ°Ð½Ð°Ð»Ð¾Ð² Ñ ÑÑÐ¾Ð¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð´Ð¸ÑÐ¿ÐµÑÑÐ¸ÐµÐ¹ ÑÐ½ÐµÑÐ³ÐµÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð²ÑÐ¸Ð³ÑÑÑ ÑÐ¾ÑÑÐ°Ð²Ð¸Ð» 1,3 Ð´Ð, Ð° ÑÐºÐ¾ÑÐ¾ÑÑÑ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ ÑÐ²ÐµÐ»Ð¸ÑÐ¸Ð»Ð°ÑÑ Ð½Ð° 20%.
description: The purpose of this research is to increase the data rate and reduce energy costs when transmitting information through the stationary frequency-selective communication channels by using a "greedy" algorithm for distributing power and entropy and QAM constellations with fractional entropy (fractional QAM constellations). During the research, algorithms for generating and demodulating signals with QAM constellations with fractional entropy and a "greedy" algorithm for distributing power and entropy across subcarriers were implemented. Based on the obtained results, a simulation model of information transmission through the frequency-selective channels has been implemented with using a "greedy" algorithm for distributing power and entropy and QAM constellations with fractional entropy. Also, the effectiveness of using the proposed method was investigated. For the research, the target value of bit error rate BER = 10^{â2} was chosen. For a given bit error rate, it has been shown that when using fractional QAM constellations in channels based on a Bessel filter, it is possible to obtain an energy gain of almost 1.6 dB, compared to using conventional QAM constellations. It is also shown that for the same type of channel it is possible to increase the data rate by 33%. For channels with chromatic dispersion, the energy gain was 1.3 dB, and the data rate was increased by 20%.