title: Ð¡ÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¿Ð¾Ð¼ÐµÑ Ð¾ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ ÑÐ¿Ð¸ÑÐ¾ÑÐ½Ð¾Ð³Ð¾ Ð´ÐµÐºÐ¾Ð´Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÐºÐ¾ÑÐ¾ÑÐºÐ¸Ñ Ð¿Ð¾Ð»ÑÑÐ½ÑÑ ÐºÐ¾Ð´Ð¾Ð² Ñ ÐºÐ¾Ð´Ð°Ð¼Ð¸ Ð´ÑÑÐ³Ð¸Ñ ÐºÐ»Ð°ÑÑÐ¾Ð²
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: Comparative analysis of the noise immunity of the list decoding of short polar codes with codes of other classes
Creators: name: ÐÐµÑÑÐ¾Ð²Ð°, ÐÐ¸ÑÑ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: Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð¿Ð¾ÑÐ»ÐµÐ´Ð¾Ð²Ð°ÑÐµÐ»ÑÐ½Ð¾Ð³Ð¾ Ð¸ÑÐºÐ»ÑÑÐµÐ½Ð¸Ñ
Ð²ÐµÑÐ¾ÑÑÐ½Ð¾ÑÑÑ Ð¾ÑÐ¸Ð±ÐºÐ¸
Ð´ÐµÐºÐ¾Ð´Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Ð¼ÐµÑÑÐ¸ÐºÐ°
Ð½Ð°Ð´ÑÐ¶Ð½Ð¾ÑÑÑ ÐºÐ°Ð½Ð°Ð»Ð°
Ð¿Ð¾Ð»ÑÑÐ¸Ð·Ð°ÑÐ¸Ñ ÐºÐ°Ð½Ð°Ð»Ð°
Ð¿Ð¾Ð»ÑÑÐ½ÑÐ¹ ÐºÐ¾Ð´
Ð¿Ð¾Ð¼ÐµÑ Ð¾ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ
Ð¿ÑÑÑ
matlab
CRC
successive cancellation algorithm
error probability
decoding
metric
channel reliability
channel polarization
polar code
noise immunity
path

description: Ð¦ÐµÐ»Ñ ÑÐ°Ð±Ð¾ÑÑ â Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¿Ð¾Ð¼ÐµÑÐ¾ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð¿Ð¾Ð»ÑÑÐ½ÑÑ ÐºÐ¾Ð´Ð¾Ð² Ð¿ÑÐ¸ SCL-Ð´ÐµÐºÐ¾Ð´Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ð¸ Ð² ÐºÐ¾Ð¼Ð±Ð¸Ð½Ð°ÑÐ¸Ð¸ Ñ CRC, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· Ð¿Ð¾Ð¼ÐµÑÐ¾ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð´Ð°Ð½Ð½ÑÑ ÐºÐ¾Ð´Ð¾Ð² Ñ ÐºÐ¾Ð´Ð°Ð¼Ð¸ Ð´ÑÑÐ³Ð¸Ñ ÐºÐ»Ð°ÑÑÐ¾Ð². Ð¡Ð¾Ð²ÑÐµÐ¼ÐµÐ½Ð½ÑÐµ Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¾Ð½Ð½ÑÐµ ÑÐ¸ÑÑÐµÐ¼Ñ Ð·Ð°ÑÐ°ÑÑÑÑ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÑÑ Ð¾Ð±Ð¼ÐµÐ½ ÐºÐ¾ÑÐ¾ÑÐºÐ¸Ð¼Ð¸ ÑÐ¾Ð¾Ð±ÑÐµÐ½Ð¸ÑÐ¼Ð¸, Ð´Ð»Ñ Ð¿ÐµÑÐµÐ´Ð°ÑÐ¸ ÑÐ»ÑÐ¶ÐµÐ±Ð½ÑÑ ÑÐ¾Ð¾Ð±ÑÐµÐ½Ð¸Ð¹ Ð¸Ð»Ð¸ Ð´Ð°Ð½Ð½ÑÑ Ð½Ð°Ð²Ð¸Ð³Ð°ÑÐ¸Ð¸, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð½Ðµ ÑÑÐµÐ±ÑÑÑ Ð±Ð¾Ð»ÑÑÐ¾Ð³Ð¾ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° Ð±Ð°Ð¹Ñ. ÐÐ´Ð½Ð°ÐºÐ¾, ÑÐ¸ÑÐ¾ÐºÐ¾ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·ÑÐµÐ¼ÑÐµ Ð² Ð½Ð°ÑÑÐ¾ÑÑÐµÐµ Ð²ÑÐµÐ¼Ñ ÑÑÑÐ±Ð¾-ÐºÐ¾Ð´Ñ Ð¸ ÐºÐ¾Ð´Ñ Ñ Ð¼Ð°Ð»Ð¾Ð¹ Ð¿Ð»Ð¾ÑÐ½Ð¾ÑÑÑÑ Ð¿ÑÐ¾Ð²ÐµÑÐ¾Ðº Ð½Ð° ÑÑÑÐ½Ð¾ÑÑÑ ÑÑÐµÐ±ÑÑÑ Ð²Ð½ÐµÑÐµÐ½Ð¸Ñ Ð²ÑÑÐ¾ÐºÐ¾Ð¹ Ð¸Ð·Ð±ÑÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð´Ð»Ñ Ð¾Ð±ÐµÑÐ¿ÐµÑÐµÐ½Ð¸Ñ Ð¿ÑÐ¸ÐµÐ¼Ð»ÐµÐ¼Ð¾Ð¹ Ð²ÐµÑÐ¾ÑÑÐ½Ð¾ÑÑÐ¸ Ð¾ÑÐ¸Ð±ÐºÐ¸ Ð´ÐµÐºÐ¾Ð´Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÐ°ÐºÐ¸Ñ ÑÐ¾Ð¾Ð±ÑÐµÐ½Ð¸Ð¹. Ð Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÐµ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ Ð¿Ð¾Ð»ÑÑÐ½ÑÐµ ÐºÐ¾Ð´Ñ Ð´Ð»Ñ ÐºÐ¾ÑÐ¾ÑÐºÐ¸Ñ Ð±Ð»Ð¾ÐºÐ¾Ð², ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÐ¹ÑÐ°Ñ Ð°ÐºÑÐ¸Ð²Ð½Ð¾ Ð¿ÑÐ¸Ð¼ÐµÐ½ÑÑÑÑÑ Ð² ÑÑÐ°Ð½Ð´Ð°ÑÑÐµ ÑÐ²ÑÐ·Ð¸ 5G. Ð ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½ ÑÐ¿Ð¸ÑÐ¾ÑÐ½ÑÐ¹ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð´ÐµÐºÐ¾Ð´Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¿Ð¾Ð»ÑÑÐ½ÑÑ ÐºÐ¾Ð´Ð¾Ð² Ð² ÐºÐ¾Ð¼Ð±Ð¸Ð½Ð°ÑÐ¸Ð¸ Ñ ÐºÐ¾Ð´Ð¾Ð¼ CRC, Ð° ÑÐ°ÐºÐ¶Ðµ, Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¿Ð¾Ð¼ÐµÑÐ¾ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ð´Ð»Ñ ÐºÐ¾ÑÐ¾ÑÐºÐ¸Ñ Ð±Ð»Ð¾ÐºÐ¾Ð² (Ð¾Ñ 2^6 Ð´Ð¾ 2^{10} Ð±Ð¸Ñ) Ð¿Ð¾Ð»ÑÑÐ½ÑÑ ÐºÐ¾Ð´Ð¾Ð² Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð¸ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ñ ÑÐ°ÐºÑÐ¾ÑÑ, Ð²Ð»Ð¸ÑÑÑÐ¸Ðµ Ð½Ð° Ð¸Ñ Ð¿Ð¾Ð¼ÐµÑÐ¾ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑ. ÐÑÐ¸Ð²ÐµÐ´ÐµÐ½Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ð¿Ð¾Ð¼ÐµÑÐ¾ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÐ¸ Ñ Ð¿Ð¾Ð¼ÐµÑÐ¾ÑÑÑÐ¾Ð¹ÑÐ¸Ð²Ð¾ÑÑÑÑ ÑÐ²ÑÑÑÐ¾ÑÐ½Ð¾Ð³Ð¾ ÐºÐ¾Ð´Ð° Ð¸ ÑÑÑÐ±Ð¾-ÐºÐ¾Ð´Ð°. ÐÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð»Ð¸ÑÑ Ð¾ÑÐºÑÑÑÑÐµ Ð¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°ÑÐµÐ»ÑÐ½ÑÐµ ÑÐµÑÑÑÑÑ Ð¿Ð¾Ð¸ÑÐºÐ° Ð¸ Ð°Ð½Ð°Ð»Ð¸Ð·Ð° Ð¸Ð½ÑÐ¾ÑÐ¼Ð°ÑÐ¸Ð¸. ÐÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð»Ð¸ÑÑ ÑÑÐµÐ´ÑÑÐ²Ð° Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸Ð·Ð°ÑÐ¸Ð¸ (Ð°Ð²ÑÐ¾Ð¼Ð°ÑÐ¸Ð·Ð¸ÑÐ¾Ð²Ð°Ð½Ð½Ð¾Ð¹) ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ¸ MATLAB. ÐÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¾ (Ð¿ÑÐ¾ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¾) Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ðµ Ð¾Ð±ÐµÑÐ¿ÐµÑÐµÐ½Ð¸Ðµ MATLAB.â
description: The aim of the work is to study the noise immunity of polar codes during SCL decoding in combination with CRC, as well as a comparative analysis of the noise immunity of these codes with codes of other classes. Modern information systems often use the exchange of short messages to transmit service messages or navigation data that do not require a large number of bytes. However, currently widely used turbo codes and codes with a low density of parity checks require high redundancy to ensure an acceptable probability of error decoding such messages. In this paper, we consider the polar codes for short blocks, which are now actively used in the 5G communication standard. As a result of the study, a list algorithm for decoding polar codes in combination with the CRC code was implemented, as well as a study of noise immunity for short blocks (from 2^6 to 2^{10} bits) of polar codes using this algorithm and factors affecting their noise immunity were determined. The noise immunity is compared with the noise immunity of convolutional code and turbo code. Open educational resources for information search and analysis were used. MATLAB automation (automated) development tools were used. MATLAB software has been applied (tested).