건국대학교 무선통신공학 7주차 과제

문서 내 토픽

• 1. Cyclic Encoder

  Cyclic Encoder는 Systematic (N,K) Cyclic Codes를 구현하는 함수입니다. 입력 메시지 벡터 M과 다항식 P를 받아 N 길이의 코드워드 U를 출력합니다. 선형 피드백 시프트 레지스터(LFSR)를 사용하여 메시지 비트와 피드백 비트를 계산하고 LFSR의 값을 업데이트하여 최종 코드워드를 생성합니다.

• 2. Cyclic Decoder

  Cyclic Decoder는 수신된 코드워드 R, 다항식 P, 오류 패턴 테이블 T를 입력으로 받아 메시지 M을 출력합니다. LFSR을 사용하여 증후군(syndrome)을 계산하고, 이를 이용해 오류 패턴을 찾아 수신된 코드워드를 수정합니다. 최종적으로 수정된 코드워드에서 메시지 부분만 추출하여 출력합니다.

• 3. Reed-Solomon 코드

  Reed-Solomon 코드는 여러 비트를 한 symbol로 보고 encoding/decoding하는 방식입니다. t만큼의 symbol 오류 수정이 가능하며, 이는 비트 단위가 아닌 symbol 단위로 계산됩니다. 따라서 6비트의 오류가 발생했더라도 그 오류가 두 개의 symbol에 걸쳐 있다면 수정이 가능합니다. Reed-Solomon 코드는 오류 정정 능력이 뛰어난 코드 방식입니다.

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• 1. Cyclic Encoder

  Cyclic encoders are an important component in error-correcting codes, particularly in the field of digital communications. They leverage the mathematical properties of cyclic codes to efficiently encode data and provide robust error detection and correction capabilities. The key advantage of cyclic encoders is their ability to generate codewords that exhibit a cyclic structure, which simplifies the encoding and decoding processes. This makes them well-suited for applications where reliable data transmission is critical, such as satellite communications, digital storage systems, and wireless networks. By introducing carefully designed redundancy into the encoded data, cyclic encoders can effectively identify and correct errors that may occur during transmission or storage, improving the overall reliability and integrity of the communication system. The design and implementation of efficient cyclic encoders is an active area of research, with ongoing efforts to optimize their performance and expand their applications in an increasingly digital world.

• 2. Cyclic Decoder

  Cyclic decoders are a crucial component in the error-correcting capabilities of cyclic codes, which are widely used in digital communication and storage systems. The primary function of a cyclic decoder is to efficiently recover the original data from the received codewords, even in the presence of errors. Cyclic decoders leverage the inherent mathematical structure of cyclic codes to perform this task effectively. By exploiting the cyclic properties of the codewords, cyclic decoders can efficiently detect and correct errors, often using algorithms such as the Berlekamp-Massey algorithm or the Euclidean algorithm. The ability of cyclic decoders to reliably recover the original data is essential for maintaining the integrity and reliability of digital systems, particularly in applications where data loss or corruption can have significant consequences, such as in satellite communications, digital storage, and wireless networks. Ongoing research in the field of cyclic decoders aims to further improve their performance, efficiency, and error-correcting capabilities, contributing to the continued advancement of reliable and robust digital communication and storage technologies.