Mã Reed-Solomon

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Tác giả: Lệ Hằng Lê, Thị Hiệp Lưu, Ngô Công Thành Nguyễn, Thị Lan Hương Nguyễn, Thị Nhung Nguyễn

Ngôn ngữ: Vie

Ký hiệu phân loại: 510 Mathematics

Thông tin xuất bản: Tạp chí Khoa học và Công nghệ Đại học Thái Nguyên, 2022

Mô tả vật lý: 102-113

Bộ sưu tập: Metadata

ID: 419639

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Mã Reed-Solomon (mã RS) là một trong những phương pháp mạnh mẽ nhất để bảo vệ tính toàn vẹn của dữ liệu khỏi các lỗi có thể xảy ra trong quá trình lưu trữ hoặc truyền tải. Kỹ thuật mã hóa này đã được chứng minh đạt được hiệu suất cao với chi phí hợp lý. Trong khi các kỹ thuật mã hóa khác truyền dữ liệu dưới dạng một chuỗi số nhị phân, mã Reed- Solomon mã hóa thông điệp dưới dạng một chuỗi ký hiệu. Điều này đem lại cho mã Reed-Solomon lợi thế trong việc xử lý lỗi hàng loạt hoặc thậm chí là lỗi xóa. Nó đóng vai trò quan trọng trong các hệ thống thông tin liên lạc hiện đại và nhiều ứng dụng khác trong cuộc sống. Một số ứng dụng có thể kể đến như là hệ thống chịu lỗi trong đĩa CD và giao thức truyền thông trong vệ tinh và tàu vũ trụ. Trong bài viết này, chúng tôi đưa ra các thuộc tính và cấu trúc cơ bản của mã Reed-Solomon bằng cách thảo luận về các mô hình toán học của nó. Quá trình mã hóa với cách tiếp cận ban đầu và cách tiếp cận BCH hiện đại. Đối với quá trình giải mã, chúng tôi nghiên cứu một loạt các thuật toán và kỹ thuật, chẳng hạn như giải mã hội chứng, thuật toán RiBM, Chien và Forney. Kết quả là một bộ mã hóa và giải mã Reed-Solomon sử dụng nền tảng MATLAB. Chúng tôi đưa ra các ví dụ về mã hóa và giải mã với các thông điệp khác nhau., Tóm tắt tiếng anh, The Reed-Solomon (RS) codes are among the most powerful methods to preserve data integrity from errors and erasures for storage or transmission purposes. This coding technique has been proven to be a high performance while maintaining a reasonable cost and productivity. Unlike some coding techniques that enforce data transmission as a sequence of binary numbers, Reed-Solomon encodes the message as non-binary symbols. This gives Reed- Solomon the advantage of handling bursts of errors or even erasure error. It plays a significant role in modern communication systems and many daily life applications. Some known applications of this coding technique are the fault- tolerant systems in CD disks, and the communication protocol in satellites and spaceships. In the paper, we give the basic properties and structures of the Reed-Solomon codes by discussing its mathematics models. The encoding process with the original approach and the modern BCH approaches. For the decoding process, we investigate a wide range of algorithms and techniques, such as Syndrome decoding, RiBM algorithm, Chien search and Forney algorithm. Finally, we present the result is a functional Reed-Solomon encoder and decoder implemented using the MATLAB platform and give examples of encoding and decoding with different messages.

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