Interleaved Reed–Solomon codes are applied in numerous data processing, data transmission, and data storage systems. They are generated by interleaving several codewords of ordinary Reed–Solomon codes. Usually, these codewords are decoded independently by classical algebraic decoding methods. However, by collaborative algebraic decoding approaches, such interleaved schemes allow the correction ...

In the last lecture, we studied codes based on univarite polynomials, also known as Reed-Solomon codes, and on multivariate polynomials, also known as Reed-Muller codes. The Reed-Solomon codes had rate R = 1 − δ, which is optimal (given by the Singleton bound), but required alphabets of large size (|Σ| ≥ n). Multivariate polynomials in a constant number of variables, however, gave codes of posi...

We propose to reduce the decoding complexity of polar codes with non-Arikan kernels by employing a (near) ML decoding algorithm for the codes generated by kernel rows. A generalization of the order statistics algorithm is presented for soft decoding of Reed-Solomon codes. Algebraic properties of the Reed-Solomon code are exploited to increase the reprocessing order. The obtained algorithm is us...

Reed-Solomon codes and Gabidulin codes have maximum Hamming distance and maximum rank distance, respectively. A general construction using skew polynomials, called skew Reed-Solomon codes, has already been introduced in the literature. In this work, we introduce a linearized version of such codes, called linearized Reed-Solomon codes. We prove that they have maximum sum-rank distance. Such dist...

Determining deep holes is an important topic in decoding Reed-Solomon codes. In a previous paper [8], we showed that the received word u is a deep hole of the standard Reed-Solomon codes [q− 1, k]q if its Lagrange interpolation polynomial is the sum of monomial of degree q− 2 and a polynomial of degree at most k− 1. In this paper, we extend this result by giving a new class of deep holes of the...

Reed–Solomon (RS) codes are widely used to identify and correct errors in storage systems and transmission and. When RS codes are used for so many memory system and reduces error in data. (255, 223) product ReedSolomon (RS) for non-volatile NAND flash memory systems. Reed-Solomon codes are the most used in digital data storage systems, but powerful for tool burst errors . To correct multiple ra...

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 quá trình lưu trữ hoặc truyền tải. Kỹ thuật mã hóa này đã được chứng minh đạt hiệu suất cao với chi phí hợp lý. Trong khi kỹ khác dưới dạng chuỗi số nhị phân, thông điệp ký hiệu. Điều đem lại cho lợi thế việc xử lý hàng loạt thậm chí xóa. Nó đóng vai trò quan trọng ...

1 Basics of Forward Error Correction (FEC) .............2 2 Theory ..................................................................... 3 2.1 Galois Fields ........................................................... 3 2.2 Reed-Solomon Codes ..............................................6 2.3 Error-Correcting Performance of Reed-Solomon Codes ..............................................9 3 SC...

In this paper we present a concrete algebraic construction of novel class convolutional codes. These codes are built upon generalized Vandermonde matrices and therefore can be seen as natural extension Reed-Solomon block to the context For reason call them weighted (WRS) We show that under some constraints on defining parameters these Maximum Distance Profile (MDP), which means they have maxima...