论文标题
基于FFT和模块化方法的芦苇 - 固体代码的新解码
New Decoding of Reed-Solomon Codes Based on FFT and Modular Approach
论文作者
论文摘要
芦苇的解码算法 - 固体（RS）代码出于实际和理论原因都引起了极大的兴趣。在本文中，设计了一种称为模块化方法（MA）的有效算法，该算法是为了求解Welch-Berlekamp（WB）密钥方程的设计。通过将MA作为关键方程求解器，我们为系统的RS代码提出了一种新的解码算法。对于$（n，k）$ rs代码，其中$ n $是代码长度，而$ k $是代码维度，建议的解码算法具有最佳的渐近计算复杂性$ o $ o（n \ log（n-k） +（n-k） +（n-k） +（n-k）\ log^2（n-k）（n-k）（n-k））$和最小的常数因子$ at at at at at at at at at at at at at at at at at at at的。通过比较所需的现场操作数量，我们表明，在解码实用的RS代码时，就计算复杂性而言，新算法明显优于现有方法。当解码$（4096，3584）$ RS代码在$ \ Mathbb {f} _ {2^{12}} $上定义的代码时，新算法的速度比基于常规综合征的方法快10倍。此外，新算法具有常规的体系结构，因此适用于硬件实现。
Decoding algorithms for Reed--Solomon (RS) codes are of great interest for both practical and theoretical reasons. In this paper, an efficient algorithm, called the modular approach (MA), is devised for solving the Welch--Berlekamp (WB) key equation. By taking the MA as the key equation solver, we propose a new decoding algorithm for systematic RS codes. For $(n,k)$ RS codes, where $n$ is the code length and $k$ is the code dimension, the proposed decoding algorithm has both the best asymptotic computational complexity $O(n\log(n-k) + (n-k)\log^2(n-k))$ and the smallest constant factor achieved to date. By comparing the number of field operations required, we show that when decoding practical RS codes, the new algorithm is significantly superior to the existing methods in terms of computational complexity. When decoding the $(4096, 3584)$ RS code defined over $\mathbb{F}_{2^{12}}$, the new algorithm is 10 times faster than a conventional syndrome-based method. Furthermore, the new algorithm has a regular architecture and is thus suitable for hardware implementation.
