论文标题
用于解码基于DNA数据存储的喷泉代码的基础调查算法
Basis-Finding Algorithm for Decoding Fountain Codes for DNA-Based Data Storage
论文作者
论文摘要
在本文中，我们考虑了在收到的符号可能有错误的喷泉代码的解码。它是由于喷泉代码在基于DNA的数据存储系统中的应用而动机，在这些数据存储系统中，内部代码解码通常存在无法检测到的错误，在外部喷泉代码解码之前执行。我们提出了一种新颖而有效的解码算法，即基辅助算法（BFA），然后进行三个实现。 BFA的关键思想是找到接收到的符号的基础，然后使用最可靠的基础元素以灭活解码来恢复源符号。高斯消除用于找到基础并确定最可靠的基础要素。结果，BFA具有多项式时间的复杂性。对于随机喷泉代码，我们能够为BFA的帧错误率（FER）得出一些理论界限。具有Luby Transform（LT）代码的广泛模拟表明，BFA的FER明显低于信念传播（BP）算法，但BFA的FER通常随着基本元素的平均重量的增加，BFA的FER通常会降低。
In this paper, we consider the decoding of fountain codes where the received symbols may have errors. It is motivated by the application of fountain codes in DNA-based data storage systems where the inner code decoding, which generally has undetectable errors, is performed before the outer fountain code decoding. We propose a novel and efficient decoding algorithm, namely basis-finding algorithm (BFA), followed by three implementations. The key idea of the BFA is to find a basis of the received symbols, and then use the most reliable basis elements to recover the source symbols with the inactivation decoding. Gaussian elimination is used to find the basis and to identify the most reliable basis elements. As a result, the BFA has polynomial time complexity. For random fountain codes, we are able to derive some theoretical bounds for the frame error rate (FER) of the BFA. Extensive simulations with Luby transform (LT) codes show that, the BFA has significantly lower FER than the belief propagation (BP) algorithm except for an extremely large amount of received symbols, and the FER of the BFA generally decreases as the average weight of basis elements increases.
