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Systematic Memory MDS Sliding Window Codes Over Erasure Channels
IEEE Transactions on Communications ( IF 7.2 ) Pub Date : 2020-11-30 , DOI: 10.1109/tcomm.2020.3041254
Xiangyu Chen , Zongpeng Li , Qifu Tyler Sun

Memory maximum-distance-separable (mMDS) sliding window codes are a type of erasure codes with high erasure-correction capability and low decoding delay. In this paper, we study two types of systematic mMDS sliding window codes over erasure channels, i.e., scalar codes defined over a finite field $GF(2^{L})$ , and vector codes defined over a vector space $GF(2)^{L}$ . We first devise an efficient heuristic algorithm to produce an mMDS sliding window scalar code over relatively small $GF(2^{L})$ . Then, we investigate a special class of mMDS sliding window vector codes whose encoding/decoding are achieved by basic circular-shift and bit-wise XOR operations, and propose a general method to generate such mMDS vector codes. Our complexity analysis shows that the proposed vector codes yield much lower encoding/decoding complexity than the scalar codes. The theoretical and numerical results also demonstrate that mMDS sliding window codes dominate MDS block codes in terms of decoding delay and erasure-correction capability.

中文翻译:

擦除通道上的系统内存MDS滑动窗口代码

存储器最大距离可分离(mMDS)滑动窗口代码是一种擦除代码,具有较高的擦除校正能力和较低的解码延迟。在本文中,我们研究了擦除通道上的两种类型的系统mMDS滑动窗口代码,IE, 在有限域上定义的标量代码 $ GF(2 ^ {L})$ ,以及在向量空间上定义的向量代码 $ GF(2)^ {L} $ 。我们首先设计一种有效的启发式算法,以在相对较小的范围内生成mMDS滑动窗口标量代码 $ GF(2 ^ {L})$ 。然后,我们研究了一类特殊的mMDS滑动窗口矢量代码,其编码/解码是通过基本的循环移位和按位XOR运算实现的,并提出了一种生成此类mMDS矢量代码的通用方法。我们的复杂度分析表明,与标量代码相比,提出的矢量代码产生的编码/解码复杂度要低得多。理论和数值结果还表明,就解码延迟和擦除校正能力而言,mMDS滑动窗口代码在MDS块代码中占主导地位。
更新日期:2020-11-30
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