Erasure codes are widely deployed in modern storage systems, leading to frequent usage of their encoding/decoding operations. The encoding/decoding process for erasure codes is generally carried out using the parity-check matrix approach. However, this approach is serial and computationally expensive, mainly due to dealing with matrix operations, which results in low encoding/decoding performance. These drawbacks are particularly evident for newer erasure codes, including SD and LRC codes. To address these limitations, this article introduces the Partitioned and Parallel Matrix (PPM) algorithm. This algorithm partitions the parity-check matrix, parallelizes encoding/decoding operations, and optimizes calculation sequence to facilitate fast encoding/decoding of these codes. Furthermore, we present a generalized PPM (gPPM) algorithm that surpasses PPM in performance by employing fine-grained dynamic matrix calculation sequence selection. Unlike PPM, gPPM is also applicable to erasure codes such as RS code. Experimental results demonstrate that PPM improves the encoding/decoding speed of SD and LRC codes by up to 210.81%. Besides, gPPM achieves up to 102.41% improvement over PPM and 32.25% improvement over RS regarding encoding/decoding speed.

纠删码广泛部署在现代存储系统中，导致其编码/解码操作的频繁使用。纠删码的编码/解码过程通常使用奇偶校验矩阵方法来执行。然而，这种方法是串行的并且计算量大，主要是由于处理矩阵运算，这导致编码/解码性能低。这些缺点对于较新的纠删码（包括 SD 和 LRC 码）尤其明显。为了解决这些限制，本文介绍了分区并行矩阵( PPM ) 算法。该算法对奇偶校验矩阵进行分区，并行化编码/解码操作，并优化计算序列以促进这些代码的快速编码/解码。此外，我们提出了一种广义 PPM（gPPM）算法，通过采用细粒度动态矩阵计算序列选择，该算法在性能上超越了 PPM。与PPM不同，gPPM也适用于RS码等纠删码。实验结果表明，PPM将SD码和LRC码的编解码速度提高了210.81%。此外，在编解码速度方面，gPPM比PPM提高了102.41%，比RS提高了32.25%。