两类多重置换阵列码的构造方法  

Construction of two classes of multi-permutation array codes

作　　者：王丹 孙蓉[2] 韩辉[1] WANG Dan;SUN Rong;HAN Hui(School of Computer Science and Technology,Xidian University,Xi’an 710071,China;State Key Laboratory of Integrated Services Networks,Xidian University,Xi’an 710071,China)

机构地区：[1]西安电子科技大学计算机科学与技术学院,陕西西安710071 [2]西安电子科技大学综合业务网理论及关键技术国家重点实验室,陕西西安710071

出　　处：《西安电子科技大学学报》2024年第6期84-90,共7页Journal of Xidian University

基　　金：国家自然科学基金(62371371);中央高校基本科研业务费专项资金资助(ZYTS24091)。

摘　　要：具有高存储密度与良好可靠性的闪存是一种重要的非易失性存储技术。读/写干扰、单元间干扰与电荷泄漏等噪声可能导致闪存数据不能被正确读出而出现删除错误。等级调制方案下置换码/多重置换码等纠错编码技术可以克服闪存中的删除/插入错误。与置换码相比较,多重置换码可以达到更高的信息存储率。近年来,学者们仅仅研究了纠单个或多个交叉插入/删除错误的几类二元码的构造及译码方法。然而,目前没有纠正交叉插入/删除错误的多重置换阵列码的相关研究工作。针对这一问题,利用置换的交织技术与重复码的思想,提出了纠单个交叉删除错误的平衡多重置换阵列码的两个构造方法,而且在其证明中给出了相应的译码方法。第一个构造方法基于置换的奇偶交织技术来确定码字阵列中被删除列的位置,而第二个构造方法基于LEVENSHTEIN置换码来确定码字阵列中被删除列的位置。而且,与第一个构造方法相比较,第二个构造方法得到的平衡多重置换阵列码可以达到更高的码率。通过实例验证了所提出的平衡多重置换阵列码的两个构造及其相应译码方法的正确性。The flash memory with a high storage density and good reliability is a dominant nonvolatile memory technology.Such noises as read/write interference,inter-cell interference,and charge leakage may cause deletion errors in flash memory data that cannot be read correctly.Error-correcting coding techniques such as permutation codes/multi-permutation codes under the rank-modulation scheme can overcome deletion/insertion errors.Moreover,multi-permutation codes can achieve a higher information rate compared with permutation codes.In recent years,only the construction and decoding methods of binary codes correcting single or multiple criss-cross insertion/deletion errors have been investigated.However,there are no studies of multi-permutation array codes correcting criss-cross insertion/deletion errors.In order to solve this problem,by using the interleaving technique of permutations and the idea of repetition codes,two constructions of balanced multi-permutation array codes capable of correcting the single criss-cross deletion error are proposed with their decoding methods included in proofs.The first construction is based on the parity interleaving technique of permutations to determine the position of the deleted column in the codeword array,while the second construction is based on the Levenshtein permutation code to determine the position of the deleted column in the codeword array.Moreover,the balanced multi-permutation array codes obtained by the second construction can achieve a higher rate compared with the first construction.The correctness of our constructions and their decoding methods is verified with examples.

关 键 词：平衡多重置换阵列码 交叉删除错误 交织技术 闪存 

分 类 号：TN911.22[电子电信—通信与信息系统]