公开(公告)号：US20020157059A1

公开(公告)日：2002-10-24

申请号：US10015949

申请日：2001-11-02

Applicant: STMicroelectronics S.r.l.

Inventor： Stefano Gregori ,  Pietro Ferrari ,  Guido Torelli

IPC: H03M013/00

CPC classification number: H03M13/00 ,  G11C2211/5641

Abstract: Described herein is a method for constructing a multipurpose error-control code for multilevel memory cells operating with a variable number of storage levels, in particular for memory cells the storage levels of which can assume the values of the set nullba1, baaa2, . . . , ba1a2. . . ahnull, with b, a1, . . . , ah positive integers; the error-control code encoding information words, formed by k q-ary symbols, i.e., belonging to an alphabet containing q different symbols, with qnullnullba1, ba1a2, . . . , ba1a2ahnull, in corresponding code words formed by n q-ary symbols, with qnullba1a2ah, and having an error-correction capacity t, each code word being generated through an operation of multiplication between the corresponding information word and a generating matrix. The construction method comprises the steps of: acquiring the values of k, t, ba1, ba1a2, . . . , ba1a2. . .ah, which constitute the design specifications of said error-control code; calculating, as a function of qnullba1, k and t, the minimum value of n such that the Hamming limit is satisfied; calculating the maximum values {circumflex over (n)} and {circumflex over (k)} respectively of n and k that satisfy the Hamming limit for qnullba1, t and ({circumflex over (n)}-{circumflex over (k)})null(n-k); determining, as a function of t, the generating matrix of the abbreviated error-control code (n-k) on the finite-element field GF(ba1); constructing binary polynomial representations of the finite-element fields GF(ba1) GF(ba1a2), . . . , GF(ba1a2. . . ah); identifying, using the aforesaid exponential representations, the elements of the finite-element field GF(ba1a2ah), which are isomorphic to the elements of the finite-element fields GF(ba1), GF(ba1a2), . . . , GF(ba1a2. . . ah-1); establishing biunique correspondences between the elements of the finite-element fields GF(ba1), GF(ba1a2), . . . , GF(ba1a2. . . ah1) and the elements of the finite-element field GF(ba1a2ah) that are isomorphic to them; and replacing each of the elements of said generating matrix with the corresponding isomorphic element of the finite-element field GF(ba1a2. . . ah), thus obtaining a multipurpose generating matrix defining, together with the aforesaid biunique correspondences, a multipurpose error-control code that can be used with memory cells the storage levels of which can assume the values of the set nullba1, ba1a2, . . . , ba1a2. . . ahnullnull.

Abstract translation: 这里描述了一种用于构建以可变数量的存储级别操作的多级存储器单元的多用途错误控制代码的方法，特别是对于存储单元，其存储级别可以采用集合{ba1，baaa2，...， 。 。 ，ba1a2。 。 。 啊}，用b，a1，。 。 。 ，正整数; 由k个q元符号形成的错误控制码编码信息字，即属于包含q个不同符号的字母，与qepsi {ba1，ba1a2，... 。 。 ，ba1a2ah}，在具有q = ba1a2ah并且具有纠错能力t的由n个q元符号形成的相应码字中，每个码字通过相应信息字与生成矩阵之间的乘法运算而产生。 该构造方法包括以下步骤：获取k，t，ba1，ba1a2，...的值。 。 。 ，ba1a2。 。 .ah，构成设计