Lower Bounds on the Number of Writing Operations by ILIFC with Inversion Cells

Abstract

Index-less Indexed Flash Code (ILIFC) is a coding scheme for flash memories, in which one bit of a data sequence is stored in a slice consisting of several cells but the index of the bit is stored implicitly. Although several modified ILIFC schemes have been proposed, in this research we consider an ILIFC with inversion cells(I-ILIFC). The I-ILIFC reduces the total number of cell level changes at each writing request. Computer simulation is used to show that the I-ILIFC improves the average performance of the ILIFC in many cases. This paper presents our derivation of the lower bounds on the number of writing operations by I-ILIFC and shows that the worst-case performance of the I-ILIFC is better than that of the ILIFC if the code length is sufficiently large. Additionally, we consider the tight lower bounds thereon. The results show that the threshold of the code length that determines whether the I-ILIFC improves the worst-case performance of the ILIFC is smaller than that in the first lower bounds.