Coding Theory: Constrained Code and Its Applications for Flash Memories.

Speaker:
Vu Van Khu (Nanyang Technological University, Singapore)
Date:
Sunday, 23.12.2018, 14:30
Place:
Taub 601

Constrained codes have been studied actively for a long time with numerous applications in data recording and data communication systems.

Recently, various types of one-dimensional and two-dimensional constrained codes have attracted significant attention owing to some applications for flash memories. ICI-free codes (Amit Berman and Yitzhak Birk - 2010), balanced q-ary ICI-free codes (Minghai Qin, Eitan Yaakobi and Paul Siegel - 2014), and weakly constrained codes(Sarit Buzaglo and Paul Siegel - 2017) are such codes. Our interest is to study constrained codes to deal with some challenges in flash memories, including inter-cell interference and charge leakage. In this work, we first investigate one-dimensional q-ary constant composition ICI-free codes. Although, the maximal asymptotic rate of these codes can be computed using known techniques (Brian Marcus and Ron Roth - 1992), we present an enumerative technique to obtain an explicit formula of the maximal size of the code and compute the maximal asymptotic rate. Based on the enumerative technique, we also can encode/decode the optimal code efficiently. Next, we investigate some generalizations of these codes such as semi(weakly)-constrained codes and two-dimensional ICI-free codes.

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