Erasure Decoding in 2D (1,3)-RLL Constraint

Abstract

In information theory, the run length limited (RLL) constraint is one of the topics that many researchers have worked on. It has many benefits in designing a code to reduce and correct errors. The 1D (d,k)-RLL constraint is a binary sequence satisfying the number of a consecutive 0’s is at most k and the number of consecutive 0’s is at least d. Looking at the trend of the digital era, every year, there is a significant increase in data produced. Scientists, especially in the field of physics and computer science, are trying to find the answer to this question: How do we store data in a more efficient way? Lately, there has been a breakthrough in storing digital data, that is, by means of holographic recording, which uses the 2D format to store data inside a crystal. Theoretically, one could store more data per unit square of area. By storing data as a picture (2D format), there is a possibility that data could be distorted horizontally and vertically. Hence, we need to expand the theory in 1D constrained sequence to 2D constrained array. In this paper, we analyze the case of 2D (1,3)-RLL constraint from erasure decoding point of view