Efficient Codes for Writing Equal-bit Information in a WOM Twice

In this paper, we concentrate on WOM coding for writing equal-bit information twice (WOM2E). We studied the definition and coding solution of WOM2E. We encoded information via a codeword table and found that WOM2E achieved a better WOM-rate. However, the codeword table for large WOM2E cells is difficult to determine. We also introduced the coding sum rate to define the WOM2E efficiency. The sum rate of WOM2E is the sum of the ratios of information bits to the number of cells each time data is written to memory. In order to obtain the maximum coding sum rate, we can utilize more cells. Furthermore, we discover that, as the number of cells in memory increases, the sum rate is perfectly asymptotic to the logarithm. We use Matlab to calculate the upper bound of the sum rate of WOM2E, and find that it has a value of 1.546.