Worst Case Performance Assessment of DC-Free Guided Scrambling Coding by Integer Programming Model

For effective dc-free coding in the optical storage systems, guided scrambling (GS) multimode coding is popularly used. To reduce digital discrepancy of the coded sequence, functions of running digital sum (RDS) are used as criteria to choose the best candidate. Among these criteria, the minimum RDS (MRDS), minimum squared weight (MSW), and minimum threshold overrun (MTO) are suggested for effective dc-suppression. In this paper, we formulate integer programming models that are equivalent to MRDS, MSW, and MTO GS coding. Incorporating the MRDS integer programming model in maxmin setting, we develop an integer programming model that computes the worst case MRDS bound given scrambling polynomial and control bit size. In the simulation, we compare the worst case MRDS bound for different scrambling polynomials and control bit sizes. We find that careful selection of scrambling polynomial and control bit size are important factors to guarantee the worst case MRDS performance.