On Runlength Limited Codes for BICM Systems

Stephan Zeitz, Florian Roth, Meik Dörpinghaus, Gerhard Fettweis

We study the use of runlength-limited (RLL) block codes in bit-interleaved coded modulation (BICM) systems. In this setting, the RLL code acts as the symbol mapper, whose assignment between input bits and RLL symbols is critical for performance. In this work, we aim at optimizing the assignment scheme of RLL codes. One of the main applications of RLL codes is the mitigation of intersymbol interference (ISI) in systems with coarse quantization. However, channel memory and quantization nonlinearity complicate information theoretic analysis. To enable analytical treatment, we consider a block channel with 1-bit analog-to-digital conversion, modeling the transmission of a single RLL code block. For this channel, we investigate the relationship between the achievable rate in BICM systems-termed BICM capacity-and the RLL code's assignment scheme. Focusing on low signal-to-noise ratios (SNRs), we derive the optimization problem yielding the optimal assignment scheme. By looking at asymptotically large block-lengths, we infer a practical optimization strategy for RLL codes with finite block-length and channels with inter-block interference. Further, we extend this optimization to two-state RLL (TS-RLL) codes, which offer higher code rates than state independent RLL codes. We demonstrate that optimized TS-RLL codes exhibit significant performance improvements over literature counterparts.