Polar Code Design for Ultra-High Density Magnetic Recording Channels

A simple Polar code optimization algorithm for a two-dimensional (2D) inter-symbol interference (ISI) channel is proposed for ultra-high density magnetic recording, such as bit-patterned magnetic recording (BPMR) and two-dimensional magnetic recording (TDMR), by exploiting the mutual information (MI) between input and output of 2D detector (2D-DET) to re-model the log-likelihood ratio (LLR) messages as Gaussian distribution. The new method, which captures the error characteristics of magnetic recording, builds a bridge of Polar code optimization between the 2D-ISI channels and AWGN channels. The “gap” due to the 2D-ISI, can be computed by the new modeling, so the classic polar code optimization techniques previously developed for the AWGN channel that are not effective can be re-used in 2D-ISI channels.