Polar code design and decoding for magnetic recording

Abstract

Powerful error-correcting codes have enabled a dramatic increase in the bit density on the recording medium of hard-disk drives (HDDs). Error-correcting codes in magnetic recording require a low-complexity decoder and a code design that delivers a target error-rate performance. This dissertation proposes an error-correcting system based on polar codes incorporating a fast, low-complexity, soft-output decoder and a design that is optimized for error-rate performance in the magnetic recording channel. LDPC codes are the state-of-the-art in HDDs, providing the required error-rate performance on high densities at the cost of increased computational complexity of the decoder. Substantial research in LDPC codes has focused on reducing decoder complexity and has resulted in many variants such as quasi-cyclic and convolutional LDPC codes. Polar codes are a recent and important breakthrough in coding theory, as they achieve capacity on a wide spectrum of channels using a low-complexity successive cancellation decoder. Polar codes make a strong case for magnetic recording, because they have low complexity decoders and adequate finite-length error-rate performance. In their current form, polar codes are not feasible for magnetic recording for two reasons. Firstly, there is no low-complexity soft-output decoder available for polar codes that is required for turbo-based equalization of the magnetic recording channel. The only soft-output decoder available to date is a message passing based belief propagation decoder that has very high computational complexity and is not suitable for practical implementations. Secondly, current polar codes are optimized for the AWGN channel only, and may not perform well under turbo-based detector for ISI channels. This thesis delivers a powerful low-complexity error-correcting system based on polar codes for ISI channels. Specifically, we propose a low-complexity soft-output decoder for polar codes that achieves better error-rate performance than the belief propagation decoder for polar codes while drastically reducing the complexity. We further propose a technique for polar code design over ISI channels that outperform codes for the AWGN channel in terms of error rate under the proposed soft-output decoder.