Embracing Interference: Signal Processing Methods for Next-Generation Data Storage and Wireless Communications

Abstract

The future of data storage is driven by user demand for higher storage density and increased lifetime. The future of wireless communication is driven by the need to maintain reliable communication in challenging propagation environments. These challenges introduce significant interference within the system, necessitating advanced signal processing methods that effectively embrace this interference. This dissertation presents such methods, addressing the practical requirements of these applications while integrating principles from coding theory, information theory, and digital signal processing.The next generation of data storage includes two-dimensional magnetic recording (TDMR) technology for magnetic recording and storage of more than one bit per cell for Flash memories. TDMR promises densities of 10 terabits per square inch but requires squeezing the tracks together and introduces inter-track interference (ITI) in addition to already existing inter-symbol interference (ISI). In Flash memories, storing more than one bit per cell requires the support of non-binary physical gates and introduces new detrimental patterns and sources for inter-cell interference. The two-dimensional (TD) nature of the interference patterns introduces new challenges and requires the design of TD constrained codes that mitigate this interference. Similarly, in the next generation of wireless communications, demand for reliable communication in high-mobility and high-frequency environments makes interference more significant, and this interference makes it more difficult to estimate the input/output relation. In the higher interference environment, the standard model-dependent approach breaks down and new modulation methods like Orthogonal Time Frequency Space (OTFS) that embrace the interference through signal processing in the delay-Doppler (DD) domain become critical for reliable communication. We consider Zak-OTFS where inverse Zak transform converts information symbols mounted on DD domain pulses to the time domain for transmission. Zak-OTFS is a framework for communications and active sensing. When the channel spread is less than the delay period of Zak-OTFS, and the Doppler spread is less than the Doppler period of Zak-OTFS, the Zak-OTFS input-output relation can be predicted from the response to a single pilot symbol. Zak-OTFS proposes a new paradigm for communications where model-free operation is possible. In this dissertation, we design and propose coding techniques that embrace interference and increase the reliability of data storage and wireless communications systems.In this dissertation, we first study constrained codes based on lexicographic indexing for modern and next-generation data storage applications. Our main focus is on TDMR technology, and we propose TD lexicographically ordered constrained codes (TD-LOCO codes) to improve the reliability of TDMR systems by reducing ISI and ITI. We also briefly introduce q-ary LOCO codes that improve the reliability of multi, triple, quad, and penta-level cell Flash memories. Next, we study the idea of integrating constrained codes with low-density parity-check (LDPC) codes through unequal data protection (UDP). LDPC codes are state-of-the-art error correction techniques in various data storage and communications standards. We exploit message-passing decoders that inherently embrace interference as a part of the iterative decoding process and study the value of engineering parity bits to be more reliable than message bits on the threshold and speed of convergence of a regular LDPC code through analysis of density evolution. Lastly, we study the effect of LDPC coding in the Zak-OTFS modulation framework and integrate our UDP idea by configuring LDPC codes on the DD domain with TD interference based on the channel estimate reliabilities. Our research produces significant and impactful findings. First, our TD constrained codes have simple encoding and decoding, they are capacity-achieving, reconfigurable and the data protection is achieved with redundancy less than 3% and at modest complexity. We obtain up to 0.65 of an order of magnitude in frame error rate (FER) performance gain when we implement our optimal TD LOCO code on a practical channel. Next, with UDP, we achieve up to 38.2% and 42.7% threshold gains for quantized and belief propagation decoders, respectively. We show that the UDP idea improves the speed at which the decoder converges. Finally, we show that LDPC coding improves the bit error rate (BER) performance in Zak-OTFS framework and with the suggested allocation strategy based on reliability, we achieve up to 0.8 of an order of magnitude gain in BER performance. We show that LDPC coding reduces sensitivity to the choice of transmit filter. We also demonstrate that LDPC coding amplifies the gains previously reported for uncoded transmission when comparing Zak-OTFS with a multicarrier approximation.TD-LOCO codes are designed to embrace ISI and ITI in TDMR, the proposed coding scheme adopting TD-LOCO codes, achieves device protection and preserves the density gains achieved by TDMR devices even after we combine with error-correcting codes. With UDP, the LDPC decoder experiences a version of the channel with a higher effective SNR and embraces the interference. We suggest that this setup can contribute to significant density/lifetime gains in various data storage and transmission systems. LDPC coding extends the range of possible Doppler spreads with reliable model-free communication and it is advantageous to allocate information symbols to more reliable bins in the DD domain. We propose that the signal processing methods introduced in this dissertation that embrace interference in data storage and wireless communications, enhance the performance and reliability of these next-generation technologies while paving the way for innovative and efficient solutions in the future.