Power spectral density of multi-level constrained sequences with applications

Date

2024-8

Author

Atak, Seral Buse

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In various data storage and transmission systems, certain data patterns are likely to result in errors when stored or transmitted. In order to enhance reliability in these systems, constrained coding is used to forbid such error-prone data patterns. Analyzing the power spectral density (PSD) of constrained sequences as random processes reveals important properties such as the average power at DC and the bandwidth. In this work, a new method is proposed to theoretically derive closed-form expressions for the PSD of multi-level constrained sequences, where the number of possible levels is greater than two, via their binary counterparts that share specific properties in regard to the constraint itself with the multi-level sequences. Constrained sequences associated with constrained codes used in modern two-dimensional magnetic recording (TDMR) and Flash memory systems are focused on. It is shown that the theoretical PSD derived matches the experimental PSD obtained via extensive Monte-Carlo simulations. Additionally, an approximation method for obtaining the PSD is proposed for codes that have more complex state diagrams. It is shown that the approximate PSD derived has a quite low mean squared error (MSE) compared to the experimental PSD obtained via Monte-Carlo simulations.

Subject Keywords

Constrained codes, Multi-level constrained sequences, Power spectral density, Flash memory, Magnetic recording

URI

https://hdl.handle.net/11511/111346

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Graduate School of Natural and Applied Sciences, Thesis