| Summary: | Generally speaking, a communication channel refers to a medium through which an information-bearing signal is corrupted by noise and distortion. A communication channel may result from data storage over time or data transmission through space. A primary task for communication engineers is to mathematically characterize the channel to facilitate the design of appropriate detection and coding systems. In this dissertation, two different channel modeling challenges for ultra-high density magnetic storage are investigated: two-dimensional magnetic recording (TDMR) and bit-patterned magnetic recording (BPMR). In the case of TDMR, we characterize the error mechanisms during the write/read process of data on a TDMR medium by a finite-state machine, and then design a state-based detector that provides soft decisions for use by an outer decoder. In the case of BPMR, we employ an insertion/deletion (I/D) model. We propose a LDPC-CRC product coding scheme that enables the error detection without the involvement of Marker codes specifically designed for an I/D channel. We also propose a generalized Gilbert-Elliott (GE) channel to approximate the I/D channel in the sense of an equivalent I/D event rate. A lower bound of the channel capacity for the BPMR channel is derived, which supports our claim that commonly used error-correction codes are effective on the I/D channel under the assumption that I/D events are limited to a finite length. Another channel model we investigated is perpendicular magnetic recording model. Advanced signal processing for the pattern-dependent-noise-predictive channel detectors is our focus. Specifically, we propose an adaptive scheme for a hardware design that reduces the complexity of the detector and the truncation/saturation error caused by a fix-point representation of values in the detector. Lastly, we designed a sequence detector for compressively sampled Bluetooth signals, thus allowing data recovery via sub-Nyquist sampling. This detector skips the conventional step of reconstructing the original signal from compressive samples prior to detection. We also propose an adaptive design of the sampling matrix, which almost achieves Nyquist sampling performance with a relatively high compression ratio. Additionally, this adaptive scheme can automatically choose an appropriate compression ratio as a function of E(b)/N₀ without explicit knowledge of it.
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