Performance evaluation for ML sequence detection in ISI channels with Gauss Markov Noise

Inter-symbol interference (ISI) channels with data dependent Gauss Markov noise have been used to model read channels in magnetic recording and other data storage systems. The Viterbi algorithm can be adapted for performing maximum likelihood sequence detection in such channels. However, the problem of finding an analytical upper bound on the bit error rate of the Viterbi detector in this case has not been fully investigated. Current techniques rely on an exhaustive enumeration of short error events and determine the BER using a union bound. In this work, we consider a subset of the class of ISI channels with data dependent Gauss-Markov noise. We derive an upper bound on the pairwise error probability (PEP) between the transmitted bit sequence and the decoded bit sequence that can be expressed as a product of functions depending on current and previous states in the (incorrect) decoded sequence and the (correct) transmitted sequence. In general, the PEP is asymmetric. The average BER over all possible bit sequences is then determined using a pairwise state diagram. Simulations results which corroborate the analysis of upper bound, demonstrate that analytic bound on BER is tight in high SNR regime. In the high SNR regime, our proposed upper bound obviates the need for computationally expensive simulation.Comment: This paper will appear in GlobeCom 201

A communications system perspective for dynamic mode atomic force microscopy, with applications to high-density storage and nanoimaging

In recent times, the atomic force microscope (AFM) has been used in various fields like biology, chemistry, physics and medicine for obtaining atomic level images. The AFM is a high-resolution microscope which can provide the resolution on the order of fractions of a nanometer. It has applications in the field of material characterization, probe based data storage, nano-imaging etc. The prevalent mode of using the AFM is the static mode where the cantilever is in continuous contact with the sample. This is harsh on the probe and the sample. The problem of probe and sample wear can be partly addressed by using the dynamic mode operation with the high quality factor cantilevers. In the dynamic mode operation, the cantilever is forced sinusoidally using a dither piezo. The oscillating cantilever gently taps the sample which reduces the probe-sample wear. In this dissertation, we demonstrate that viewing the dynamic mode operation from a communication systems perspective can yield huge gains in nano-interrogation speed and fidelity. In the first part of the dissertation, we have considered a data storage system that operates by encoding information as topographic profiles on a polymer medium. A cantilever probe with a sharp tip (few nm radius) is used to create and sense the presence of topographic profiles, resulting in a density of few Tb per square inch. The usage of the static mode is harsh on the probe and the media. In this work, the high quality factor dynamic mode operation, which alleviates the probe-media wear, is analyzed. The read operation is modeled as a communication channel which incorporates system memory due to inter-symbol interference and the cantilever state. We demonstrate an appropriate level of abstraction of this complex nanoscale system that obviates the need for an involved physical model. Next, a solution to the maximum likelihood sequence detection problem based on the Viterbi algorithm is devised. Experimental and simulation results demonstrate that the performance of this detector is several orders of magnitude better than the performance of other existing schemes. In the second part of the dissertation, we have considered another interesting application of the dynamic mode AFM in the field of nano-imaging. Nano-imaging has played a vital role in biology, chemistry and physics as it enables interrogation of material with sub-nanometer resolution. However, current nano-imaging techniques are too slow to be useful in the high speed applications of interest such as studying the evolution of certain biological processes over time that involve very small time scales. In this work, we present a high speed one-bit imaging technique using the dynamic mode AFM with a high quality factor cantilever. We propose a communication channel model for the cantilever based nano-imaging system. Next, we devise an imaging algorithm that incorporates a learned prior from the previous scan line while detecting the features on the current scan line. Experimental results demonstrate that our proposed algorithm provides significantly better image resolution compared to current nano-imaging techniques at high scanning speed. While modeling the probe-based data storage system and the cantilever based nano-imaging system, it has been observed that the channel models exhibit the behavior similar to intersymbol-interference (ISI) channel with data dependent time-correlated noise. The Viterbi algorithm can be adapted for performing maximum likelihood sequence detection in such channels. However, the problem of finding an analytical upper bound on the bit error rate of the Viterbi detector in this case has not been fully investigated. In the third part of the dissertation, we have considered a subset of the class of ISI channels with data dependent Gauss-Markov noise. We derive an upper bound on the pairwise error probability (PEP) between the transmitted bit sequence and the decoded bit sequence that can be expressed as a product of functions depending on current and previous states in the (incorrect) decoded sequence and the (correct) transmitted sequence. In general, the PEP is asymmetric. The average BER over all possible bit sequences is then determined using a pairwise state diagram. Simulations results demonstrate that analytic bound on BER is tight in high SNR regime

Performance Evaluation for ML Sequence Detection in ISI Channels with Gauss Markov Noise

Inter-symbol interference (ISI) channels with data dependent Gauss Markov noise have been used to model read channels in magnetic recording and other data storage systems. The Viterbi algorithm can be adapted for performing maximum likelihood sequence detection in such channels. However, the problem of finding an analytical upper bound on the bit error rate of the Viterbi detector in this case has not been fully investigated. Current techniques rely on an exhaustive enumeration of short error events and determine the BER using a union bound. In this work, we consider a subset of the class of ISI channels with data dependent Gauss-Markov noise. We derive an upper bound on the pairwise error probability (PEP) between the transmitted bit sequence and the decoded bit sequence that can be expressed as a product of functions depending on current and previous states in the (incorrect) decoded sequence and the (correct) transmitted sequence. In general, the PEP is asymmetric. The average BER over all possible bit sequences is then determined using a pairwise state diagram. Simulations results which corroborate the analysis of upper bound, demonstrate that analytic bound on BER is tight in high SNR regime. In the high SNR regime, our proposed upper bound obviates the need for computationally expensive simulation.This is a manuscript from the IEEE Global Telecommunications Conference (2010), doi:10.1109/GLOCOM.2010.5683963. Posted with permission.</p