Precise BER Formulas for Asynchronous QPSK-Modulated DS-CDMA Systems Using Random Quaternary Spreading Over Rayleigh Channels

Precise bit-error-ratio (BER) analysis of an asynchronous QPSK-modulated direct-sequence code-division multiple-access system using random quaternary spreading sequences for transmission over Rayleigh channels is performed based on the characteristic-function approach. Its accuracy is verified by our numerical simulation results and also compared with those of the Gaussian approximation. Index Terms—Asynchronous direct-sequence code-division multiple-access (DS-CDMA), bit-error-ratio (BER), precise, QPSK, quarternary spreading, Rayleigh

Distinguishing Hidden Markov Chains

Hidden Markov Chains (HMCs) are commonly used mathematical models of probabilistic systems. They are employed in various fields such as speech recognition, signal processing, and biological sequence analysis. We consider the problem of distinguishing two given HMCs based on an observation sequence that one of the HMCs generates. More precisely, given two HMCs and an observation sequence, a distinguishing algorithm is expected to identify the HMC that generates the observation sequence. Two HMCs are called distinguishable if for every $\varepsilon > 0$ there is a distinguishing algorithm whose error probability is less than $\varepsilon$. We show that one can decide in polynomial time whether two HMCs are distinguishable. Further, we present and analyze two distinguishing algorithms for distinguishable HMCs. The first algorithm makes a decision after processing a fixed number of observations, and it exhibits two-sided error. The second algorithm processes an unbounded number of observations, but the algorithm has only one-sided error. The error probability, for both algorithms, decays exponentially with the number of processed observations. We also provide an algorithm for distinguishing multiple HMCs. Finally, we discuss an application in stochastic runtime verification.Comment: This is the full version of a LICS'16 pape

Nanopore Sequencing Technology and Tools for Genome Assembly: Computational Analysis of the Current State, Bottlenecks and Future Directions

Nanopore sequencing technology has the potential to render other sequencing technologies obsolete with its ability to generate long reads and provide portability. However, high error rates of the technology pose a challenge while generating accurate genome assemblies. The tools used for nanopore sequence analysis are of critical importance as they should overcome the high error rates of the technology. Our goal in this work is to comprehensively analyze current publicly available tools for nanopore sequence analysis to understand their advantages, disadvantages, and performance bottlenecks. It is important to understand where the current tools do not perform well to develop better tools. To this end, we 1) analyze the multiple steps and the associated tools in the genome assembly pipeline using nanopore sequence data, and 2) provide guidelines for determining the appropriate tools for each step. We analyze various combinations of different tools and expose the tradeoffs between accuracy, performance, memory usage and scalability. We conclude that our observations can guide researchers and practitioners in making conscious and effective choices for each step of the genome assembly pipeline using nanopore sequence data. Also, with the help of bottlenecks we have found, developers can improve the current tools or build new ones that are both accurate and fast, in order to overcome the high error rates of the nanopore sequencing technology.Comment: To appear in Briefings in Bioinformatics (BIB), 201

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 class of algorithms for rational approximation of functions formally defined by power series

Corresponding sequence algorithms are defined and shown to exist for a wide range of corresponding continued fractions. Particular examples of these algorithms are given, including an algorithm for forming Pade approximants, and an error analysis is given in one case

Modeling of Quantum Key Distribution System for Secure Information Transfer

This chapter is an analysis of commercial quantum key distribution systems. Upon analysis, the general- ized structure of QKDS with phase coding of a photon state is presented. The structure includes modules that immediately participate in the task of distribution and processing of quantum states. Phases of key sequence productions are studied. Expressions that allow the estimation of physical characteristics of optoelectronic components, as well as information processing algorithms impact to rate of key sequence production, are formed. Information security infrastructure can be utilized, for instance, to formulate requirements to maximize tolerable error level in quantum channel with a given rate of key sequence production