Sampling Time Jitter

Electrical systems which use voltage transitions to represent timing information suffer from a degrading phenomenon called timing jitter. Sampling time jitter is the deviation of sampling clock from its ideal position. As transmission rates raise above couple of GHz, deviations become significant comparing to signalling interval, jitter becomes a fundamental performance bottleneck. Especially in band-limited communication systems that imperfect sampling times result in Inter-Symbol Interference (ISI) jitter is a very limiting factor to decode correct transmitted data. In this case, jitter timing error translates into amplitude error. At first, the effect of sampling time jitter at the received signal is modelled as an additive noise .This additive noise signal which we call it jitter noise is a coloured noise that also depends on input signal. Expressions for jitter noise correlation factors, its cross- correlation with input signal are derived. These correlations depend on input spectral density, timing jitter characteristic function (Fourier transform of jitter probability density function) and whether timing jitter is white or coloured. In case of first order Gauss-Markov process for sampling time jitter it is observed that in high memory regime (highly correlated timing jitter) the spectral density of additive jitter noise is concentrated around higher frequencies. Exploiting this quality, a spectral shaping scheme is used to improve the performance in terms of Bit Error Rate (BER) for an AWGN channel with discrete input corrupted by sampling time jitter. Simulation results comparing the proposed scheme performance with a minimum distance decoder are provided. As another approach the well-known Viterbi Algorithm is used for decoding same AWGN channel suffering from ISI terms due to sampling jitter. The Viterbi algorithm, which basically is a dynamic programming algorithm, finds the most likely input data and jitter times based on observed output sequence. A quantized version of jitter times is used to be able to work with a finite state trellis and to find likelihoods along the paths of the diagram. Then Bit Error Rate curves for different jitter quantization levels and different impulse response lengths of channel are presented

Models and information-theoretic bounds for nanopore sequencing

Nanopore sequencing is an emerging new technology for sequencing DNA, which can read long fragments of DNA (~50,000 bases) in contrast to most current short-read sequencing technologies which can only read hundreds of bases. While nanopore sequencers can acquire long reads, the high error rates (20%-30%) pose a technical challenge. In a nanopore sequencer, a DNA is migrated through a nanopore and current variations are measured. The DNA sequence is inferred from this observed current pattern using an algorithm called a base-caller. In this paper, we propose a mathematical model for the "channel" from the input DNA sequence to the observed current, and calculate bounds on the information extraction capacity of the nanopore sequencer. This model incorporates impairments like (non-linear) inter-symbol interference, deletions, as well as random response. These information bounds have two-fold application: (1) The decoding rate with a uniform input distribution can be used to calculate the average size of the plausible list of DNA sequences given an observed current trace. This bound can be used to benchmark existing base-calling algorithms, as well as serving a performance objective to design better nanopores. (2) When the nanopore sequencer is used as a reader in a DNA storage system, the storage capacity is quantified by our bounds