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Abstract
In this dissertation, we investigate the fundamental impact of timing jitter on the storage and transmission of information. In Part I, we consider transmission using hard-limiting channels, in the presence of timing jitter. We introduce the Discrete Memoryless Jitter Channel (DMJC), an information theoretic channel model having a quantized time axis, that reflects timing jitter on a hard-limited channel. We derive bounds on the channel capacity of the DMJC for d-constrained inputs, and we prove the coding theorem and its converse for the DMJC. We introduce the Continuous-Time Memoryless Jitter Channel (CT-MJC), that reflects timing jitter on a similar hard-limited channel without time quantization. We also derive bounds on the capacity of the CT-MJC. We study spectral properties of timing jitter on a hard-limited channel. The obtained results are used to analyse carrier to noise ratio (CNR) measurements in the field of optical recording. We compare linear density estimates of the CT-MJC with those of classical information theoretic channel models, which are based on additive noise.
In Part II, we consider the combination of additive noise and sampling timing jitter, which act as signal impairments for band-limited, Gaussian signals. We introduce timing jitter as a random process and study its influence on the signal dependent amplitude deviations of the resulting samples. We introduce the Additive White Gaussian Noise and Jitter channel (AWGN&J), that models the combination of additive noise and sampling jitter. We obtain tight bounds on the mutual information of the AWGN&J channel for a Gaussian input. For Gaussian signals, we derive the optimum spectral input distribution. It turns out that a kind of 'distorted waterfilling' is found that, dependent on the ratio between additive and jitter noise, leads to an optimal power spectral density that peaks at the low frequencies. In particular, we find that for Gaussian signals, sampling timing jitter leads to a finite capacity, independent of the input power.
