Prediction of the Spectrum of a Digital Delta–Sigma Modulator Followed by a Polynomial Nonlinearity

This paper presents a mathematical analysis of the power spectral density of the output of a nonlinear block driven by a digital delta-sigma modulator. The nonlinearity is a memoryless third-order polynomial with real coefficients. The analysis yields expressions that predict the noise floor caused by the nonlinearity when the input is constant

A joint coding concept for runlength and charge-limited channels

By making the conventional (d,k) constraint time dependent as a function of the channel process, the wide sense RLL channel has been defined. With the help of the new concept several existing constraints can be described alternatively and many new ones can be constructed. A bit stuff algorithm is suggested for coding wide sense RLL channels. We determine the rate of the bit stuff algorithm as the function of the stuffing probability. We present a few examples for calculating the rate of different constrained codes complying with the newly introduced constraint

Estimating the Sizes of Binary Error-Correcting Constrained Codes

In this paper, we study binary constrained codes that are resilient to bit-flip errors and erasures. In our first approach, we compute the sizes of constrained subcodes of linear codes. Since there exist well-known linear codes that achieve vanishing probabilities of error over the binary symmetric channel (which causes bit-flip errors) and the binary erasure channel, constrained subcodes of such linear codes are also resilient to random bit-flip errors and erasures. We employ a simple identity from the Fourier analysis of Boolean functions, which transforms the problem of counting constrained codewords of linear codes to a question about the structure of the dual code. We illustrate the utility of our method in providing explicit values or efficient algorithms for our counting problem, by showing that the Fourier transform of the indicator function of the constraint is computable, for different constraints. Our second approach is to obtain good upper bounds, using an extension of Delsarte's linear program (LP), on the largest sizes of constrained codes that can correct a fixed number of combinatorial errors or erasures. We observe that the numerical values of our LP-based upper bounds beat the generalized sphere packing bounds of Fazeli, Vardy, and Yaakobi (2015).Comment: 51 pages, 2 figures, 9 tables, to be submitted to the IEEE Journal on Selected Areas in Information Theor