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We consider the Interval-Passing Algorithm (IPA), an iterative reconstruction algorithm for reconstruction of non-negative sparse real-valued signals from noise-free measurements. We first generalize the IPA by relaxing the original constraint that the measurement matrix must be binary. The new algorithm operates on any non-negative sparse measurement matrix. We give a performance comparison of the generalized IPA with the reconstruction algorithms based on 1) linear programming and 2) verification decoding. Then we identify signals not recoverable by the IPA on a given measurement matrix, and show that these signals are related to stopping sets responsible to failures of iterative decoding algorithms on the binary erasure channel (BEC). Contrary to the results of the iterative decoding on the BEC, the smallest stopping set of a measurement matrix is not the smallest configuration on which the IPA fails. We analyze the recovery of sparse signals on subsets of stopping sets via the IPA and provide sufficient conditions on the exact recovery of sparse signals. Reconstruction performance of the IPA using the IEEE 802.16e LDPC codes as measurement matrices are given to show the effect of stopping sets in the performance of the IPA.

Multilevel run-length-limited (RLL) dc-free codes for optical storage systems are introduced. Theoretically achievable code rates are calculated and spectra determined, and it is demonstrated that the proposed modulating codes have good spectral characteristics. An example of code construction is given using the Adler, Coppersmith, and Hassner algorithm.

A new method for evaluating the power spectral density of multitrack constrained sequences is demonstrated for multitrack (0, G/I) constraints. (0, G/I) constrained sequences are used in magnetic recording systems that employ partial response maximum likelihood (PRML) signalling. Using the proposed approach, the number of states in a directed graph representing the given (0, G/I) constraint is reduced remarkably so that the power spectral density can be easily calculated.

A new method of spectral analysis for coded sequences is introduced. An autocorrelation function is expressed by a system of difference equations. A translation of the system into the frequency domain by a z transform enables an expression for a code spectrum to be obtained after a few simple algebraic transformations. As an example the HDBn code spectrum is evaluated.

A scrambling method for nonequiprobable signalling is proposed. This method uses a lossless compression decoder to produce symbols with unequal probabilities. The relative symbol frequencies and correlation characteristics are calculated and the noisy channel error performance is discussed. In one application of this nonequiprobable signalling procedure it is shown that 0.68 dB of a possible 1.53 dB gain is easily obtained for signal constellation shaping applications.