Skip-Sliding Window Codes

Constrained coding is used widely in digital communication and storage systems. In this paper, we study a generalized sliding window constraint called the skip-sliding window. A skip-sliding window (SSW) code is defined in terms of the length $L$ of a sliding window, skip length $J$, and cost constraint $E$ in each sliding window. Each valid codeword of length $L + kJ$ is determined by $k+1$ windows of length $L$ where window $i$ starts at $(iJ + 1)$th symbol for all non-negative integers $i$ such that $i \leq k$; and the cost constraint $E$ in each window must be satisfied. In this work, two methods are given to enumerate the size of SSW codes and further refinements are made to reduce the enumeration complexity. Using the proposed enumeration methods, the noiseless capacity of binary SSW codes is determined and observations such as greater capacity than other classes of codes are made. Moreover, some noisy capacity bounds are given. SSW coding constraints arise in various applications including simultaneous energy and information transfer.Comment: 28 pages, 11 figure

Non Data Aided Parameter Estimation for Multi-User ARGOS Receivers

In this paper, parameter estimators are analyzed in the context of Successive Interference Cancelation (SIC) receivers for the ARGOS system. A Non Data Aided (NDA) feed forward estimator is proposed for the amplitude and the carrier phase parameters. Time delays are assumed to be known. A Window Accumulator (WA) is used to reduce the influence of the additive noise. In the presence of frequency offset, the window length L cannot be chosen arbitrarily large but an optimal length Lopt can be determined. However, because the estimator induces a different optimal length for each parameter, a trade-off must be made. We show that a window length of around 35 samples induces mean square errors (MSEs) lower than 0.012 for both parameters. The MSE of the proposed estimator is also compared to the Modified Cram´er Rao Bound (MCRB)

Window Length Selection and Signal-Noise Separation and Reconstruction in Singular Spectrum Analysis

In Singular Spectrum Analysis (SSA) window length is a critical tuning parameter that must be assigned by the practitioner. This paper provides a theoretical analysis of signal-noise separation and reconstruction in SSA that can serve as a guide to optimal window choice. We establish numerical bounds on the mean squared reconstruction error and present their almost sure limits under very general regularity conditions on the underlying data generating mechanism. We also provide asymptotic bounds for the mean squared separation error. Evidence obtained using simulation experiments indicates that the theoretical properties are reflected in observed behaviour, even in relatively small samples, and the results indicate how an optimal choice for the window length can be made.Dimension, Embedding, Mean squared error, Reconstruction, Signal-noise separation, Window length.

An attempt to observe economy globalization: the cross correlation distance evolution of the top 19 GDP's

Economy correlations between the 19 richest countries are investigated through their Gross Domestic Product increments. A distance is defined between increment correlation matrix elements and their evolution studied as a function of time and time window size. Unidirectional and Bidirectional Minimal Length Paths are generated and analyzed for different time windows. A sort of critical correlation time window is found indicating a transition for best observations. The mean length path decreases with time, indicating stronger correlations. A new method for estimating a realistic minimal time window to observe correlations and deduce macroeconomy conclusions from such features is thus suggested.Comment: to be published in the Dyses05 proceedings, in Int. J. Mod Phys C 15 pages, 5 figures, 1 tabl