arXiv subjects

Susanna E. Rumsey

Publications and source records attributed to Susanna E. Rumsey.

3 recordsLinked to original sources

arXiv2025

Quasicyclic Principal Component Analysis

We present quasicyclic principal component analysis (QPCA), a generalization of principal component analysis (PCA), that determines an optimized basis for a dataset in terms of families of shift-orthogonal principal vectors. This is of particular interest when analyzing cyclostationary data, whose cyclic structure is not exploited by the standard PCA algorithm. We first formulate QPCA as an optimization problem, which we show may be decomposed into a series of PCA problems in the frequency domain. We then formalize our solution as an explicit algorithm and analyze its computational complexity. Finally, we provide some examples of applications of QPCA to cyclostationary signal processing data, including an investigation of carrier pulse recovery, a presentation of methods for estimating an unknown oversampling rate, and a discussion of an appropriate approach for pre-processing data with a non-integer oversampling rate in order to better apply the QPCA algorithm.

math.NA↗

arXiv2024

Soft Demapping of Spherical Codes from Cartesian Powers of PAM Constellations

For applications in concatenated coding for optical communications systems, we examine soft-demapping of short spherical codes constructed as constant-energy shells of the Cartesian power of pulse amplitude modulation constellations. These are unions of permutation codes having the same average power. We construct a list decoder for permutation codes by adapting Murty's algorithm, which is then used to determine mutual information curves for these permutation codes. In the process, we discover a straightforward expression for determining the likelihood of large subcodes of permutation codes called orbits. We introduce a simple process, called orbit demapping, that allows us to extract soft information from noisy permutation codewords. In a sample communication system with probabilistic amplitude shaping protected by a standard low-density parity-check code that employs short permutation codes, we demonstrate that orbit demapping provides a gain of about 0.3 dB in signal-to-noise ratio compared to the traditional symbol-by-symbol demapping. By using spherical codes composed of unions of permutation codes, we can increase the input entropy compared to using permutation codes alone. In one scheme, we consider a union of a small number of permutation codes. In this case, orbit demapping provides about 0.2 dB gain compared to the traditional method. In another scheme, we use all possible permutations to form a spherical code that exhibits a computationally feasible trellis representation. The soft information obtained using the BCJR algorithm outperforms the traditional symbol-by-symbol method by 0.1 dB. Using the spherical codes containing all possible permutation codes of the same average power and the BCJR algorithm, a gain of 0.5 dB is observed. Comparison of the achievable information rates of bit-metric decoding verifies the observed gains.

cs.IT↗

arXiv2022

Information Density in Multi-Layer Resistive Memories

Resistive memories store information in a crossbar arrangement of two-terminal devices that can be programmed to patterns of high or low resistance. While extremely compact, this technology suffers from the "sneak-path" problem: certain information patterns cannot be recovered, as multiple low resistances in parallel make a high resistance indistinguishable from a low resistance. In this paper, a multi-layer device is considered, and the number of bits it can store is derived exactly and asymptotic bounds are developed. The information density of a series of isolated arrays with extreme aspect ratios is derived in the single- and multi-layer cases with and without peripheral selection circuitry. This density is shown to be non-zero in the limit, unlike that of the arrays with moderate aspect ratios previously considered. A simple encoding scheme that achieves capacity asymptotically is presented.

cs.IT↗