Searcharxiv⌕ Search

arXiv subjects

Frank R. Kschischang

Publications and source records attributed to Frank R. Kschischang.

At least 19 recordsLinked to original sources
arXiv2026

Channel Estimation and LDPC Decoding for Bursty Phase Noise

Time-varying distortions in communication systems can significantly degrade the performance of soft-decision forward error correction. This paper presents a burst-aware (BA) low-density parity-check (LDPC) decoding scheme for channels affected by bursty phase noise. By applying differential coding to a Wiener process with time-varying innovation variance, bursty differential phase noise is obtained. Simulation results demonstrate that, compared to conventional decoding, the BA scheme achieves gains in the signal-to-noise ratio of up to $0.7$~dB at a bit error rate (BER) of $4\cdot10^{-3}$ and more than $1$~dB at a packet error rate (PER) of $1\cdot10^{-2}$. Furthermore, by iterating between channel estimation and \ac{ldpc} decoding, forming the proposed iterative burst-aware (IBA) decoding scheme, the gains increase to $1.4$~dB and more than $3$~dB, respectively. More importantly, the IBA scheme significantly improves robustness to bursty phase noise. Compared with the conventional scheme, the IBA scheme can reduce both \ac{ber} and \ac{per} by up to two orders of magnitude under severe bursty phase noise.

eess.SP↗
arXiv2025

New Difference Triangle Sets by an FPGA-Based Search Technique

We provide some difference triangle sets with scopes that improve upon the best known values. These are found with purpose-built digital circuits realized with field-programmable gate arrays (FPGAs) rather than software algorithms running on general-purpose processors.

cs.IT↗
arXiv2025

Polarization-Dependent Loss Mitigation via Orthogonal Design Precoding and Interference Cancellation

Recent work by Shehadeh and Kschischang provides a simple capacity-achieving scheme for channels with polarization-dependent loss (PDL) under common modeling assumptions via a careful choice of orthogonal-design-based precoding and interference cancellation. This letter extends that work with a simulation-based demonstration showing that this scheme remains highly effective at mitigating PDL in the highly practical setting of 16-QAM with Chase-decoded extended Hamming inner codes rather than the near-capacity inner codes considered in the original work. An alternative near-optimal variation of this scheme is also provided requiring only one inner code rather than two and suffering no penalty in the absence of PDL, making it much more practical.

cs.IT↗
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↗
arXiv2025

Communicating at a record 14.5 bits per received photon through a photon-starved channel

Exploration of the Universe requires communication with Earth, either on a direct path or through a cascade of proximate celestial bodies. Microwaves have traditionally been used for space communication, but electromagnetic waves of higher frequencies, such as in the optical domain, will enable probing farther in space due to their considerably lower diffraction loss. At a given data rate, the ultimate limit to point-to-point optical communication is determined by the received signal power and the photon information efficiency. The latter measures the number of information bits extracted per photon incident on a detector. As distances across space and, consequently, path loss increases, the system that can achieve the highest photon information efficiency will determine the longest distance at which communication is possible. We report here an experimental demonstration of optical detection at a record photon information efficiency of 14.5 bits per incident photon, or 17.8 bits per detected photon, after 87.5 dB of attenuation. Expressed in terms of energy per bit, this corresponds to 8.84 zeptojoules per bit, or 0.069 photons per bit at 1550 nm. To our knowledge, this is the highest photon information efficiency or lowest energy per bit detection system ever demonstrated at optical frequencies. Such a sensitive detection system holds promise for a wide range of applications.

physics.optics↗
arXiv2025

Higher-Order Staircase Codes: A Unified Generalization of High-Throughput Coding Techniques

We introduce a unified generalization of several well-established high-throughput coding techniques including staircase codes, tiled diagonal zipper codes, continuously interleaved codes, open forward error correction (OFEC) codes, and Robinson-Bernstein convolutional codes as special cases. This generalization which we term "higher-order staircase codes" arises from the marriage of two distinct combinatorial objects: difference triangle sets and finite-geometric nets, which have typically been applied separately to code design. We illustrate one possible realization of these codes, obtaining powerful, high-rate, low-error-floor, and low-complexity coding schemes based on simple iterative syndrome-domain decoding of coupled Hamming component codes. We study some properties of difference triangle sets having minimum scope and sum-of-lengths, which correspond to memory-optimal higher-order staircase codes.

cs.IT↗
arXiv2025

Performance-Complexity-Latency Trade-offs of Concatenated RS-SDBCH Codes

Concatenated bit-interleaved and multilevel coded modulation with outer Reed--Solomon codes, inner Chase-algorithm-based soft-decision-decoded Bose--Ray-Chaudhuri--Hocquenghem codes, and four-level pulse amplitude modulation is considered. A semi-analytical formula is derived for estimating the decoded frame error rate (FER) at the output of the additive white Gaussian noise channel, obviating the need for time-consuming Monte Carlo simulations. The formula is used to search a large space of codes (including the KP4 code) to find those achieving good trade-offs among performance (measured by the gap to the constrained Shannon limit at $10^{-13}$ FER), complexity (measured by the number of elementary decoder operations), and latency (measured by overall block length).

cs.IT↗
arXiv2024

Higher-Order Staircase Codes

We generalize staircase codes and tiled diagonal zipper codes, preserving their key properties while allowing each coded symbol to be protected by arbitrarily many component codewords rather than only two. This generalization which we term "higher-order staircase codes" arises from the marriage of two distinct combinatorial objects: difference triangle sets and finite-geometric nets, which have typically been applied separately to code design. We demonstrate one possible realization of these codes, obtaining powerful, high-rate, low-error-floor, and low-complexity coding schemes based on simple iterative syndrome-domain decoding of coupled Hamming component codes. We anticipate that the proposed codes could improve performance--complexity--latency tradeoffs in high-throughput communications applications, most notably fiber-optic, in which classical staircase codes and zipper codes have been applied. We consider the construction of difference triangle sets having minimum scope and sum-of-lengths, which lead to memory-optimal realizations of higher-order staircase codes. These results also enable memory reductions for early families of convolutional codes constructed from difference triangle sets.

cs.IT↗
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↗
arXiv2024

Performance-Complexity-Latency Trade-offs of Concatenated RS-SDBCH Codes

Performance-complexity-latency trade-off curves for rate-0.88 concatenated outer Reed--Solomon codes and inner Chase-algorithm-based soft-decision Bose--Ray-Chaudhuri--Hocquenghem codes with PAM4 constellation using bit-interleaved coded modulation and multilevel coding coded modulation schemes over the AWGN channel are presented.

cs.IT↗
arXiv2024

On Binary Shadow Codes

We generalize the shadow codes of Cherubini and Micheli to include basic polynomials having arbitrary degree, and show that restricting basic polynomials to have degree one or less can result in improved lower bounds on the minimum distance of the code. However, even these improved lower bounds suggest that shadow codes have considerably inferior distance-rate characteristics compared with the concatenation of a Reed-Solomon outer code and a first-order Reed-Muller inner code.

cs.IT↗
arXiv2024

Secure Storage using Maximally Recoverable Locally Repairable Codes

This paper considers data secrecy in distributed storage systems (DSSs) using maximally recoverable locally repairable codes (MR-LRCs). Conventional MR-LRCs are in general not secure against eavesdroppers who can observe the transmitted data during a global repair operation. This work enables nonzero secrecy dimension of DSSs encoded by MR-LRCs through a new repair framework. The key idea is to associate each local group with a central processing unit (CPU), which aggregates and transmits the contribution from the intact nodes of their group to the CPU of a group needing a global repair. The aggregation is enabled by so-called local polynomials that can be generated independently in each group. Two different schemes -- direct repair and forwarded repair -- are considered, and their secrecy dimension using MR-LRCs is derived. Positive secrecy dimension is enabled for several parameter regimes.

cs.IT↗
arXiv2024

Generalized Staircase Codes with Arbitrary Bit Degree

We introduce a natural generalization of staircase codes in which each bit is protected by arbitrarily many component codewords rather than two. This enables powerful energy-efficient FEC based on iterative decoding of Hamming components.

cs.IT↗
arXiv2024

Performance-Complexity-Latency Trade-offs of Concatenated RS-BCH Codes

Using a generating function approach, a computationally tractable expression is derived to predict the frame error rate arising at the output of the binary symmetric channel when a number of outer Reed--Solomon codes are concatenated with a number of inner Bose--Ray-Chaudhuri--Hocquenghem codes, thereby obviating the need for time-consuming Monte Carlo simulations. Measuring (a) code performance via the gap to the Shannon limit, (b) decoding complexity via an estimate of the number of operations per decoded bit, and (c) decoding latency by the overall frame length, a code search is performed to determine the Pareto frontier for performance-complexity-latency trade-offs.

cs.IT↗
arXiv2023

Generalized Spatially-Coupled Product-Like Codes Using Zipper Codes With Irregular Degree

Zipper codes with irregular variable degree are studied. Two new interleaver maps -- chevron and half-chevron -- are described. Simulation results with shortened double-error-correcting Bose--Chaudhuri--Hocquenghem constituent codes show that zipper codes with chevron and half-chevron interleaver maps outperform staircase codes when the rate is below 0.86 and 0.91, respectively, at $10^{-8}$ output bit error rate operating point. In the miscorrection-free decoding scheme, both zipper codes with chevron and half-chevron interleaver maps outperform staircase codes. However, constituent decoder miscorrections induce additional performance gaps.

cs.IT↗
arXiv2023

Practical Considerations in Direct Detection Under Tukey Signalling

The deliberate introduction of controlled intersymbol interference (ISI) in Tukey signalling enables the recovery of signal amplitude and (in part) signal phase under direct detection, giving rise to significant data rate improvements compared to intensity modulation with direct detection (IMDD). The use of an integrate-and-dump detector makes precise waveform shaping unnecessary, thereby equipping the scheme with a high degree of robustness to nonlinear signal distortions introduced by practical modulators. Signal sequences drawn from star quadrature amplitude modulation (SQAM) formats admit an efficient trellis description that facilitates codebook design and low-complexity near maximum-likelihood sequence detection in the presence of both shot noise and thermal noise. Under the practical (though suboptimal) allocation of a 50% duty cycle between ISI-free and ISI-present signalling segments, at a symbol rate of 50 Gbaud and a launch power of -10 dBm the Tukey scheme has a maximum theoretically achievable throughput of 200 Gb/s with an (8,4)-SQAM constellation, while an IMDD scheme achieves about 145 Gb/s using PAM-8. Note that the two mentioned constellations have the same number of magnitude levels and the difference in throughput is resulting from exploiting phase information under using a complex-valued signal constellation.

cs.IT↗