arXiv subjects

Po-Ning Chen

Publications and source records attributed to Po-Ning Chen.

At least 19 recordsLinked to original sources

arXiv2025

Toward Universal Decoding of Binary Linear Block Codes via Enhanced Polar Transformations

Binary linear block codes (BLBCs) are essential to modern communication, but their diverse structures often require tailor-made decoders, increasing complexity. This work introduces enhanced polar decoding ($\mathsf{PD}^+$), a universal soft decoding algorithm that transforms any BLBC into a polar-like code compatible with efficient polar code decoders such as successive cancellation list (SCL) decoding. Key innovations in $\mathsf{PD}^+$ include pruning polar kernels, shortening codes, and leveraging a simulated annealing algorithm to optimize transformations. These enable $\mathsf{PD}^+$ to achieve competitive or superior performance to state-of-the-art algorithms like OSD and GRAND across various codes, including extended BCH, extended Golay, and binary quadratic residue codes, with significantly lower complexity. Moreover, $\mathsf{PD}^+$ is designed to be forward-compatible with advancements in polar code decoding techniques and AI-driven search methods, making it a robust and versatile solution for universal BLBC decoding in both present and future systems.

cs.IT↗

arXiv2024

Near horizon limit of the Wang--Yau quasi-local mass

In this article, we compute the limit of the Wang--Yau quasi-local mass on a family of surfaces approaching the apparent horizon (the near horizon limit). Recently, Pook-Kolb, Zhao, Andersson, Krishnan, and Yau investigated the near horizon limit of the Wang--Yau quasi-local mass in binary black hole mergers in \cite{PK-Z-A-K-Y} and conjectured that the optimal embeddings approach the isometric embedding of the horizon into $\R^3$. Moreover, the quasi-local mass converges to the total mean curvature of the horizon in $\R^3$. The vanishing of the norm of the mean curvature vector implies special properties for the Wang--Yau quasi-local energy and the optimal embedding equation. We utilize these features to prove the existence and uniqueness of the optimal embedding and investigate the minimization of the Wang--Yau quasi-local energy. In particular, we prove the continuity of the quasi-local mass in the near horizon limit.

gr-qc↗

arXiv2023

Singularity formation for the higher dimensional Skyrme model in the strong field limit

This paper concerns the formation of singularities in the classical $(5+1)$-dimensional, co-rotational Skyrme model. While it is well established that blowup is excluded in $(3+1)$-dimensions, nothing appears to be known in the higher dimensional case. We prove that the model, in the so-called strong field limit, admits an explicit self-similar solution which is asymptotically stable within backwards light cones. From a technical point of view, the main obstacle to this result is the presence of derivative nonlinearities in the corresponding evolution equation. These introduce first order terms in the linearized flow which render standard techniques useless. We demonstrate how this problem can be bypassed by using structural properties of the Skyrme model.

math.AP↗

arXiv2023

Two rigidity results for surfaces in Schwarzschild spacetimes

We prove two rigidity results for surfaces lying in the standard null hypersurfaces of Schwarzschild spacetime satisfying certain mean curvature type equations. The first is for the equation $α_H = - d\log |H|$ studied in \cite{WWZ}. The second is for the mean curvature vector of constant norm. The latter is related to the Liouville and Obata Theorem in conformal geometry.

math.DG↗

arXiv2023

Transformation of mass-angular momentum aspect under BMS transformations

In this article, we present the definitive transformation formulae of the mass aspect and angular momentum aspect under BMS transformations. Two different approaches that lead to the same formulae are taken. In the first approach, the formulae are derived by reading off the aspect functions from the curvature tensor. While in the second and more traditional approach, we read them off from the metric coefficients. As an application of the angular momentum aspect transformation formula, we directly verify a relation concerning the Dray-Streubel angular momentum. It also enables us to reinterpret our calculations in terms of differential forms on null infinity, and leads to an exact expression of the Drey-Streubel angular momentum of a general section. The formulae we obtained played crucial roles in our recent work on supertranslation invariant charges, and resolved some inconsistencies in the literature.

gr-qc↗

arXiv2023

On Decoder Ties for the Binary Symmetric Channel with Arbitrarily Distributed Input

The error probability of block codes sent under a non-uniform input distribution over the memoryless binary symmetric channel (BSC) and decoded via the maximum a posteriori (MAP) decoding rule is investigated. It is proved that the ratio of the probability of MAP decoder ties to the probability of error when no MAP decoding ties occur grows at most linearly in blocklength, thus showing that decoder ties do not affect the code's error exponent. This result generalizes a similar recent result shown for the case of block codes transmitted over the BSC under a uniform input distribution.

cs.IT↗

arXiv2022

Cross-Section Continuity of Definitions of Angular Momentum

We introduce a notion of "cross-section continuity" as a criterion for the viability of definitions of angular momentum, $J$, at null infinity: If a sequence of cross-sections, ${\mathcal C}_n$, of null infinity converges uniformly to a cross-section ${\mathcal C}$, then the angular momentum, $J_n$, on ${\mathcal C}_n$ should converge to the angular momentum, $J$, on ${\mathcal C}$. The Dray-Streubel (DS) definition of angular momentum automatically satisfies this criterion by virtue of the existence of a well defined flux associated with this definition. However, we show that the one-parameter modification of the DS definition proposed by Compere and Nichols (CN) -- which encompasses numerous other alternative definitions -- does not satisfy cross-section continuity. On the other hand, we prove that the Chen-Wang-Yau (CWY) definition does satisfy the cross-section continuity criterion.

gr-qc↗

arXiv2022

Co-dimension one stable blowup for the quadratic wave equation beyond the light cone

We study the stability of an explicitly known, non-trivial self-similar blowup solution of the quadratic wave equation in the lowest energy supercritical dimension $d = 7$. This solution blows up at a single point and extends naturally away from the singularity. By using hyperboloidal similarity coordinates, we prove the conditional nonlinear asymptotic stability of this solution under small, compactly supported radial perturbations in a region of spacetime which can be made arbitrarily close to the Cauchy horizon of the singularity. To achieve this, we rigorously solve the underlying spectral problem and show that the solution has exactly one genuine instability. The unstable nature of the solution requires a careful construction of suitably adjusted initial data at $t = 0$, which, when propagated to a family of spacelike hypersurfaces of constant hyperboloidal time, takes the required form to guarantee convergence. By this, we introduce a new canonical method to investigate unstable self-similar solutions for nonlinear wave equations within the framework of hyperboloidal similarity coordinates.

math.AP↗

arXiv2022

The Story of $1/e$: ALOHA-based and Reinforcement-Learning-based Random Access for Delay-Constrained Communications

Motivated by the proliferation of real-time applications in multimedia communication systems, tactile Internet, and cyber-physical systems, supporting delay-constrained traffic becomes critical for such systems. In delay-constrained traffic, each packet has a hard deadline; when it is not delivered before its deadline is up, it becomes useless and will be removed from the system. In this work, we focus on designing random access schemes for delay-constrained wireless communications. We first investigate three ALOHA-based schemes and prove that the system timely throughput of all three schemes under corresponding optimal transmission probabilities asymptotically converges to $1/e$, same as the well-known throughput limit for delay-unconstrained ALOHA systems. The fundamental reason why ALOHA-based schemes cannot achieve asymptotical system timely throughput beyond $1/e$ is that all active ALOHA stations access the channel with the same probability in any slot. To go beyond $1/e$, we propose a reinforcement-learning-based scheme for delay-constrained wireless communications, called RLRA-DC, under which different stations collaboratively attain different transmission probabilities by only interacting with the access point. Our numerical result shows that the system timely throughput of RLRA-DC can be as high as 0.8 for tens of stations and can still reach 0.6 even for thousands of stations, much larger than $1/e$.

cs.IT↗

arXiv2022

Conserved quantities in general relativity -- the view from null infinity

In general relativity, an idealized distant observer is situated at future null infinity where light rays emitted from the source approach. This article concerns conserved quantities such as mass, energy-momentum, angular momentum, and center of mass at future null infinity. The classical definitions of Bondi mass at future null infinity ascertains the mass radiated away in gravitational waves distinctively. However, the same question for other conserved quantities such as angular momentum has been a subtle issue since the discovery of "supertranslation ambiguity" in the 1960's. Recently, new definitions of angular momentum and center of mass were proposed and proved to be free of such ambiguity [12,14]. These new definitions arise as limits of the Chen-Wang-Yau quasilocal conserved quantities, which are based on the theory of optimal isometric embedding and quasilocal mass of Wang-Yau. It is the purpose of this note to discuss these recent developments

gr-qc↗

arXiv2022

Supertranslation invariance of angular momentum at null infinity in double null gauge

The supertranslation invariance of the Chen-Wang-Yau (CWY) angular momentum in the Bondi-Sachs formalism/gauge was ascertained by the authors in \cite{CKWWY_evol, CWWY_atmp}. In this article, we study the corresponding problem in the double null gauge. In particular, supertranslation ambiguity of this gauge is identified and the CWY angular momentum is proven to be free of this ambiguity. A similar result is obtained for the CWY center of mass integral.

gr-qc↗

arXiv2021

Decoder Ties Do Not Affect the Error Exponent of the Memoryless Binary Symmetric Channel

The generalized Poor-Verdu error lower bound established in [1] for multihypothesis testing is studied in the classical channel coding context. It is proved that for any sequence of block codes sent over the memoryless binary symmetric channel (BSC), the minimum probability of error (under maximum likelihood decoding) has a relative deviation from the generalized bound that grows at most linearly in blocklength. This result directly implies that for arbitrary codes used over the BSC, decoder ties can only affect the subexponential behavior of the minimum probability of error.

cs.IT↗

arXiv2021

BMS charges without supertranslation ambiguity

The asymptotic symmetry of an isolated gravitating system, or the Bondi-Metzner-Sachs (BMS) group, contains an infinite-dimensional subgroup of supertranslations. Despite decades of study, the difficulties with the "supertranslation ambiguity" persisted in making sense of fundamental notions such as the angular momentum carried away by gravitational radiation. The issues of angular momentum and center of mass were resolved by the authors recently. In this paper, we address the issues for conserved charges with respect to both the classical BMS algebra and the extended BMS algebra. In particular, supertranslation ambiguity of the classical charge for the BMS algebra, as well as the extended BMS algebra, is completely identified. We then propose a new invariant charge by adding correction terms to the classical charge. With the presence of these correction terms, the new invariant charge is then shown to be free from any supertranslation ambiguity. Finally, we prove that both the classical and invariant charges for the extended BMS algebra are invariant under the boost transformations.

gr-qc↗

arXiv2021

Evolution of angular momentum and center of mass at null infinity

We study how conserved quantities such as angular momentum and center of mass evolve with respect to the retarded time at null infinity, which is described in terms of a Bondi-Sachs coordinate system. These evolution formulae complement the classical Bondi mass loss formula for gravitational radiation. They are further expressed in terms of the potentials of the shear and news tensors. The consequences that follow from these formulae are (1) Supertranslation invariance of the fluxes of the CWY conserved quantities. (2) A conservation law of angular momentum à la Christodoulou. (3) A duality paradigm for null infinity. In particular, the supertranslation invariance distinguishes the CWY angular momentum and center of mass from the classical definitions.

gr-qc↗

arXiv2021

Supertranslation invariance of angular momentum

LIGO's successful detection of gravitational waves has revitalized the theoretical understanding of the angular momentum carried away by gravitational radiation. An infinite dimensional supertranslation ambiguity has presented an essential difficulty for decades of study. Recent advances were made to address and quantify the supertranslation ambiguity in the context of compact binary coalescence. Here we present the first definition of angular momentum in general relativity that is completely free from supertranslation ambiguity. The new definition was derived from the limit of the quasilocal angular momentum defined previously by the authors. A new definition of center of mass at null infinity is also proposed and shown to be supertranslation invariant. Together with the classical Bondi-Sachs energy-momentum, they form a complete set of conserved quantities at null infinity that transform according to basic physical laws.

gr-qc↗

arXiv2020

Update Bandwidth for Distributed Storage

In this paper, we consider the update bandwidth in distributed storage systems~(DSSs). The update bandwidth, which measures the transmission efficiency of the update process in DSSs, is defined as the total amount of data symbols transferred in the network when the data symbols stored in a node are updated. This paper contains the following contributions. First, we establish the closed-form expression of the minimum update bandwidth attainable by irregular array codes. Second, after defining a class of irregular array codes, called Minimum Update Bandwidth~(MUB) codes, which achieve the minimum update bandwidth of irregular array codes, we determine the smallest code redundancy attainable by MUB codes. Third, the code parameters, with which the minimum code redundancy of irregular array codes and the smallest code redundancy of MUB codes can be equal, are identified, which allows us to define MR-MUB codes as a class of irregular array codes that simultaneously achieve the minimum code redundancy and the minimum update bandwidth. Fourth, we introduce explicit code constructions of MR-MUB codes and MUB codes with the smallest code redundancy. Fifth, we establish a lower bound of the update complexity of MR-MUB codes, which can be used to prove that the minimum update complexity of irregular array codes may not be achieved by MR-MUB codes. Last, we construct a class of $(n = k + 2, k)$ vertical maximum-distance separable (MDS) array codes that can achieve all of the minimum code redundancy, the minimum update bandwidth and the optimal repair bandwidth of irregular array codes.

cs.IT↗

arXiv2020

Quasi-local Penrose inequalities with electric charge

The Riemannian Penrose inequality is a remarkable geometric inequality between the ADM mass of an asymptotically flat manifold with non-negative scalar curvature and the area of its outermost minimal surface. A version of the Riemannian Penrose inequality has also been established for the Einstein-Maxwell equations, where the lower bound on the mass also depends on the electric charge. In the context of quasi-local mass, one is interested in determining if, and for which quasi-local mass definitions, a quasi-local version of these inequalities also holds. It is known that the Brown-York quasi-local mass satisfies a quasi-local Riemannian Penrose inequality, however in the context of the Einstein-Maxwell equations, one expects that a quasi-local Riemannian Penrose inequality should also include a contribution from the electric charge. This article builds on ideas of Lu and Miao and of the first-named author to prove some charged quasi-local Penrose inequalities for a class of compact manifolds with boundary. In particular, we impose that the boundary is isometric to a closed surface in a suitable Reissner-Nordström manifold, which serves as a reference manifold for the quasi-local mass that we work with. In the case where the reference manifold has zero mass and non-zero electric charge, the lower bound on quasi-local mass is exactly the lower bound on the ADM mass given by the charged Riemannian Penrose inequality.

math.DG↗

arXiv2020

The Asymptotic Generalized Poor-Verdu Bound Achieves the BSC Error Exponent at Zero Rate

The generalized Poor-Verdu error lower bound for multihypothesis testing is revisited. Its asymptotic expression is established in closed-form as its tilting parameter grows to infinity. It is also shown that the asymptotic generalized bound achieves the error exponent (or reliability function) of the memoryless binary symmetric channel at zero coding rates.

cs.IT↗