arXiv subjects

Cheng-Shang Chang

Publications and source records attributed to Cheng-Shang Chang.

At least 19 recordsLinked to original sources

arXiv2026

Dynamic Hierarchical Birkhoff-von Neumann Decomposition for All-to-All GPU Communication

All-to-all GPU communication is a critical bottleneck in large-scale training clusters, where completion time is constrained by per-port bandwidth and can be severely impacted by traffic skew across GPUs and network interface cards (NICs). This issue is amplified by the two-tier structure of modern GPU systems, which combine fast intra-server links with much slower inter-server networks. Motivated by recent system observations that highlight the importance of traffic reshaping and hierarchy awareness, we study all-to-all scheduling from an online switching and queueing-theoretic perspective. We propose a dynamic hierarchical Birkhoff--von Neumann (BvN) decomposition framework tailored to two-tier GPU fabrics. At each frame boundary, traffic is first balanced within each server using simple local operations to mitigate micro-level GPU/NIC skew while preserving aggregate server-to-server demand. A hierarchical BvN decomposition is then applied at the server level and refined into GPU-level matchings, significantly reducing decomposition complexity relative to a flat GPU-level approach. By integrating this construction with the dynamic frame sizing (DFS) principle, we obtain an online scheduler with provable stability under admissible Poisson arrivals. Simulations demonstrate substantial reductions in mean frame length, particularly under server-localized hotspot traffic.

cs.NI↗

arXiv2025

Efficient Multichannel Rendezvous Algorithms without Global Channel Enumeration

The multichannel rendezvous problem (MRP) is a critical challenge for neighbor discovery in IoT applications, requiring two users to find each other by hopping among available channels over time. This paper addresses the MRP in scenarios where a global channel enumeration system is unavailable. To tackle this challenge, we propose a suite of low-complexity multichannel rendezvous algorithms based on locality-sensitive hashing (LSH), tailored for environments where channel labels are unique L-bit identifiers rather than globally coordinated indices. Inspired by consistent hashing techniques in distributed systems, we develop the LC-LSH and LC-LSH4 algorithms for synchronous and asynchronous settings, respectively. These algorithms significantly reduce implementation complexity while maintaining expected time-to-rendezvous (ETTR) performance comparable to state-of-the-art methods that require global channel enumeration. To ensure bounded maximum time-to-rendezvous (MTTR) in the asynchronous setting, we further introduce the ASYM-LC-LSH4 and QR-LC-LSH4 algorithms by embedding multiset-enhanced modular clock and quasi-random techniques into our framework. Extensive simulations demonstrate that the proposed algorithms achieve performance comparable to state-of-the-art LSH algorithms in both synchronous and asynchronous settings, even without a global channel enumeration system.

cs.NI↗

arXiv2025

Consistent Channel Hopping Algorithms for the Multichannel Rendezvous Problem with Heterogeneous Available Channel Sets

We propose a theoretical framework for consistent channel hopping algorithms to address the multichannel rendezvous problem (MRP) in wireless networks with heterogeneous available channel sets. A channel selection function is called consistent if the selected channel remains unchanged when the available channel set shrinks, provided the selected channel is still available. We show that all consistent channel selection functions are equivalent to the function that always selects the smallest-index channel under appropriate channel relabeling. This leads to a natural representation of a consistent channel hopping algorithm as a sequence of permutations. For the two-user MRP, we characterize rendezvous time slots using a fictitious user and derive tight bounds on the maximum time-to-rendezvous (MTTR) and expected time-to-rendezvous (ETTR). Notably, the ETTR is shown to be the inverse of the Jaccard index when permutations are randomly selected. We also prove that consistent channel hopping algorithms maximize the rendezvous probability. To reduce implementation complexity, we propose the modulo algorithm, which uses modular arithmetic with one-cycle permutations and achieves performance comparable to locality-sensitive hashing (LSH)-based algorithms. The framework is extended to multiple users, with novel strategies such as stick-together, spread-out, and a hybrid method that accelerates rendezvous in both synchronous and asynchronous settings. Simulation results confirm the effectiveness and scalability of the proposed algorithms.

cs.NI↗

arXiv2025

Fast Multichannel Topology Discovery in Cognitive Radio Networks

In Cognitive Radio Networks (CRNs), secondary users (SUs) must efficiently discover each other across multiple communication channels while avoiding interference from primary users (PUs). Traditional multichannel rendezvous algorithms primarily focus on enabling pairs of SUs to find common channels without explicitly considering the underlying network topology. In this paper, we extend the rendezvous framework to explicitly incorporate network topology, introducing the \emph{multichannel topology discovery problem}. We propose a novel \emph{pseudo-random sweep algorithm with forward replacement}, designed to minimize correlation between consecutive unsuccessful rendezvous attempts, thereby significantly reducing the expected time-to-discovery (ETTD). Additionally, we introduce a \emph{threshold-based stick-together strategy} that dynamically synchronizes user hopping sequences based on partially known information, further enhancing discovery efficiency. Extensive simulation results validate our theoretical analysis, demonstrating that the proposed algorithms substantially outperform conventional (sequential) sweep methods.

cs.NI↗

arXiv2024

Convolutional Coded Poisson Receivers

In this paper, we present a framework for convolutional coded Poisson receivers (CCPRs) that incorporates spatially coupled methods into the architecture of coded Poisson receivers (CPRs). We use density evolution equations to track the packet decoding process with the successive interference cancellation (SIC) technique. We derive outer bounds for the stability region of CPRs when the underlying channel can be modeled by a $ϕ$-ALOHA receiver. The stability region is the set of loads that every packet can be successfully received with a probability of 1. Our outer bounds extend those of the spatially-coupled Irregular Repetition Slotted ALOHA (IRSA) protocol and apply to channel models with multiple traffic classes. For CCPRs with a single class of users, the stability region is reduced to an interval. Therefore, it can be characterized by a percolation threshold. We study the potential threshold by the potential function of the base CPR used for constructing a CCPR. In addition, we prove that the CCPR is stable under a technical condition for the window size. For the multiclass scenario, we recursively evaluate the density evolution equations to determine the boundaries of the stability region. Numerical results demonstrate that the stability region of CCPRs can be enlarged compared to that of CPRs by leveraging the spatially-coupled method. Moreover, the stability region of CCPRs is close to our outer bounds when the window size is large.

cs.IT↗

arXiv2024

A Mathematical Theory for Learning Semantic Languages by Abstract Learners

Recent advances in Large Language Models (LLMs) have demonstrated the emergence of capabilities (learned skills) when the number of system parameters and the size of training data surpass certain thresholds. The exact mechanisms behind such phenomena are not fully understood and remain a topic of active research. Inspired by the skill-text bipartite graph model proposed by Arora and Goyal for modeling semantic languages, we develop a mathematical theory to explain the emergence of learned skills, taking the learning (or training) process into account. Our approach models the learning process for skills in the skill-text bipartite graph as an iterative decoding process in Low-Density Parity Check (LDPC) codes and Irregular Repetition Slotted ALOHA (IRSA). Using density evolution analysis, we demonstrate the emergence of learned skills when the ratio of the number of training texts to the number of skills exceeds a certain threshold. Our analysis also yields a scaling law for testing errors relative to this ratio. Upon completion of the training, the association of learned skills can also be acquired to form a skill association graph. We use site percolation analysis to derive the conditions for the existence of a giant component in the skill association graph. Our analysis can also be extended to the setting with a hierarchy of skills, where a fine-tuned model is built upon a foundation model. It is also applicable to the setting with multiple classes of skills and texts. As an important application, we propose a method for semantic compression and discuss its connections to semantic communication.

cs.CL↗

arXiv2023

InterAct: Exploring the Potentials of ChatGPT as a Cooperative Agent

This research paper delves into the integration of OpenAI's ChatGPT into embodied agent systems, evaluating its influence on interactive decision-making benchmark. Drawing a parallel to the concept of people assuming roles according to their unique strengths, we introduce InterAct. In this approach, we feed ChatGPT with varied prompts, assigning it a numerous roles like a checker and a sorter, then integrating them with the original language model. Our research shows a remarkable success rate of 98% in AlfWorld, which consists of 6 different tasks in a simulated household environment, emphasizing the significance of proficient prompt engineering. The results highlight ChatGPT's competence in comprehending and performing intricate tasks effectively in real-world settings, thus paving the way for further advancements in task planning.

cs.AI↗

arXiv2023

Degree-degree Correlated Low-density Parity-check Codes Over a Binary Erasure Channel

Most existing works on analyzing the performance of a random ensemble of low-density parity-check (LDPC) codes assume that the degree distributions of the two ends of a randomly selected edge are independent. In the paper, we take one step further and consider ensembles of LDPC codes with degree-degree correlations. For this, we propose two methods to construct an ensemble of degree-degree correlated LDPC codes. We then derive a system of density evolution equations for such degree-degree correlated LDPC codes over a binary erasure channel (BEC). By conducting extensive numerical experiments, we show how the degree-degree correlation affects the performance of LDPC codes. Our numerical results show that LDPC codes with negative degree-degree correlation could improve the maximum tolerable erasure probability. Moreover, increasing the negative degree-degree correlation could lead to better unequal error protection (UEP) design.

cs.IT↗

arXiv2023

A Simple Explanation for the Phase Transition in Large Language Models with List Decoding

Various recent experimental results show that large language models (LLM) exhibit emergent abilities that are not present in small models. System performance is greatly improved after passing a certain critical threshold of scale. In this letter, we provide a simple explanation for such a phase transition phenomenon. For this, we model an LLM as a sequence-to-sequence random function. Instead of using instant generation at each step, we use a list decoder that keeps a list of candidate sequences at each step and defers the generation of the output sequence at the end. We show that there is a critical threshold such that the expected number of erroneous candidate sequences remains bounded when an LLM is below the threshold, and it grows exponentially when an LLM is above the threshold. Such a threshold is related to the basic reproduction number in a contagious disease.

cs.CL↗

arXiv2022

A Degree Based Approximation of an SIR Model with Contact Tracing and Isolation

In this paper we study a susceptible infectious recovered (SIR) model with asymptomatic patients, contact tracing and isolation on a configuration network. Using degree based approximation, we derive a system of differential equations for this model. This system can not be solved analytically. We present an early-time analysis for the model. The early-time analysis produces an epidemic threshold. On one side of the threshold, the disease dies out quickly. On the other side, a significant fraction of the population are infected. The threshold only depends on the parameters of the disease, the mean access degree of the network, and the fraction of asymptomatic patients. The threshold does not depend on the parameter of contact tracing and isolation policy. We present an approximate analysis which greatly reduces computational complexity. The nonlinear system derived from the approximation is not almost linear. We present a stability analysis for this system. We simulate the SIR model with contact tracing and isolation on five real-world networks. Simulation results show that contact tracing and isolation are useful to contain epidemics.

cs.SI↗

arXiv2022

Using Locality-sensitive Hashing for Rendezvous Search

The multichannel rendezvous problem is a fundamental problem for neighbor discovery in many IoT applications. The existing works in the literature focus mostly on improving the worst-case performance, and the average-case performance is often not as good as that of the random algorithm. As IoT devices (users) are close to each other, their available channel sets, though they might be different, are similar. Using the locality-sensitive hashing (LSH) technique in data mining, we propose channel hopping algorithms that exploit the similarity between the two available channel sets to increase the rendezvous probability. For the synchronous setting, our algorithms have the expected time-to-rendezvous (ETTR) inversely proportional to a well-known similarity measure called the Jaccard index. For the asynchronous setting, we use dimensionality reduction to speed up the rendezvous process. Our numerical results show that our algorithms can outperform the random algorithm in terms of ETTR.

cs.NI↗

arXiv2022

Resource Allocation for URLLC and eMBB Traffic in Uplink Wireless Networks

In this paper we consider two resource allocation problems of URLLC traffic and eMBB traffic in uplink 5G networks. We propose to divide frequencies into a common region and a grant-based region. Frequencies in the grant-based region can only be used by eMBB traffic, while frequencies in the common region can be used by eMBB traffic as well as URLLC traffic. In the first resource allocation problem we propose a two-player game to address the size of the grant-based region and the size of the common region. We show that this game has specific pure Nash equilibria. In the second resource allocation problem we determine the number of packets that each eMBB user can transmit in a request-grant cycle. We propose a constrained optimization problem to minimize the variance of the number of packets granted to the eMBB users. We show that a water-filling algorithm solves this constrained optimization problem. From simulation, we show that our scheme, consisting of resource allocation according to Nash equilibria of a game, persistent random retransmission of URLLC packets and allocation of eMBB packets by a water-filling algorithm, works better than four other heuristic methods.

cs.NI↗

arXiv2022

A generalized configuration model with triadic closure

In this paper we present a generalized configuration model with random triadic closure (GCTC). This model possesses five fundamental properties: large clustering coefficient, power law degree distribution, short path length, non-zero Pearson degree correlation, and existence of community structures. We analytically derive the Pearson degree correlation coefficient and the clustering coefficient of the proposed model. We select a few datasets of real-world networks. By simulation, we show that the GCTC model matches very well with the datasets in terms of Pearson degree correlations and clustering coefficients. We also test three well-known community detection algorithms on our model, the datasets and other three prevalent benchmark models. We show that the GCTC model performs equally well as the other three benchmark models. Finally, we perform influence diffusion on the GCTC model using the independent cascade model and the linear threshold model. We show that the influence spreads of the GCTC model are much closer to those of the datasets than the other benchmark models. This suggests that the GCTC model is a suitable tool to study network science problems where degree correlation or clustering plays an important role.

cs.SI↗

arXiv2021

A Hierarchical Stitching Algorithm for Coded Compressed Sensing

Recently, a novel coded compressed sensing (CCS) approach was proposed in [1] for dealing with the scalability problem for large sensing matrices in massive machine-type communications. The approach is to divide the compressed sensing (CS) problem into smaller CS sub-problems. However, such an approach requires stitching the results from the sub-problems to recover the result in the original CS problem. For this stitching problem, we propose a hierarchical stitching algorithm that is easier to implement in hardware for parallelization than the tree coding algorithm in [1]. For our algorithm, we also derive an upper bound on the probability of recovery errors.

cs.NI↗

arXiv2021

On the Stability Regions of Coded Poisson Receivers with Multiple Classes of Users and Receivers

Motivated by the need to provide differentiated quality-of-service (QoS) in grant-free uplink transmissions in 5G networks and beyond, we extend the probabilistic analysis of coded Poisson receivers (CPR) to the setting with multiple classes of users and receivers. For such a CPR system, we prove (under certain technical conditions) that there is a region, called the stability region in this paper. Each transmitted packet can be successfully received with probability 1 when the offered load to the system is within the stability region. On the other hand, if the offered load is outside the stability region, there is a nonzero probability that a packet will fail to be received. We then extend the stability region to the $\epsilon$-stability region for CPR systems with decoding errors. We also demonstrate the capability of providing differentiated QoS in such CPR systems by comparing the stability regions under various parameter settings.

cs.NI↗

arXiv2021

Constructions and Comparisons of Pooling Matrices for Pooled Testing of COVID-19

In comparison with individual testing, group testing (also known as pooled testing) is more efficient in reducing the number of tests and potentially leading to tremendous cost reduction. As indicated in the recent article posted on the US FDA website, the group testing approach for COVID-19 has received a lot of interest lately. There are two key elements in a group testing technique: (i) the pooling matrix that directs samples to be pooled into groups, and (ii) the decoding algorithm that uses the group test results to reconstruct the status of each sample. In this paper, we propose a new family of pooling matrices from packing the pencil of lines (PPoL) in a finite projective plane. We compare their performance with various pooling matrices proposed in the literature, including 2D-pooling, P-BEST, and Tapestry, using the two-stage definite defectives (DD) decoding algorithm. By conducting extensive simulations for a range of prevalence rates up to 5%, our numerical results show that there is no pooling matrix with the lowest relative cost in the whole range of the prevalence rates. To optimize the performance, one should choose the right pooling matrix, depending on the prevalence rate. The family of PPoL matrices can dynamically adjust their column weights according to the prevalence rates and could be a better alternative than using a fixed pooling matrix.

q-bio.PE↗

arXiv2021

PPoL: A Periodic Channel Hopping Sequence with Nearly Full Rendezvous Diversity

We propose a periodic channel hopping (CH) sequence, called PPoL (Packing the Pencil of Lines in a finite projective plane), for the multichannel rendezvous problem. When $N-1$ is a prime power, its period is $N^2-N+1$, and the number of distinct rendezvous channels of PPoL is at least $N-2$ for any nonzero clock drift. By channel remapping, we construct CH sequences with the maximum time-to-rendezvous (MTTR) bounded by $N^2+3N+3$ if the number of commonly available channels is at least two. This achieves a roughly 50% reduction of the state-of-the-art MTTR bound in the literature.

cs.DC↗

arXiv2021

Positively Correlated Samples Save Pooled Testing Costs

The group testing approach that achieves significant cost reduction over the individual testing approach has received a lot of interest lately for massive testing of COVID-19. Many studies simply assume samples mixed in a group are independent. However, this assumption may not be reasonable for a contagious disease like COVID-19. Specifically, people within a family tend to infect each other and thus are likely to be positively correlated. By exploiting positive correlation, we make the following two main contributions. One is to provide a rigorous proof that further cost reduction can be achieved by using the Dorfman two-stage method when samples within a group are positively correlated. The other is to propose a hierarchical agglomerative algorithm for pooled testing with a social graph, where an edge in the social graph connects frequent social contacts between two persons. Such an algorithm leads to notable cost reduction (roughly 20%-35%) compared to random pooling when the Dorfman two-stage algorithm is applied.

stat.ME↗