arXiv subjects

Yunghsiang S. Han

Publications and source records attributed to Yunghsiang S. Han.

At least 37 records · Page 2Linked to original sources

arXiv2022

Generalized Universal Coding of Integers

Universal coding of integers~(UCI) is a class of variable-length code, such that the ratio of the expected codeword length to $\max\{1,H(P)\}$ is within a constant factor, where $H(P)$ is the Shannon entropy of the decreasing probability distribution $P$. However, if we consider the ratio of the expected codeword length to $H(P)$, the ratio tends to infinity by using UCI, when $H(P)$ tends to zero. To solve this issue, this paper introduces a class of codes, termed generalized universal coding of integers~(GUCI), such that the ratio of the expected codeword length to $H(P)$ is within a constant factor $K$. First, the definition of GUCI is proposed and the coding structure of GUCI is introduced. Next, we propose a class of GUCI $\mathcal{C}$ to achieve the expansion factor $K_{\mathcal{C}}=2$ and show that the optimal GUCI is in the range $1\leq K_{\mathcal{C}}^{*}\leq 2$. Then, by comparing UCI and GUCI, we show that when the entropy is very large or $P(0)$ is not large, there are also cases where the average codeword length of GUCI is shorter. Finally, the asymptotically optimal GUCI is presented.

cs.IT↗

arXiv2022

Reputation and Audit Bit Based Distributed Detection in the Presence of Byzantine

In this paper, two reputation based algorithms called Reputation and audit based clustering (RAC) algorithm and Reputation and audit based clustering with auxiliary anchor node (RACA) algorithm are proposed to defend against Byzantine attacks in distributed detection networks when the fusion center (FC) has no prior knowledge of the attacking strategy of Byzantine nodes. By updating the reputation index of the sensors in cluster-based networks, the system can accurately identify Byzantine nodes. The simulation results show that both proposed algorithms have superior detection performance compared with other algorithms. The proposed RACA algorithm works well even when the number of Byzantine nodes exceeds half of the total number of sensors in the network. Furthermore, the robustness of our proposed algorithms is evaluated in a dynamically changing scenario, where the attacking parameters change over time. We show that our algorithms can still achieve superior detection performance.

cs.CR↗

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

Enhanced Audit Bit Based Distributed Bayesian Detection in the Presence of Strategic Attacks

This paper employs an audit bit based mechanism to mitigate the effect of Byzantine attacks. In this framework, the optimal attacking strategy for intelligent attackers is investigated for the traditional audit bit based scheme (TAS) to evaluate the robustness of the system. We show that it is possible for an intelligent attacker to degrade the performance of TAS to the system without audit bits. To enhance the robustness of the system in the presence of intelligent attackers, we propose an enhanced audit bit based scheme (EAS). The optimal fusion rule for the proposed scheme is derived and the detection performance of the system is evaluated via the probability of error for the system. Simulation results show that the proposed EAS improves the robustness and the detection performance of the system. Moreover, based on EAS, another new scheme called the reduced audit bit based scheme (RAS) is proposed which further improves system performance. We derive the new optimal fusion rule and the simulation results show that RAS outperforms EAS and TAS in terms of both robustness and detection performance of the system. Then, we extend the proposed RAS for a wide-area cluster based distributed wireless sensor networks (CWSNs). Simulation results show that the proposed RAS significantly reduces the communication overhead between the sensors and the FC, which prolongs the lifetime of the network.

cs.CR↗

arXiv2021

Reinforcement Learning Random Access for Delay-Constrained Heterogeneous Wireless Networks: A Two-User Case

In this paper, we investigate the random access problem for a delay-constrained heterogeneous wireless network. As a first attempt to study this new problem, we consider a network with two users who deliver delay-constrained traffic to an access point (AP) via a common unreliable collision wireless channel. We assume that one user (called user 1) adopts ALOHA and we optimize the random access scheme of the other user (called user 2). The most intriguing part of this problem is that user 2 does not know the information of user 1 but needs to maximize the system timely throughput. Such a paradigm of collaboratively sharing spectrum is envisioned by DARPA to better dynamically match the supply and demand in the future [1], [2]. We first propose a Markov Decision Process (MDP) formulation to derive a modelbased upper bound, which can quantify the performance gap of any designed schemes. We then utilize reinforcement learning (RL) to design an R-learning-based [3]-[5] random access scheme, called TSRA. We finally carry out extensive simulations to show that TSRA achieves close-to-upper-bound performance and better performance than the existing baseline DLMA [6], which is our counterpart scheme for delay-unconstrained heterogeneous wireless network. All source code is publicly available in https://github.com/DanzhouWu/TSRA.

cs.NI↗

arXiv2021

Lower Bound on the Optimal Access Bandwidth of ($K+2,K,2$)-MDS Array Code with Degraded Read Friendly

Accessing the data in the failed disk (degraded read) with low latency is crucial for an erasure-coded storage system. In this work, the maximum distance separable (MDS) array code with the property of degraded-read friendly (DRF) is discussed. For the DRF MDS array code with 2 redundant nodes and the sub-packetization level of 2, the lower bound of its access bandwidth is derived.

cs.IT↗

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

On the Exact Lower Bounds of Encoding Circuit Sizes of Hamming Codes and Hadamard Codes

In this paper, we investigate the encoding circuit size of Hamming codes and Hadamard codes. To begin with, we prove the exact lower bound of circuit size required in the encoding of (punctured)~Hadamard codes and (extended)~Hamming codes. Then the encoding algorithms for (punctured)~Hadamard codes are presented to achieve the derived lower bounds. For (extended)~Hamming codes, we also propose encoding algorithms that achieve the lower bounds.

cs.IT↗

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↗

arXiv2019

Multi-Layer Transformed MDS Codes with Optimal Repair Access and Low Sub-Packetization

An $(n,k)$ maximum distance separable (MDS) code has optimal repair access if the minimum number of symbols accessed from $d$ surviving nodes is achieved, where $k+1\le d\le n-1$. Existing results show that the sub-packetization $α$ of an $(n,k,d)$ high code rate (i.e., $k/n>0.5$) MDS code with optimal repair access is at least $(d-k+1)^{\lceil\frac{n}{d-k+1}\rceil}$. In this paper, we propose a class of multi-layer transformed MDS codes such that the sub-packetization is $(d-k+1)^{\lceil\frac{n}{(d-k+1)η}\rceil}$, where $η=\lfloor\frac{n-k-1}{d-k}\rfloor$, and the repair access is optimal for any single node. We show that the sub-packetization of the proposed multi-layer transformed MDS codes is strictly less than the existing known lower bound when $η=\lfloor\frac{n-k-1}{d-k}\rfloor>1$, achieving by restricting the choice of $d$ specific helper nodes in repairing a failed node. We further propose multi-layer transformed EVENODD codes that have optimal repair access for any single node and lower sub-packetization than the existing binary MDS array codes with optimal repair access for any single node. With our multi-layer transformation, we can design new MDS codes that have the properties of low computational complexity, optimal repair access for any single node, and relatively small sub-packetization, all of which are critical for maintaining the reliability of distributed storage systems.

cs.IT↗

arXiv2018

Delay-Constrained Input-Queued Switch

In this paper, we study the delay-constrained input-queued switch where each packet has a deadline and it will expire if it is not delivered before its deadline. Such new scenario is motivated by the proliferation of real-time applications in multimedia communication systems, tactile Internet, networked controlled systems, and cyber-physical systems. The delay-constrained input-queued switch is completely different from the well-understood delay-unconstrained one and thus poses new challenges. We focus on three fundamental problems centering around the performance metric of timely throughput: (i) how to characterize the capacity region? (ii) how to design a feasibility/throughput-optimal scheduling policy? and (iii) how to design a network-utility-maximization scheduling policy? We use three different approaches to solve these three fundamental problems. The first approach is based on Markov Decision Process (MDP) theory, which can solve all three problems. However, it suffers from the curse of dimensionality. The second approach breaks the curse of dimensionality by exploiting the combinatorial features of the problem. It gives a new capacity region characterization with only a polynomial number of linear constraints. The third approach is based on the framework of Lyapunov optimization, where we design a polynomial-time maximum-weight T-disjoint-matching scheduling policy which is proved to be feasibility/throughput-optimal. Our three approaches apply to the frame-synchronized traffic pattern but our MDP-based approach can be extended to more general traffic patterns.

cs.NI↗

arXiv2018

On the Maximum Size of Block Codes Subject to a Distance Criterion

We establish a general formula for the maximum size of finite length block codes with minimum pairwise distance no less than $d$. The achievability argument involves an iterative construction of a set of radius-$d$ balls, each centered at a codeword. We demonstrate that the number of such balls that cover the entire code alphabet cannot exceed this maximum size. Our approach can be applied to codes $i)$ with elements over arbitrary code alphabets, and $ii)$ under a broad class of distance measures, thereby ensuring the generality of our formula. Our formula indicates that the maximum code size can be fully characterized by the cumulative distribution function of the distance measure evaluated at two independent and identically distributed random codewords. When the two random codewords assume a uniform distribution over the entire code alphabet, our formula recovers and obtains a natural generalization of the Gilbert-Varshamov (GV) lower bound. We also establish a general formula for the zero-error capacity of any sequence of channels. Finally, we extend our study to the asymptotic setting, where we establish first- and second-order bounds on the asymptotic code rate subject to a normalized minimum distance constraint.

cs.IT↗

arXiv2018

A Unified Form of EVENODD and RDP Codes and Their Efficient Decoding

Array codes have been widely employed in storage systems, such as Redundant Arrays of Inexpensive Disks (RAID). The row-diagonal parity (RDP) codes and EVENODD codes are two popular double-parity array codes. As the capacity of hard disks increases, better fault tolerance by using array codes with three or more parity disks is needed. Although many extensions of RDP codes and EVENODD codes have been proposed, the high decoding complexity is the main drawback of them. In this paper, we present a new construction for all families of EVENODD codes and RDP codes, and propose a unified form of them. Under this unified form, RDP codes can be treated as shortened codes of EVENODD codes. Moreover, an efficient decoding algorithm based on an LU factorization of Vandermonde matrix is proposed when the number of continuous surviving parity columns is no less than the number of erased information columns. The new decoding algorithm is faster than the existing algorithms when more than three information columns fail. The proposed efficient decoding algorithm is also applicable to other Vandermonde array codes. Thus the proposed MDS array code is practically very meaningful for storage systems that need higher reliability.

cs.IT↗

arXiv2016

Cauchy MDS Array Codes With Efficient Decoding Method

Array codes have been widely used in communication and storage systems. To reduce computational complexity, one important property of the array codes is that only XOR operation is used in the encoding and decoding process. In this work, we present a novel family of maximal-distance separable (MDS) array codes based on Cauchy matrix, which can correct up to any number of failures. We also propose an efficient decoding method for the new codes to recover the failures. We show that the encoding/decoding complexities of the proposed approach are lower than those of existing Cauchy MDS array codes, such as Rabin-Like codes and CRS codes. Thus, the proposed MDS array codes are attractive for distributed storage systems.

cs.IT↗

arXiv2016

FFT Algorithm for Binary Extension Finite Fields and its Application to Reed-Solomon Codes

Recently, a new polynomial basis over binary extension fields was proposed such that the fast Fourier transform (FFT) over such fields can be computed in the complexity of order $\mathcal{O}(n\lg(n))$, where $n$ is the number of points evaluated in FFT. In this work, we reformulate this FFT algorithm such that it can be easier understood and be extended to develop frequency-domain decoding algorithms for $(n=2^m,k)$ systematic Reed-Solomon~(RS) codes over $\mathbb{F}_{2^m},m\in \mathbb{Z}^+$, with $n-k$ a power of two. First, the basis of syndrome polynomials is reformulated in the decoding procedure so that the new transforms can be applied to the decoding procedure. A fast extended Euclidean algorithm is developed to determine the error locator polynomial. The computational complexity of the proposed decoding algorithm is $\mathcal{O}(n\lg(n-k)+(n-k)\lg^2(n-k))$, improving upon the best currently available decoding complexity $\mathcal{O}(n\lg^2(n)\lg\lg(n))$, and reaching the best known complexity bound that was established by Justesen in 1976. However, Justesen's approach is only for the codes over some specific fields, which can apply Cooley-Tucky FFTs. As revealed by the computer simulations, the proposed decoding algorithm is $50$ times faster than the conventional one for the $(2^{16},2^{15})$ RS code over $\mathbb{F}_{2^{16}}$.

cs.IT↗

arXiv2014

Permutation Trellis Coded Multi-level FSK Signaling to Mitigate Primary User Interference in Cognitive Radio Networks

We employ Permutation Trellis Code (PTC) based multi-level Frequency Shift Keying signaling to mitigate the impact of Primary Users (PUs) on the performance of Secondary Users (SUs) in Cognitive Radio Networks (CRNs). The PUs are assumed to be dynamic in that they appear intermittently and stay active for an unknown duration. Our approach is based on the use of PTC combined with multi-level FSK modulation so that an SU can improve its data rate by increasing its transmission bandwidth while operating at low power and not creating destructive interference for PUs. We evaluate system performance by obtaining an approximation for the actual Bit Error Rate (BER) using properties of the Viterbi decoder and carry out a thorough performance analysis in terms of BER and throughput. The results show that the proposed coded system achieves i) robustness by ensuring that SUs have stable throughput in the presence of heavy PU interference and ii) improved resiliency of SU links to interference in the presence of multiple dynamic PUs.

cs.IT↗

arXiv2014

Distributed Bayesian Detection with Byzantine Data

In this paper, we consider the problem of distributed Bayesian detection in the presence of Byzantines in the network. It is assumed that a fraction of the nodes in the network are compromised and reprogrammed by an adversary to transmit false information to the fusion center (FC) to degrade detection performance. The problem of distributed detection is formulated as a binary hypothesis test at the FC based on 1-bit data sent by the sensors. The expression for minimum attacking power required by the Byzantines to blind the FC is obtained. More specifically, we show that above a certain fraction of Byzantine attackers in the network, the detection scheme becomes completely incapable of utilizing the sensor data for detection. We analyze the problem under different attacking scenarios and derive results for different non-asymptotic cases. It is found that existing asymptotics-based results do not hold under several non-asymptotic scenarios. When the fraction of Byzantines is not sufficient to blind the FC, we also provide closed form expressions for the optimal attacking strategies for the Byzantines that most degrade the detection performance.

cs.IT↗

arXiv2014

Asymptotic Analysis of Distributed Bayesian Detection with Byzantine Data

In this letter, we consider the problem of distributed Bayesian detection in the presence of data falsifying Byzantines in the network. The problem of distributed detection is formulated as a binary hypothesis test at the fusion center (FC) based on 1-bit data sent by the sensors. Adopting Chernoff information as our performance metric, we study the detection performance of the system under Byzantine attack in the asymptotic regime. The expression for minimum attacking power required by the Byzantines to blind the FC is obtained. More specifically, we show that above a certain fraction of Byzantine attackers in the network, the detection scheme becomes completely incapable of utilizing the sensor data for detection. When the fraction of Byzantines is not sufficient to blind the FC, we also provide closed form expressions for the optimal attacking strategies for the Byzantines that most degrade the detection performance.

stat.AP↗