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Yuan-Hsun Lo

Publications and source records attributed to Yuan-Hsun Lo.

33 records · Page 2Linked to original sources
arXiv2018

Forwarding and Optical Indices in an All-Optical BCube Network

BCube is a highly scalable and cost-effective networking topology, which has been widely applied to modular datacenters. Optical technologies based on Wavelength Division Multiplexing (WDM) are gaining popularity for Data Center Networks (DCNs) due to their technological strengths such as low communication latency, low power consumption, and high link bandwidth. Therefore, it is worth investigating optical techniques into the BCube architecture for future DCNs. For this purpose, we study the forwarding and optical indices in an all-optical BCube network. Consider an all-optical BCube network in which every host sets up a connection with every other host. The optical index is the minimum number of wavelengths required by the network to support such a host-to-host traffic, under the restriction that each connection is assigned a wavelength that remains constant in the network. A routing is a set of directed paths specified for all host pairs. By defining the maximum link load of a routing as the maximum number of paths passing through any link, the forwarding index is measured to be the minimum of maximum link load over all possible routings. The forwarding index turns out to be a natural lower bound of the optical index. In this paper, we first compute the forwarding index of an all-optical BCube network. Then, we derive an upper bound of the optical index by providing an oblivious routing and wavelength assignment (RWA) schemes, which attains the lower bound given by the forwarding index in some small cases. Finally, a tighter upper bound is obtained by means of the chromatic numbers in Graph Theory.

cs.DC↗
arXiv2017

Optimal Slotted ALOHA under Delivery Deadline Constraint for Multiple-Packet Reception

This paper considers the slotted ALOHA protocol in a communication channel shared by N users. It is assumed that the channel has the multiple-packet reception (MPR) capability that allows the correct reception of up to M ($1 \leq M < N$) time-overlapping packets. To evaluate the reliability in the scenario that a packet needs to be transmitted within a strict delivery deadline D ($D \geq 1$) (in unit of slot) since its arrival at the head of queue, we consider the successful delivery probability (SDP) of a packet as performance metric of interest. We derive the optimal transmission probability that maximizes the SDP for any $1 \leq M < N$ and any $D \geq 1$, and show it can be computed by a fixed-point iteration. In particular, the case for D = 1 (i.e., throughput maximization) is first completely addressed in this paper. Based on these theoretical results, for real-life scenarios where N may be unknown and changing, we develop a distributed algorithm that enables each user to tune its transmission probability at runtime according to the estimate of N. Simulation results show that the proposed algorithm is effective in dynamic scenarios, with near-optimal performance.

cs.IT↗
arXiv2017

New CRT sequence sets for a collision channel without feedback

Protocol sequences are binary and periodic sequences used for deterministic multiple access in a collision channel without feedback. In this paper, we focus on user-irrepressible (UI) protocol sequences that can guarantee a positive individual throughput per sequence period with probability one for a slot-synchronous channel, regardless of the delay offsets among the users. As the sequence period has a fundamental impact on the worst-case channel access delay, a common objective of designing UI sequences is to make the sequence period as short as possible. Consider a communication channel that is shared by $M$ active users, and assume that each protocol sequence has a constant Hamming weight $w$. To attain a better delay performance than previously known UI sequences, this paper presents a CRTm construction of UI sequences with $w=M+1$, which is a variation of the previously known CRT construction. For all non-prime $M\geq 8$, our construction produces the shortest known sequence period and the shortest known worst-case delay of UI sequences. Numerical results show that the new construction enjoys a better average delay performance than the optimal random access scheme and other constructions with the same sequence period, in a variety of traffic conditions. In addition, we derive an asymptotic lower bound on the minimum sequence period for $w=M+1$ if the sequence structure satisfies some technical conditions, called equi-difference, and prove the tightness of this lower bound by using the CRTm construction.

cs.IT↗
arXiv2016

Partially user-irrepressible sequence sets and conflict-avoiding codes

In this paper we give a partial shift version of user-irrepressible sequence sets and conflict-avoiding codes. By means of disjoint difference sets, we obtain an infinite number of such user-irrepressible sequence sets whose lengths are shorter than known results in general. Subsequently, the newly defined partially conflict-avoiding codes are discussed.

cs.IT↗
arXiv2016

Channel Hopping Sequences for Maximizing Rendezvous Diversity in Cognitive Radio Networks

In cognitive radio networks (CRNs), establishing a communication link between a pair of secondary users (SUs) requires them to rendezvous on a common channel which is not occupied by primary users (PUs). Under time-varying PU traffic, asynchronous sequence-based channel hopping (CH) with the maximal rendezvous diversity is a representative technique to guarantee an upper bounded time-torendezvous (TTR) for delay-sensitive services in CRNs, without requiring global clock synchronization. Maximum TTR (MTTR) and maximum conditional TTR (MCTTR) are two commonly considered metrics for evaluating such CH sequences, and minimizing these two metrics is the primary goal in the sequence design of various paper reported in the literature. In this paper, to investigate the fundamental limits of these two metrics, we first derive lower bounds on the MCTTR and MTTR, and then propose an asymmetric design which has the minimum MCTTR and an improvement on MTTR than other previously known algorithms. Moreover, when the number of licensed channels is odd, our proposed design achieves the minimum MTTR. We also present the TTR performance of the proposed design via simulation.

cs.IT↗
arXiv2015

The Global Packing Number for an Optical Network

The global packing number problem arises from the investigation of optimal wavelength allocation in an optical network that employs Wavelength Division Multiplexing (WDM). Consider an optical network that is represented by a connected, simple graph $G$. We assume all communication channels are bidirectional, so that all links and paths are undirected. It follows that there are ${|G|\choose 2}$ distinct node pairs associated with $G$, where $|G|$ is the number of nodes in $G$. A path system $\mathcal{P}$ of $G$ consists of ${|G|\choose 2}$ paths, one path to connect each of the node pairs. The global packing number of a path system $\mathcal{P}$, denoted by $Φ(G,\mathcal{P})$, is the minimum integer $k$ to guarantee the existence of a mapping $ω:\mathcal{P}\to\{1,2,\ldots,k\}$, such that $ω(P)\neqω(P')$ if $P$ and $P'$ have common edge(s). The global packing number of $G$, denoted by $Φ(G)$, is defined to be the minimum $Φ(G,\mathcal{P})$ among all possible path systems $\mathcal{P}$. If there is no wavelength conversion along any optical transmission path for any node pair in the network, the global packing number signifies the minimum number of wavelengths required to support simultaneous communication for all pairs in the network. In this paper, the focus is on ring networks, so that $G$ is a cycle. Explicit formulas for the global packing number of a cycle is derived. The investigation is further extended to chain networks. A path system, $\mathcal{P}$, that enjoys $Φ(G,\mathcal{P})=Φ(G)$ is called ideal. A characterization of ideal path systems is also presented. We also describe an efficient heuristic algorithm to assign wavelengths that can be applied to a general network with more complicated traffic load.

cs.DM↗
arXiv2014

Codes with the Identifiable Parent Property for Multimedia Fingerprinting

Let ${\cal C}$ be a $q$-ary code of length $n$ and size $M$, and ${\cal C}(i) = \{{\bf c}(i) \ | \ {\bf c}=({\bf c}(1), {\bf c}(2), \ldots, {\bf c}(n))^{T} \in {\cal C}\}$ be the set of $i$th coordinates of ${\cal C}$. The descendant code of a sub-code ${\cal C}^{'} \subseteq {\cal C}$ is defined to be ${\cal C}^{'}(1) \times {\cal C}^{'}(2) \times \cdots \times {\cal C}^{'}(n)$. In this paper, we introduce a multimedia analogue of codes with the identifiable parent property (IPP), called multimedia IPP codes or $t$-MIPPC$(n, M, q)$, so that given the descendant code of any sub-code ${\cal C}^{'}$ of a multimedia $t$-IPP code ${\cal C}$, one can always identify, as IPP codes do in the generic digital scenario, at least one codeword in ${\cal C}^{'}$. We first derive a general upper bound on the size $M$ of a multimedia $t$-IPP code, and then investigate multimedia $3$-IPP codes in more detail. We characterize a multimedia $3$-IPP code of length $2$ in terms of a bipartite graph and a generalized packing, respectively. By means of these combinatorial characterizations, we further derive a tight upper bound on the size of a multimedia $3$-IPP code of length $2$, and construct several infinite families of (asymptotically) optimal multimedia $3$-IPP codes of length $2$.

cs.IT↗
arXiv2014

Optimal strongly conflict-avoiding codes of even length and weight three

Strongly conflict-avoiding codes (SCACs) are employed in a slot-asynchronous multiple-access collision channel without feedback to guarantee that each active user can send at least one packet successfully in the worst case within a fixed period of time. Assume all users are assigned distinct codewords, the number of codewords in an SCAC is equal to the number of potential users that can be supported. SCACs have different combinatorial structure compared with conflict-avoiding codes (CACs) due to additional collisions incurred by partially overlapped transmissions. In this paper, we establish upper bounds on the size of SCACs of even length and weight three. Furthermore, it is shown that some optimal CACs can be used to construct optimal SCACs of weight three.

cs.IT↗
arXiv2014

The sorting index on colored permutations and even-signed permutations

We define a new statistic $\mathsf{sor}$ on the set of colored permutations $\mathsf{G}_{r,n}$ and prove that it has the same distribution as the length function. For the set of restricted colored permutations corresponding to the arrangements of $n$ non-attacking rooks on a fixed Ferrers shape we show that the following two sequences of set-valued statistics are joint equidistributed: $(\ell,\mathsf{Rmil}^0,\mathsf{Rmil}^1,...,\mathsf{Rmil}^{r-1}$, $\mathsf{Lmil}^0,\mathsf{Lmil}^1,...,\mathsf{Lmil}^{r-1}$, $\mathsf{Lmal}^0,\mathsf{Lmal}^1,...,\mathsf{Lmal}^{r-1}$, $\mathsf{Lmap}^0,\mathsf{Lmap}^1,...,\mathsf{Lmap}^{r-1})$ and $(\mathsf{sor},\mathsf{Cyc}^0,\mathsf{Cyc}^{r-1},...,\mathsf{Cyc}^{1}$, $\mathsf{Lmic}^0,\mathsf{Lmic}^{r-1},...,\mathsf{Lmic}^{1}$, $\mathsf{Lmal}^0,\mathsf{Lmal}^1,...,\mathsf{Lmal}^{r-1}$, $\mathsf{Lmap}^0,\mathsf{Lmap}^1,...,\mathsf{Lmap}^{r-1})$. Analogous results are also obtained for Coxeter group of type $D$. Our results extend recent results of Petersen, Chen-Gong-Guo and Poznanović.

math.CO↗
arXiv2014

Multicolored Isomorphic Spanning Trees in Complete Graphs

In this paper, we first prove that if the edges of $K_{2m}$ are properly colored by $2m-1$ colors in such a way that any two colors induce a 2-factor of which each component is a 4-cycle, then $K_{2m}$ can be decomposed into $m$ isomorphic multicolored spanning trees. Consequently, we show that there exist three disjoint isomorphic multicolored spanning trees in any properly (2$m-$1)-edge-colored $K_{2m}$ for $m\geq 14$.

math.CO↗
arXiv2014

The sorting index and set-valued joint equidistributions of $\mathcal{B}_n$ and $\mathcal{D}_n$

The sorting indices $\text{sor}_B$ and $\text{sor}_D$ on the Coxeter groups of type $B$ and $D$ respectively are defined by Petersen and it is proved that $(\text{inv}_B, \text{rlmin})$ and $(\text{sor}_B, \ell'_B)$ have the same joint distribution for type $B$ while $\text{inv}_D$ and $\text{sor}_D$ have the same distribution for type $D$. These results, including a set-valued extension of type $B$ involving two equildistributed pairs of three statistics, are proved combinatorially by Chen et al. via two mappings $φ:=\text{(B-code)}^{-1}\circ \text{(A-code)}$ and $ψ:=\text{(D-code)}^{-1}\circ \text{(C-code)}$. In this paper we further extend these results. In type $B$ we prove a set-valued joint equildistribution between a pair of seven statistics, and find a five-variable generating function. In type $D$ we define new set-valued statistics, among them $\text{Cyc}^+_D$ and $\text{Cyc}^-_D$, and firstly find a set-valued joint equidistribution between a pair of five statistics and find a four-variable generating function.

math.CO↗
arXiv2014

Protocol Sequences for Multiple-Packet Reception

Consider a time slotted communication channel shared by $K$ active users and a single receiver. It is assumed that the receiver has the ability of the multiple-packet reception (MPR) to correctly receive at most $γ$ ($1 \leq γ< K$) simultaneously transmitted packets. Each user accesses the channel following a specific periodical binary sequence, called the protocol sequence, and transmits a packet within a channel slot if and only if the sequence value is equal to one. The fluctuation in throughput is incurred by inevitable random relative shifts among the users due to the lack of feedback. A set of protocol sequences is said to be throughput-invariant (TI) if it can be employed to produce invariant throughput for any relative shifts, i.e., maximize the worst-case throughput. It was shown in the literature that the TI property without considering MPR (i.e., $γ=1$) can be achieved by using shift-invariant (SI) sequences, whose generalized Hamming cross-correlation is independent of relative shifts. This paper investigates TI sequences for MPR; results obtained include achievable throughput value, a lower bound on the sequence period, an optimal construction of TI sequences that achieves the lower bound on the sequence period, and intrinsic structure of TI sequences. In addition, we present a practical packet decoding mechanism for TI sequences that incorporates packet header, forward error-correcting code, and advanced physical layer blind signal separation techniques.

cs.IT↗
arXiv2014

Edge-colorings of $K_{m,n}$ which Forbid Multicolored Cycles

A subgraph in an edge-colored graph is multicolored if all its edges receive distinct colors. In this paper, we study the proper edge-colorings of the complete bipartite graph $K_{m,n}$ which forbid multicolored cycles. Mainly, we prove that (1) for any integer $k\geq 2$, if $n\geq 5k-6$, then any properly $n$-edge-colored $K_{k,n}$ contains a multicolored $C_{2k}$, and (2) determine the order of the properly edge-colored complete bipartite graphs which forbid multicolored $C_6$.

math.CO↗
arXiv2014

Set-valued sorting index and joint equidistributions

Recently Petersen defined a new Mahonian index sor over the symmetric group $\mathfrak{S}_n$ and proved that $(\text{inv}, \text{rlmin})$ and $(\text{sor}, \text{cyc})$ have the same joint distribution. Foata and Han proved that the pairs of set-valued statistics $(\text{Cyc}, \text{Rmil}), (\text{Cyc}, \text{Lmap}), (\text{Rmil}, \text{Lmap})$ have the same joint distribution over $\mathfrak{S}_n$. In this paper we introduce the set-valued statistics $\text{Inv}, \text{Lmil}, \text{Sor}$ and $\text{Lmicycl}_1$ and generalize simultaneously results of Petersen and Foata-Han and find many equidistributed triples of set-valued statistics and quadruples of statistics.

math.CO↗