Bella Bose's research while affiliated with Oregon State University and other places

Publications (141)

Article
We study the problem of virtual machine (VM) placement and migration in a data center. In the current approaches, VMs are assigned to physical servers using on-demand provisioning. Such an approach is simple but it often results in a poor performance due to resource fragmentation. Additionally, sub-optimal VM placement usually generates unneeded VM...
Article
Shannon in his 1956 seminal paper introduced the concept of the zero error capacity, C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> , of a noisy channel. This is defined as the least upper bound of rates, at which, it is possible to transmit information with zero probability of error. At pre...
Article
Full-text available
A new efficient design of second-order spectral-null (2-OSN) codes is presented. The new codes are obtained by applying the technique used to design parallel decoding balanced (i.e., 1-OSN) codes to the random walk method introduced by some of the authors for designing 2-OSN codes. This gives new non-recursive efficient code designs, which are less...
Article
Many communication algorithms in parallel systems can be efficiently solved by obtaining edge disjoint Hamiltonian cycles in the interconnection topology of the network. The Eisenstein-Jacobi (EJ) network generated by α=a+bρ, where ρ=(1+i3)/2, is a degree six symmetric interconnection network. The hexagonal network is a special case of the EJ netwo...
Patent
Full-text available
A computer-implemented method and computer program product comprising optimal, systematic q-ary codes for correcting all asymmetric and symmetric errors of limited magnitude are provided.
Article
Gaussian interconnection networks have been introduced as a useful alternative to the classical toroidal networks, and in this paper this concept is generalized to higher dimensions. We also explore many important properties of this new topology, including distance distribution and the decomposition of higher dimensional Gaussian networks into edge...
Article
Gaussian networks are degree four symmetric networks and these are designed based on the concept of Gaussian integers. The Gaussian network can be described in terms of a generator alpha = a + bi, where a and b are integers and i = root-1. When gcd (a, b) = 1, how to find edge disjoint Hamiltonian cycles has been shown before. In this paper for any...
Article
Full-text available
We study the problem of assigning users to servers with an emphasis on the distributed algorithmic solutions. Typical online social network applications, such as Facebook and Twitter, are built on top of an infrastructure of servers that provides the services on behalf of the users. For a given communication pattern among users, the loads of the se...
Article
Some new classes of Hamming metric Gray codes over Zpn , where p is a prime and n is an integer power of 2, are described; then, how these Gray codes can be used to generate the maximum number of edge-disjoint Hamiltonian cycles in an n-dimensional generalized hypercube (GHC), Qpn, is shown. For Qpn, the number of edge-disjoint Hamiltonian cycles g...
Article
In multilevel flash memories, leakage of charges results in errors, and the errors are asymmetric, of increasing type and of limited magnitude. On the other hand, low data retention may result in asymmetric errors of decreasing type and usually of smaller magnitude. Therefore, we have unbalanced error types. In this paper, some codes for correcting...
Conference Paper
The hexagonal torus network is a degree six toroidal network with rich topological properties. It was used in the design of HARTS machine at the University of Michigan, and more recently it has been proposed for cellular networks. The low diameter and less average hop distance of this network make it advantageous over other 2D toroidal network such...
Conference Paper
The general theory on partially asymmetric (t, t+)-EC/(d-, d+)-ED m-ary codes for the L1 distance is developed. In this metric, such codes are capable of correcting t- or less negative errors, detecting d or less negative errors, correcting t+ or less positive errors, and simultaneously detecting d+ or less positive errors. Based on the elementary...
Conference Paper
Full-text available
A new efficient coding scheme is given for second-order spectral-null (2-OSN) codes. The new method applies the Knuth's optimal parallel decoding scheme for balanced (i.e., 1-OSN) codes to the random walk method introduced by Tallini and Bose to design 2-OSN codes. If k ∈ IN is the length of a 1-OSN code then the new 2-OSN coding scheme has length...
Article
In a multiprocessor system, a limited number of resources need to be uniformly distributed so that all processor nodes can have equal access to these resources. This is referred to as the resource placement problem. In a perfect t--placement each nonresource node is at a distance of t or less from exactly one resource node. Here, we first find all...
Conference Paper
Based on the elementary symmetric functions, this paper gives a new wide class of Goppa like codes capable of correcting/detecting errors measured under the (symmetric) L1 distance defined over the m-ary words, 2 ≤ m ≤ +∞. All these codes can be efficiently decoded by algebraic means with the Extended Euclidean Algorithm (EEA). In particular it is...
Conference Paper
This paper gives some new theory and design of codes capable of correcting/detecting errors measured under the Lee distance defined over m-ary words, m ∈ IN. Based on the elementary symmetric functions (instead of the power sums), a key equation is derived which can be used to design new symmetric (or, asymmetric) error control algorithms for some...
Article
Full-text available
In an unordered code, no code word is contained in any other code word. Unordered codes are all unidirectional error detecting (AUED) codes. In the binary case, it is well known that among all systematic codes with k information bits, Berger codes are optimal unordered codes with r=[log2(k+1)] ≅ log2k check bits. This paper gives some new theory on...
Article
In this paper, we show that the hexagonal mesh networks developed in the early 1990s are a special case of the EJ networks that have been considered more recently. Using a node addressing scheme based on the EJ number system, we give a shortest path routing algorithm for hexagonal mesh networks. We also extend the known efficient one-to-all broadca...
Conference Paper
This paper gives some theory and design of efficient codes capable of controlling (i. e., correcting/detecting/correcting erasure) errors measured under the L<sub>1</sub> distance defined over m-ary words, 2 ≤ m ≤ +∞. We give the combinatorial characterizations of such codes, some general code designs and the efficient decoding algorithms. Then, we...
Article
Full-text available
A relatively new model of error correction is the limited magnitude error model. That is, it is assumed that the absolute difference between the sent and received symbols is bounded above by a certain value l . In this paper, we propose systematic codes for asymmetric limited magnitude channels that are able to correct a single error. We also show...
Conference Paper
This paper shows that the first order Reed-Muller codes punctured in one component fall into a class of t-asymmetric error correcting (t-AEC) codes with very fast decoding. Hence, these linear Reed-Muller codes give a nice example of t-AEC codes which are very simple to both encode and decode. Decoding of these codes is much simpler than the usual...
Conference Paper
The error types in some VLSI systems and some communication media is of asymmetrie in nature. In this paper, for selective-repeat ARQ protocol over m(≥2)-ary asymmetrie channel, some analysis of the throughput when using All Asymmetric Error Detecting (AAED) codes are given. For these codes, the number of retransmissions needed to receive all codew...
Article
Earlier authors have used quotient rings of Gaussian and Eisenstein-Jacobi integers to construct interconnection networks with good topological properties. In this paper, we present a unified study of these two types of networks. Our results include decomposing the edges into disjoint Hamiltonian cycles, a simplification of the calculation of the E...
Conference Paper
An m-ary block code, m = 2, 3, 4, ..., of length n ∈ IN is called balanced if, and only if, every codeword is balanced; that is, the real sum of the codeword components, or weight, is equal to ⌊(m - 1)n/2⌋. This paper presents a tight generalization of Knuth's complementation method with parallel (hence, fast) decoding scheme. Let (wn)m indicate th...
Conference Paper
This paper gives the theory and design of efficient codes capable of correcting errors caused by the insertion and deletion of a repeated symbol in the information sequence. Two efficient methods are described. For any fixed t+, t- ∈ IN, one method gives a fixed length scheme to encode k information bits into a systematic code of length n = k + r,...
Article
Systematic q-ary ( q > 2) codes capable of correcting all asymmetric errors of maximum magnitude l , where l ¿ q - 2, are given. These codes are shown to be optimal. Further, simple encoding/decoding algorithms are described. The proposed code can be modified to design codes correcting all symmetric errors of maximum magnitude l , where l ¿ ( q -...
Conference Paper
In the asymmetric error model, a symbol a over an alphabet Z<sub>q</sub> = {0,1,..., q - 1} may be modified during transmission into b, where b <; a (assuming that the dominant error type is the decreasing error). For some applications, the error magnitude b - a is not likely to exceed a certain threshold l. One such application is the multi-level...
Article
In diversity combining automatic repeat request (ARQ), erroneous packets are combined together forming a single, more reliable, packet. In this paper, we give a diversity combining scheme for the m-ary unidirectional channel. A system using the given scheme with a t-unidirectional error detecting code is able to correct up to E<sub>max</sub> = [t/2...
Article
Let p be the 1 to 0 bit error probability and h(p)=-p log2 p-(1-p) log2 (1-p). The capacity of the Z-channel is given by CZ=log2 (1+(1-p)pp(1-p)/). For small p, it is shown that CZ≈1-(1/2)h(p) (vs., CBS(p)=1-h(p) for the binary symmetric channel). Coding schemes are also given that almost achieve the Z-channel capacity.
Conference Paper
Full-text available
In an unordered code no codeword is contained in any other codeword. Unordered codes are all unidirectional error detecting (AUED) codes. In the binary case, it is well known that among all systematic codes with k information bits, Berger codes are optimal unordered codes with r = ¿log<sub>2</sub>(k+1)¿ check bits. This paper gives some new theor...
Conference Paper
Systematic q-ary (q > 2) codes capable of correcting all asymmetric errors of maximum magnitude l, where l ¿ q-2, are given. These codes are shown to be optimal. Further, simple encoding/decoding algorithms are described.
Article
Full-text available
In this paper, we investigate a hybrid network coding technique to be used at a wireless base station (BS) or access point (AP) to increase the throughput efficiency of single-hop wireless networks. Traditionally, to provide reliability, lost packets from different flows (applications) are retransmitted separately, leading to inefficient use of wir...
Conference Paper
The error detecting problem for limited magnitude errors over high radix channels is studied. In this error model, the error magnitude does not exceed a certain limit known beforehand. For asymmetric and unidirectional channels, both all and t error detecting codes are studied. Further, close-to-optimal codes are proposed. For symmetric channels, o...
Article
Traditional approaches to reliably transmit information over an error-prone network employ either forward error correction (FEC) or retransmission techniques. In this paper, we propose some network coding schemes to reduce the number of broadcast transmissions from one sender to multiple receivers. The main idea is to allow the sender to combine an...
Article
In this note, we give a correction to the Proof of Theorem 2 in L. G. Tallini, S. Al-Bassam, and B. Bose, "Feedback Codes Achieving the Capacity of the Z-Channel," IEEE Transactions on Information Theory, vol. 54, pp. 1357-1362, March 2008.
Conference Paper
A general key equation based on elementary symmetric functions is developed for decoding some binary error control codes. Here, the syndrome is obtained by computing the elementary symmetric functions (instead of the power-sums) of the received word. A new class of codes is introduced in this paper which can correct up to t<sub>0</sub> 0 rarr 1 err...
Conference Paper
This paper proposes hybrid ARQ-random network coding frameworks for real-time media broadcast over single-hop wireless networks. We model the wireless channel as a packet erasure channel and our proposed schemes aim at minimizing the packet erasure rate in order to enhance the media quality at receivers. We consider two forms of random network codi...
Article
Given the 1 to 0 bit error probability, pisin[0, 1], the capacity of the Z-channel is given by C<sub>z</sub>=log<sub>2</sub>(1+p<sup>p/(1-p)</sup>-p<sup>1/(1-p)</sup>). Some new error free feedback coding schemes that achieve the Z-channel capacity are presented.
Conference Paper
Reliable transmission over an error-prone channel is typically accomplished via channel coding or retransmission of the lost information. In this paper, we investigate a joint network-channel coding technique to increase the bandwidth efficiency of wireless networks. In particular, we show that the proposed joint network-channel coding approach whi...
Article
Gray codes, where two consecutive codewords differ in exactly one position by plusmn1, are given. In a single-radix code, all dimensions have the same base, say, kappa, whereas, in a mixed-radix code, the base in one dimension can be different from the base in another dimension. Constructions of new classes of mixed-radix Gray codes are presented....
Article
Some new classes of systematic t-unidirectional error-detecting codes over Z<sub>m</sub> are designed. It is shown that the constructed codes can detect two errors using two check digits. Furthermore, the constructed codes can detect up to m<sup>r-2</sup> + r-2 errors using r ges 3 check bits. A bound on the maximum number of detectable errors usin...
Conference Paper
Gray codes, where two consecutive codewords differ in exactly one position by ±1, are given. In a single radix code, all dimensions have the same base, say k, whereas in a mixed radix code the base in one dimension can be different from the base in another dimension. Constructions of new classes of mixed radix Gray codes are presented. It is shown...
Article
Forward error control (FEC) and automatic-repeat request (ARQ) is two main techniques used for reliable data transmission in computer and communication systems. In this paper, some simple, low cost error control techniques for ARQ protocols used with binary unidirectional channels are described. The proposed schemes can correct up to [t/2] unidirec...
Article
New cyclic n-digit Gray codes are constructed over f0; 1; : : : ; R 1g for all R 3, n 2. These codes have the property that the distribution of the digit changes (transition counts) is close to uniform: For each n 2, every transition count is within R 1 of the average Rn=n, and for the 2-digit codes every transition count is either bR2=2c or dR2=2e...
Article
In the automatic repeat request (ARQ) protocol, the sender keeps retransmitting a code word until it receives a positive acknowledgment from the receiver sent through the feedback channel. This correspondence proposes plain and diversity combining hybrid ARQ protocol communication schemes suitable for the m(ges2)-ary asymmetric channel using t-asym...
Article
A fault-tolerant routing method that can tolerate solid faults using only two virtual channels is presented. The proposed routing algorithm, called FT-Ecube, not only uses a fewer number of virtual channels but also tolerates f-chains in the meshes. Furthermore, the proposed scheme misroutes messages both clockwise and counter clockwise directions...
Article
Let Φ<sub>m</sub>⊆ C be the set of all mth roots of unity, m∈ IN. A balanced code over Φ<sub>m</sub> is a block code over the alphabet Φ<sub>m</sub> such that each code word is balanced; that is, the complex sum of its components (or weight) is equal to 0. Let B<sub>m</sub>(n) be the set of all balanced words of length n over Φ<sub>m</sub>. In this...
Conference Paper
In the ARQ (Automatic Retransmission Request) protocol, the sender keeps retransmitting a codeword until it receives a positive acknowledgment from the receiver sent through the feedback channel. This paper proposes Plain and Diversity Combining ARQ Hybrid protocol communication schemes suitable for the m(≥ 2)-ary asymmetric channel using t-Asymmet...
Article
This work addresses the problem of having a limited number of resources in a multicomputer system that each processing element needs to access. Placing these resources in the system so that all processing elements can access them in a comparable manner is called the “resource placement problem”. In this paper, we present resource placement methods...
Article
Corrupted packets that cause retransmission requests in automatic retransmission request (ARQ) systems can be reused. They can be combined with additional stored copies of the transmitted packet in order to obtain a single packet which is more reliable than any of the constituents. A scheme which suits the Z-channel is proposed here and the perform...
Article
Bose and Lin introduced a class of systematic codes for the detection of asymmetric errors (or equivalently, unidirectional errors). The determination of the probability of undetected error for these codes has been an open problem for many years. In this correspondence, the undetectable errors are characterized and the probability of undetected err...
Article
This paper introduces a type-I hybrid ARQ scheme for the Z-channel, based on a class of codes which can correct t asymmetric errors and further detect d (d > t) more. The specific parameters of the ARQ schemes are considered and an upper bound on the probability of undetected error is derived. We give a couple of detailed examples based on classic...
Conference Paper
Many web servers and database servers make efficient use of clustering from cost, scalability and availability standpoints. Existing cluster interconnects use switching schemes which minimize transmission latency but do not provide any guarantee on the delay (e.g., Wormhole switching). The variety of applications which are run on clusters mandate t...
Conference Paper
In this paper, the code that capable of correcting t-errors and detecting unidirectional errors (t-EC-AUED code) is presented. The t-EC AUED code is studied with the maximal size by using Sperner's theorem. The theorem says that the balanced code is an optimal all unidirectional error detecting code with the maximum number of code words.
Conference Paper
Bose and Lin introduced a class of systematics codes for the detection of unidirectional errors (or equivalently, asymmetric errors). The codes are described, the undetectable errors are characterized, and the probability of undetected error for these codes is determined.
Conference Paper
Due to the increasing popularity of mobile networking systems, the scalability becomes a significant new challenge for ad hoc network protocols. To provide a scalable solution for mobile ad hoc networks, we introduce a Position-Based Topology-Independent Scheduling (PB-TIS) algorithm. Since the topology-transparent scheduling algorithms in the lite...
Article
Solutions for decomposing a higher dimensional torus to edge disjoint lower dimensional tori, in particular, edge disjoint Hamiltonian cycles are obtained based on the coding theory approach. First, Lee distance Gray codes in Z/sub k//sup n/ are presented and then it is shown how these codes can directly be used to generate edge disjoint Hamiltonia...
Article
In this paper, we introduce two encoding and decoding methods for balanced codes. The proposed methods are more efficient in terms of computational complexity. The first one complements several appropriate bits at a time instead of complementing one bit at a time as done in Knuth's method. The second one is a parallel implementation of Knuth's meth...
Article
Perfect distance-d placements in 3D tori is investigated. It is proved that there exists no linear perfect distance-1 placement other than the known ones so far. Perfect distance-d placements in 3D tori, where at least one of the dimensions is 2, are presented. Furthermore, quasi-perfect placements for 3D tori are introduced.
Conference Paper
A lower bound for the detected error probability for systematic asymmetric error detecting (AED) codes is introduced, using the Z-channel model. This bound finds applicability in evaluating any feedback control system for asymmetric transmission channels.
Article
A construction of perfect/quasiperfect Lee distance codes in Z<sub>K</sub><sup>2</sup> is introduced. For this class of codes, a constant time encoding scheme is defined, the minimum code distance is derived, and the maximum covering radius is calculated. Efficient decoding schemes are investigated and developed. In general, a code of this class ca...
Article
In asynchronous systems, the sender encodes a data word with a code word from an unordered code and transmits the code word on the parallel bus lines. In this paper, a transmission time analysis for the above parallel asynchronous communication scheme is presented. It is proven that the average transmission time for a code word is a strictly increa...
Conference Paper
This paper completely solves the coding problem for balanced codes over Φ<sub>m</sub>, when m = 4. In fact, it reduces the problem of designing efficient coding schemes for balanced codes over Φ<sub>4</sub> to the design of efficient balanced codes over Φ4 = {-1,+1}. In particular, the paper proposes efficient constructions for balanced codes over...
Conference Paper
In ARQ systems packets that cause retransmission requests can be reused. A diversity combining scheme for the Z-channel is proposed here, which significantly improves the throughput and the accepted packet error rate of a pure ARQ protocol using asymmetric error detection.
Conference Paper
Lee distance Gray codes over Z<sub>k</sub><sup>n</sup> are designed and then it is shown how these codes can be used to generate edge disjoint Hamiltonian cycles in k-ary n-cubes and binary hypercubes.
Article
The k-ary n-cube is one of the popular topologies for interconnecting processors in multicomputers. This paper studies the difference in communication requirements between two Lee distance Gray codes when moving data from processors in normal radix k order to those in Gray code order in k -ary n-cube networks. Algorithms for k-ary to Gray code conv...
Article
A construction of perfect/quasi-perfect Lee distance codes over ZK2 for any K is designed. The minimum distance and the covering radius of these codes are proved. Efficient decoding algorithms are investigated.
Article
The asymmetric nature of bit errors in optical communication provides the grounds for efficient error control techniques; the Z-channel and systematic asymmetric error detection (AED) codes can be succesfully combined with ARQ protocols for feedback error control enhancement. The throughput and the accepted packet error rate for such systems are de...
Conference Paper
The errors in optical communication are of the asymmetric type. Using the Z-channel model, the Bose-Lin asymmetric error detecting codes are analyzed as part of a feedback communication system. The probabilities of detectable and undetectable errors are derived from the code construction using certain properties of the information and check sequenc...
Conference Paper
Mobile hosts typically have scarce energy due to short battery lifetimes. We propose a scheduling algorithm which is suitable for battery-constrained multihop packet radio networks. The proposed algorithm, called ECTS (energy conserving transmission scheduling), focuses on conserving battery power while preserving topology transparency, guaranteed...
Conference Paper
In this paper, based on coding theory concepts, a new time scheduling algorithm for multihop packet radio networks is described. Each mobile host is assigned a word from an appropriate constant weight code of length n, distance d and weight w. The host can send a message at the j<sup>th</sup> slot provided the assigned code has a 1 in this j <sup>t...
Article
It is proved that for all values of code length n, except when n=2, 4, and 8 and possibly when n=2<sup>r</sup> and n=2<sup>r</sup>+1, where r&ges;1, the Hamming codes are also optimal systematic single asymmetric error-correcting codes. For the cases n=2<sup>r</sup> and n=2 <sup>r</sup>+1, r&ges;4, when not all information words are used, two effic...
Conference Paper
A binary code of length n is called a balanced code if each codeword contains exactly [n/2] (or [n/2]) ones and [n/2] (or [n/2]) zeros. In this paper, we give two improved methods for encoding and decoding balanced codes. The first one, called improved single map, improves the computation complexity of Knuth's single map function. This method, inst...
Conference Paper
A fault ring is a connection of only nonfaulty adjacent nodes and links such that the interior of the ring contains only faulty components. This paper proposes two wormhole routing algorithms that deal with more relaxed shapes of fault rings than previously known algorithms in the mesh networks. As a result, the number of components to be made disa...
Conference Paper
In a constant weight w code of length n, each code word has w 1s and n-w 0s. If the ratio w/n is low, the code is referred to as a low constant weight (LCW) code. In this paper, some simple designs of LCW codes are presented. Further, the speed performance of these codes is derived and then it is shown that these codes have much better performance...
Conference Paper
Lee distance Gray codes are shown to be useful in edge disjoint decomposition of higher dimensional torus to lower dimensional tori, particularly edge disjoint Hamiltonian cycles. The mapping functions, which map a node in radix number system to the corresponding Gray codewords are simple. For k-ary n-cube, it is required to calculate only one mapp...
Article
Let S (N,q) be the set of all words of length N over the bipolar alphabet (-1,+1), having a qth order spectral-null at zero frequency. Any subset of S (N,q) is a spectral-null code of length N and order q. This correspondence gives an equivalent formulation of S(N,q) in terms of codes over the binary alphabet (0,1), shows that S(N,2) is equivalent...
Article
Fault-tolerant communication algorithms for k-ary n-cubes are introduced. These include: One-to-all broadcasting, all-to-all broadcasting, one-to-all personalized communication, and all-to-all personalized communication. Each of these algorithms can tolerate up to (2n-2) node failures provided that k>(2n-2) and k>3. Extensions of these algorithms w...
Article
A balanced code with k information bits and r check bits is a binary code of length n=k+r and cardinality 2<sup>k</sup> such that the number of 1s in each code word is equal to [n/2]. This paper describes the design of efficient balanced codes with parallel encoding and parallel decoding. In this case, since area and delay of such circuits are crit...
Article
Efficient utilization of processing resources in a large, multiuser parallel computer depends on processor allocation algorithms that minimize system fragmentation. We propose three processor allocation algorithms for the k-ary n-cube class of parallel architectures, which includes the hypercube and multidimensional torus. The k-ary Partner strateg...
Conference Paper
In asynchronous buses, the sender encodes a data word with a code word from an unordered code and transmits it on the parallel bus lines. In this paper some transmission time analysis for the above parallel asynchronous communication scheme are presented. It is proved that the average transmission time for a code word is a strictly increasing funct...
Conference Paper
In asynchronous buses, the sender encodes a data word with a code word from an unordered code and transmits it on the parallel bus lines. In this paper, some transmission time analyses for the above parallel asynchronous communication scheme are presented. It is proved that the average transmission time for a code word is a strictly increasing func...
Article
The torus is a topology that is the basis for the communication network of several multicomputers in use today. This paper briefly explores several topological characteristics of a generalized torus network using concepts from Coding theory and Graph theory. From Coding theory, the Lee distance metric and Gray codes are extended to mixed radix numb...
Conference Paper
Non-redundant fault-tolerant communication algorithms for faulty k-ary n-cubes are introduced. These include: one-to-all broadcasting, all-to-all broadcasting, one-to-all personalized communication and all-to-all personalized communication. Each of these algorithms can tolerate up to (2n-2) node failures provided that k>(2n-2) and k>3. The communic...
Article
Recently, Matsuzawa and Fujiwara (1988) proposed a novel scheme to mask line faults of bus line circuits (such as address buses) due to short circuit defects between adjacent lines. In this paper, first we propose the fundamental theory and then present some efficient designs of these codes. Some lower and upper bounds for the optimal codes are als...
Article
A constant weight, w, code with k information bits and r check bits is a binary code of length n=k+r and cardinality 2<sup>k</sup> such that the number of 1s in each code word is equal to w. When w=[n/2], the code is called balanced. This paper describes the design of balanced and constant weight codes with parallel encoding and parallel decoding....
Conference Paper
Results on how to place a limited number of resources in two dimensional torus-based parallel systems are described. The resources are placed so that every non-resource node is within a given distance d from some resource node. It is proved that the proposed methods are optimal in terms of reducing the maximum distance between the resource and the...
Conference Paper
A non-redundant fault-tolerant broadcasting algorithm in a faulty k-ary n-cube is designed. The algorithm can adapt up to (2n-2) node failures. Compared to the optimal algorithm in a fault-free k-ary n-cube, the proposed algorithm requires at most 3 extra communication steps in the case of cut through packet routing and (n + 1) extra steps in the c...
Article
This paper considers the problem of single-node broadcasting in a faulty k-ary n-cube. First the natural broadcast algorithm for a non-faulty k-ary n-cube, the Basic Broadcast Algorithm (BBA), is reviewed. Then the Partner Fault-Tolerant Broadcasting Algorithm (PFTBA) is presented. The Partner Fault-Tolerant Broadcast Algorithm is designed to broad...
Article
This paper investigates methods to locate system resources, such as expensive hardware or software modules, to provide the most effective cost/performance trade-offs in a torus parallel machine. This paper contains some solutions to perfect distance-t and perfect/quasi-perfect j-adjacency placement in a k-ary n-cube and a torus using Lee distance e...
Article
A new fault-tolerant all-to-all broadcasting algorithm in an n-dimensional hypercube with up to [n/2] faulty links is given. An extension of this algorithm that can tolerate up to [n/2] faulty nodes is also described. These algorithms assume a multiport I/O model, meaning each node can send and receive messages from all its adjacent nodes simultane...

Citations

... So there is a difference in the models, and that is why in our model the capacity increases with feedback. Additionally our model is different from the classical automatic repeat request (ARQ) [1], [7], [17] [21,Chapter 22] [26], [29], [31], [32]. In an ARQ system an error detecting code is used, and if the receiver detects some errors then it requests the sender to retransmit the same data. ...