Minimum-cost multicast over coded packet networks

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved

Exponential Error Bounds for Algebraic Soft-Decision Decoding of Reed-Solomon Codes

Algebraic soft decision decoding of Reed-Solomon codes is a promising technique for exploiting reliability information in the decoding process. While the algorithmic aspects of the decoding algorithm are reasonably well understood and, in particular, complexity is polynomially bounded in the length of the code, the performance analysis has relied almost entirely on simulation results. Analytic exponential error bounds that can be used to tightly bound the performance of Reed-Solomon codes under algebraic soft decision decoding are presented in this paper. The analysis is used in a number of examples and several extensions and consequences of the results are presented

Optimized Network Coding for Wireline and Aref Networks

97 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2006.With the aim of understanding network coding in wireless scenarios, we investigate multicasting in Aref networks. These networks do not capture interference, but they do incorporate deterministic broadcasting. We characterize the multicast capacity of Aref networks, the achievability of which is shown using an ensemble of random codes. In order to construct structured capacity achieving codes, we consider a natural layered coding scheme and show that this coding scheme is suboptimal.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD

Asynchronous Network Coded Multicast

We consider the problem of setting up a multicast connection of minimum cost using network coding. It is well-known that this can be posed in the form of a convex program. Our contribution is an asynchronous algorithm for solving the optimization problem, in analogy to the well-known distributed asynchronous Bellman-Ford algorithm for routing. Furthermore, we provide extensive simulation results showing fast convergence despite the lack of any central clock in the network and robustness with respect to link- or node failures

Minimal network coding for multicast

Abstract — We give an information flow interpretation for multicasting using network coding. This generalizes the fluid model used to represent flows to a single receiver. Using the generalized model, we present a decentralized algorithm to minimize the number of packets that undergo network coding. We also propose a decentralized algorithm to construct capacity achieving multicast codes when the processing at some nodes is restricted to routing. The proposed algorithms can be coupled with existing decentralized schemes to achieve minimum cost muticast. I

Minimal network coding for multicast

Abstract — We give an information flow interpretation for multicasting using network coding. This generalizes the fluid model used to represent flows to a single receiver. Using the generalized model, we present a decentralized algorithm to minimize the number of packets that undergo network coding. We also propose a decentralized algorithm to construct capacity achieving multicast codes when the processing at some nodes is restricted to routing. The proposed algorithms can be coupled with existing decentralized schemes to achieve minimum cost muticast. I

Achieving Minimum-Cost Multicast: A Decentralized Approach Based on Network Coding

We present decentralized algorithms that compute minimum-cost subgraphs for establishing multicast connections in networks that use coding. These algorithms, coupled with existing decentralized schemes for constructing network codes, constitute a fully decentralized approach for achieving minimum-cost multicast. Our approach is in sharp contrast to the prevailing approach based on approximation algorithms for the directed Steiner tree problem, which is suboptimal and generally assumes centralized computation with full network knowledge. We also give extensions beyond the basic problem of fixed-rate multicast in networks with directed point-to-point links, and consider the problem of minimum-energy multicast in wireless networks as well as the case of a concave utility function at the sender

Estimation of the annual cumulative radiation dose received by the dentist in dental clinics in Chennai

Aim and Objectives: To estimate the annual cumulative radiation dose received by a dentist in a ′less than an ideally sized clinic′ in Chennai. The objective of the study is to estimate the annual cumulative radiation dose received by the dentist at various distances and various angulations from the x-ray tube. Study Design: The head of a mannequin model was mounted on the dental chair to simulate a patient′s head and three thermoluminescent dosimeter (TLD) chips were kept at various distances and various angulations, at a constant height. The standard conventional intraoral dental radiographic unit was used, which was kept stationary, with a constant voltage of 70 Kv, 8 mA current, and a constant exposure time of 0.3 seconds. Ninety-two TLD chips were exposed 20 times a day with constant horizontal angulations for a period of one year. The reading from the TLD chips was obtained on a computer through a TLD Badge Reader. Statistical Analysis: Post Hoc tests and One-way analysis of variance (ANOVA) were used. Results and Conclusion: A decreasing trend was obtained in the average radiation doses, as the distance increased from the x-ray source, and a highly significant difference in doses (P < 0.001%) was found between 4 and 5.5 feet (ft). We found a minimum average radiation dose at an angle of 60° to 80° and behind the tube. The purpose of this study was to create awareness among dental professionals, who had ′less than an ideally sized clinic′. We recommend that the dentist follow guidelines suggested by the National Council on Radiation Protection and Measurements (NCRP), USA. From this study, it is clear that most clinics are of sizes that do not permit this distance (6 ft), and hence, it is recommended that they use suitable barriers