Secure Communication over Trellis Using Fundamental Cut-set and Fundamental Circuits☆
TL;DR: A reliable and secure communication system which provides reliability by the Error Correction Techniques and Security by the graph based Cryptosystem is proposed and intruder's access to the information can be avoided.
About: This article is published in Procedia Computer Science.The article was published on 2015-01-01 and is currently open access. It has received 2 citations till now. The article focuses on the topics: Space–time trellis code & Decoding methods.
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TL;DR: Graph Theory with Applications to Engineering and Computer as mentioned in this paper is an excellent introductory treatment of graph theory and its applications that has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject.
Abstract: Graph Theory with Applications to Engineering and Computer ... This outstanding introductory treatment of graph theory and its applications has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject. The first nine chapters constitute an excellent overall introduction, requiring only some knowledge of set theory and matrix algebra.
16 citations
TL;DR: It has been shown that the proposed communication framework achieves the goal of reliability and security considering the channel noise and cryptanalytic attacks.
Abstract: Ensuring reliability and security has been a challenge in modern communication systems. To achieve these challenges, a novel reliable and secure communication system is designed in this paper. Reliability is achieved by constructing a class of error correcting codes called concatenated kernel codes. Security in terms of source authentication is achieved from using graph nature of trellis employing techniques from graph theory namely fundamental cut-set and fundamental circuit. It has been shown that the proposed communication framework achieves the goal of reliability and security considering the channel noise and cryptanalytic attacks. The theoretical basis of the proposed framework is validated and its performance is evaluated through simulations.
Cites background or methods from "Secure Communication over Trellis U..."
...In adding the security feature to the spanning tree (Selvakumar and Gupta, 2012; Selvakumar et al., 2015), i....
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...In adding the security feature to the spanning tree (Selvakumar and Gupta, 2012; Selvakumar et al., 2015), i.e., adding encryption and decryption, the following theorems (Deo, 2004) are useful....
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References
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TL;DR: The general problem of estimating the a posteriori probabilities of the states and transitions of a Markov source observed through a discrete memoryless channel is considered and an optimal decoding algorithm is derived.
Abstract: The general problem of estimating the a posteriori probabilities of the states and transitions of a Markov source observed through a discrete memoryless channel is considered. The decoding of linear block and convolutional codes to minimize symbol error probability is shown to be a special case of this problem. An optimal decoding algorithm is derived.
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TL;DR: This outstanding introductory treatment of graph theory and its applications has had a long life in the instruction of advanced undergraduates and graduate students in all areas that require knowledge of this subject.
1,161 citations
25 Jun 2000
TL;DR: Any state realization of a code can be put into normal form without essential change in the corresponding graph or in its decoding complexity; this fundamental result has many applications, including to dual state spaces, dual minimal trellises, duals to Tanner (1981) graphs, dual input/output (I/O) systems, and dual kernel and image representations.
Abstract: A generalized state realization of the Wiberg (1996) type is called normal if symbol variables have degree 1 and state variables have degree 2. A natural graphical model of such a realization has leaf edges representing symbols, ordinary edges representing states, and vertices representing local constraints. Such a graph can be decoded by any version of the sum-product algorithm. Any state realization of a code can be put into normal form without essential change in the corresponding graph or in its decoding complexity. Group or linear codes are generated by group or linear state realizations. On a cycle-free graph, there exists a well-defined minimal canonical realization, and the sum-product algorithm is exact. However, the cut-set bound shows that graphs with cycles may have a superior performance-complexity tradeoff, although the sum-product algorithm is then inexact and iterative, and minimal realizations are not well-defined. Efficient cyclic and cycle-free realizations of Reed-Muller (RM) codes are given as examples. The dual of a normal group realization, appropriately defined, generates the dual group code. The dual realization has the same graph topology as the primal realization, replaces symbol and state variables by their character groups, and replaces primal local constraints by their duals. This fundamental result has many applications, including to dual state spaces, dual minimal trellises, duals to Tanner (1981) graphs, dual input/output (I/O) systems, and dual kernel and image representations. Finally a group code may be decoded using the dual graph, with appropriate Fourier transforms of the inputs and outputs; this can simplify decoding of high-rate codes.
643 citations