中意绿色能源实验室建设事宜通报-instituteofnetworkcoding

Upper Bounds on Relative Length/Dimension Profile,Zhuojun Zhuang, Yuan LuoShanghai Jiao Tong UniversityINC. the Chinese Hong Kong UniversityAugust 2012,Bounds on relative length/dimension profile (RLDP), the related bound refinement and transformation will be discussed. The results describe the security of the wiretap channel of type II and can also be applied to trellis complexity and secure network coding. RLDP is a generalization of the length/dimension profile (i.e. generalized Hamming weight) of a linear block code, one of the most famous concepts in coding theory.,1. Background,2. Upper Bounds on RLDP,3. Bound Refinement and Transformation,Agenda,4. Code Constructions and Existence Bounds,4,1. Background,The length/dimension profile (LDP) Forney 94 IT, also referred as generalized Hamming weight (GHW) Wei 91 IT, of a linear block code has been applied to trellis complexity (esp. in the satellite system of NASA), secure communication, multiple access communication and puncturing codes.The relative length/dimension profile (RLDP) extends LDP and has been applied to secure communication Luo 05 IT, trellis complexity Zhuang 11 DCC and secure network coding Zhang 09 ChinaCom/ITW.,5,Forney 94 IT G. D. Forney, Dimension/length profiles and trellis complexity of linear block codes,” IEEE Trans. Inform. Theory, vol. 40, no. 6, pp. 1741-1752, 1994.Wei 91 IT V. K. Wei, Generalized Hamming weights for linear codes,” IEEE Trans. Inform. Theory, vol. 37, no. 5, pp. 1412-1418, 1991.Luo 05 IT Y. Luo, C. Mitrpant, A. J. Han Vinck, K. F. Chen, Some new characters on the wire-tap channel of type II,” IEEE Trans. Inform. Theory, vol. 51, no. 3, pp. 1222-1229, 2005.Zhuang 11 DCC Z. Zhuang, Y. Luo, B. Dai, A. J. Han Vinck, On the relative profiles of a linear code and a subcode,” submitted to Des. Codes Cryptogr., under 2nd round review, 2011.Zhang 09 ChinaCom Z. Zhang, Wiretap networks II with partial information leakage,” in 4th International Conference on Communications and Networking in China, Xian, China, Aug. 2009, pp. 1-5.Zhang 09 ITW Z. Zhang, B. Zhuang, An application of the relative network generalized Hamming weight to erroneous wiretap networks,” in 2009 IEEE Information Theory Workshop, Taormina, Sicily, Italy, Oct. 2009, pp. 70-74.,6,Wiretap Channel of Type II with Illegitimate Parties,7,Coset Coding Scheme,8,Security Analysis,9,Subcode and Projection,10,An Example,11,Three Equivalent Concepts,12,Three Equivalent Concepts (cont.),13,Bounds on Sequences,14,Equivalence,15,Upper Bounds on RLDP and Wiretap Channel,16,2. Upper Bounds on RLDP,The bound cannot be achieved in most cases and the conditions for meeting it is rigid.Sharper bounds and code constructions?,Generalized Singleton bound,17,Generalized Plotkin Bound,We say (C,C1) satisfying (4) meets the weak Plotkin bound.,18,We shall see the refined generalized Plotkin bound on RLDP is always sharper than the generalized Singleton bound on RLDP.,19,Generalized Griesmer Bound,20,21,22,Relative Constant-Weight (RCW) Codes,23,RCW Bound,We say (C,C1) satisfying (8) meets the weak RCW bound.,24,If C1 is a zero code, both the RCW bound and the generalized Plotkin bound on RLDP (i.e. RGHW) reduce to the generalized Plotkin bound on LDP (i.e. GHW). Otherwise, the relation is uncertain.,25,26,3. Bound Refinement and Transformation,Bound Refinement,27,Simple Refinement,Without loss of generality we can always assume u is strictly increasing.,28,Refined Bounds and Generalized Singleton Bound,29,Bound Transformation,Bound Transformation (cont.),Bound Transformation (cont.),Generalized Singleton Bounds on RDLP and IRDLP,Improving Generalized Singleton Bounds,36,An Application to Wiretap Channel,37,4. Code Constructions and Existence Bounds,Bounds can be achieved Code constructions,Bounds cannot be achieved Good code pairs Existence bounds,Z. Zhuang, Y. Luo, B. Dai, Code constructions and existence bounds for relative generalized Hamming weight,” Des. Codes Cryptogr., published online, Apr. 2012.,38,Code Constructions,Indirect construction: A technique of constructing code pairs meeting a bound from the existing ones. Direct construction: Focus on the structure of generator matrices with respect to code pairs meeting bounds.,39,Indirect Construction,40,Code Pair Equivalence and Canonical Forms,41,Direct Construction,42,43,Code Pairs Meeting Weak Plotkin Bound,44,Code Pairs Meeting Weak Plotkin Bound (cont.),45,Code Pairs Meeting Weak Plotkin Bound (cont.),46,Code Pairs Meeting Weak Plotkin Bound (cont.),47,Code Pairs Meeting Weak RCW Bound,48,Code Pairs Meeting Weak RCW Bound (cont.),49,Good Code Pairs and Existence Bounds,50,