J.-P. Tillich and G. Zemor. Discrete isoperimetric inequalities and the probability of a decoding error. Combin. Probab. Comput., 9(5):465-479, 2000. Home/Search Document Details and Download
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Estimates of the Distance Distribution of Codes and Designs - Ashikhmin, Barg, Litsyn (Correct)
....0.25 0.3 0.35 0.4 0.45 0.5 0.25 0.3 0.35 0.4 0.45 0.5 ffi Figure 1: Region in the (ffi; plane, marked with a , where (18) is the best estimate of the distance distribution exponential growth than jCj: However, there is a range of code parameters when the bound in [20] is better than both. In [26] the authors study the threshold probability of a code C with a given distance d, i.e. the crossover probability (C) of a binary symmetric channel such that the error probability of maximum likelihood decoding of C in this channel equals 1=2: They give a lower bound on (C) via an upper bound on ....
J.-P. Tillich and G. Z'emor, Discrete isoperimetric inequalities and the probability of decoding error, Combinatorics, Probability and Computing, to appear. 24
The Gaussian isoperimetric inequality and decoding error.. - Tillich, Zémor (2001) Self-citation (Tillich Emor) (Correct)
....1 to error exponents for the best possible spherical codes : we shall see that even in this case, the very general exponential upper bound of Theorem 1 misses the right exponent by only a small constant. 2 Overview of the proof of Theorem 1 The proof of Theorem 1 follows ideas developed in [10, 11] where a result of a similar nature is proved for the binary symmetric channel. The basic idea is to 4 derive an inequality of the form d d P e ( f(P e ( through a geometric interpretation of P e ( and d d P e ( and then integrate this inequality to obtain Theorem 1. The ....
J.P. Tillich and G. Zemor, \Discrete isoperimetric inequalities and the probability of a decoding error," Combinatorics, Probability and Computing, vol. 9, pp. 465-479, 2000. 11
Surface Measures and Related Functional Inequalities on.. - Houdre, Privault (2003) (Correct)
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J.-P. Tillich and G. Zemor. Discrete isoperimetric inequalities and the probability of a decoding error. Combin. Probab. Comput., 9(5):465-479, 2000.
Surface Measures and Related Functional Inequalities on.. - Houdre, al. (2003) (Correct)
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J.-P. Tillich and G. Zemor. Discrete isoperimetric inequalities and the probability of a decoding error. Combin. Probab. Comput., 9(5):465-479, 2000.
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