Code spectrum and the reliability function: Binary symmetric channel
نویسنده
چکیده
A new approach for upper bounding the channel reliability function using the code spectrum is described. It allows to treat in a unified way both a low and a high rate cases. In particular, the earlier known upper bounds are improved, and a new derivation of the sphere-packing bound is presented.
منابع مشابه
Supplement to: Code Spectrum and Reliability Function: Binary Symmetric Channel
A much simpler proof of Theorem 1 from [1] is presented below, using notation and formulas numeration of [1]. The text below replaces the subsection General case from §4 of [1, p. 11]. General case. In the general case for some ω we are interested in a pairs (xi,xj) with dij = ωn. But there may exist a pairs (xk,xl) with dkl < ωn. Using the “cleaning” procedure [2] we show that the influence of...
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In the paper notation from [1] is used. A binary symmetric channel (BSC) with crossover probability 0 < p < 1/2 and q = 1 − p is considered. Let F n denote the set of all 2 binary n-tuples, and d(x,y), x,y ∈ F n denote the Hamming distance between x and y. A subset C = C(M,n) = {x1, . . . ,xM} ⊆ F n is called a code of length n and cardinality M . The minimum distance of the code C is d(C) = mi...
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Though the schemes are different, both Horstein’s and Kudryashov’s non-block strategies for communication with feedback over the binary-symmetric channel asymptotically achieve the identical reliability function (error exponent); a function that displays some curious features. For positive rates their reliability function is strictly larger than Burnashev’s and transitions discontinuously at th...
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ورودعنوان ژورنال:
- Probl. Inf. Transm.
دوره 42 شماره
صفحات -
تاریخ انتشار 2006