We give new bounds on the reliability function of a typewriter channel with 5 inputs and crossover probability 1/2. The lower bound is more of theoretical than practical importance; it improves very marginally the expurgated bound, providing a counterexample to a conjecture on its tightness by Shannon, Gallager and Berlekamp which does not need the construction of algebraic-geometric codes previously used by Katsman, Tsfasman and VlǍduţ. The upper bound is derived by using an adaptation of the linear programming bound and it is essentially useful as a low-rate anchor for the straight line bound.
Bounds on the reliability of a typewriter channel
DALAI, Marco;
2016-01-01
Abstract
We give new bounds on the reliability function of a typewriter channel with 5 inputs and crossover probability 1/2. The lower bound is more of theoretical than practical importance; it improves very marginally the expurgated bound, providing a counterexample to a conjecture on its tightness by Shannon, Gallager and Berlekamp which does not need the construction of algebraic-geometric codes previously used by Katsman, Tsfasman and VlǍduţ. The upper bound is derived by using an adaptation of the linear programming bound and it is essentially useful as a low-rate anchor for the straight line bound.File in questo prodotto:
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