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Binary transmissions over additive Gaussian noise: A closed-form expression for thechannel capacity

Nasif Ahmed O., Karystinos Georgios

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Summary

We derive a closed-form expression forthe capacity of the additive-Gaussian-noise memorylesschannel with binary input. The capacity expressionthat we obtain contains an infinite series. Truncationof the series -for computation reasons- at an oddor even number of terms results in a lower or upper,respectively, bound on the channel capacity; we provethat the tightness of the bound increases monotonicallywith the number of terms that are included inthe truncated series. Numerical results confirm that,as long as at least the first six terms of the series arecalculated, the corresponding lower or upper boundbecomes indistinguishable from the exact channel capacity.Therefore, with small computational complexitywe obtain accurately the capacity of the Gaussianchannel with binary input.

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