I apologize if this belongs in the EE section; I figured that I might get a better response if I posted it in the math section.(adsbygoogle = window.adsbygoogle || []).push({});

This question regards a lower bound on the channel capacity of an arbitrary channel (single channel, per use) by means of the 'power inequality'.

I really want to solve this myself so if someone could just nudge me in the right direction I would be very grateful. The upper bound in terms of theentropy poweris trivial to show, but for some reason in employing theentropy power inequalityI cannot arrive at the result that I seek.

The channel is noise additive using the relations that Y = X + Z, where Z is the noise source and X is the channel symbol.

By defining

[tex]Q \triangleq (2\pi e)^{-1} 2^{2h(z)}[/tex]

and using the inequality

[tex]e^{2h(y)} \geq e^{2h(x)} + e^{2h(z)}[/tex]

I wish to derive a lower bound on the channel capacity in terms of [itex]P[/itex] and [itex]Q[/itex]. The upper bound on the capacity (in terms of the entropy power) is simply [itex]C \leq \frac{1}{2}log(\frac{P+N}{Q})[/itex], where N is the noise power.

Any shove in the right direction would be greatly appreciated!

All the best

-Brendan

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# Lower bound

Can you offer guidance or do you also need help?

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