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Lower bound

  1. May 16, 2008 #1
    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.

    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 the entropy power is trivial to show, but for some reason in employing the entropy power inequality I 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
    Last edited: May 16, 2008
  2. jcsd
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