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Register a new userThe Poisson Channel at Low Input Powers
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Added by
Ligong Wang
Publication date
2008
fields
Informatics Engineering
and research's language is
English
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The asymptotic capacity at low input powers of an average-power limited or an average- and peak-power limited discrete-time Poisson channel is considered. For a Poisson channel whose dark current is zero or decays to zero linearly with its average input power $E$, capacity scales like $Elogfrac{1}{E}$ for small $E$. For a Poisson channel whose dark current is a nonzero constant, capacity scales, to within a constant, like $Eloglogfrac{1}{E}$ for small $E$.
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We consider a channel-independent decoder which is for i.i.d. random codes what the maximum mutual-information decoder is for constant composition codes. We show that this decoder results in exactly the same i.i.d. random coding error exponent and almost the same correct-decoding exponent for a given codebook distribution as the maximum-likelihood decoder. We propose an algorithm for computation of the optimal correct-decoding exponent which operates on the corresponding expression for the channel-independent decoder. The proposed algorithm comes in t
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This work considers a Poisson noise channel with an amplitude constraint. It is well-known that the capacity-achieving input distribution for this channel is discrete with finitely many points. We sharpen this result by introducing upper and lower bounds on the number of mass points. Concretely, an upper bound of order $mathsf{A} log^2(mathsf{A})$ and a lower bound of order $sqrt{mathsf{A}}$ are established where $mathsf{A}$ is the constraint on the input amplitude. In addition, along the way, we show several other properties of the capacity and capacity-achieving distribution. For example, it is shown that the capacity is equal to $ - log P_{Y^star}(0)$ where $P_{Y^star}$ is the optimal output distribution. Moreover, an upper bound on the values of the probability masses of the capacity-achieving distribution and a lower bound on the probability of the largest mass point are established. Furthermore, on the per-symbol basis, a nonvanishing lower bound on the probability of error for detecting the capacity-achieving distribution is established under the maximum a posteriori rule.
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