Stefan M. Moser

On the Capacity of Free-Space Optical Intensity Channels

Upper and lower bounds are derived on the capacity of the free-space optical intensity channel. This channel has a nonnegative input (representing the transmitted optical intensity), which is corrupted by additive white Gaussian noise. To preserve the battery and for safety reasons, the input is constrained in both its average and its peak power. For a fixed ratio of the allowed average power to the allowed peak power, the difference between the upper and the lower bound tends to zero as the average power tends to infinity and their ratio tends to one as the average power tends to zero. When only an average power constraint is imposed on the input, the difference between the bounds tends to zero as the allowed average power tends to infinity, and their ratio tends to a constant as the allowed average power tends to zero.

On the Capacity of the Discrete-Time Poisson Channel

The large-inputs asymptotic capacity of a peak-power and average-power limited discrete-time Poisson channel is derived using a new firm (nonasymptotic) lower bound and an asymptotic upper bound. The upper bound is based on the dual expression for channel capacity and the notion of capacity-achieving input distributions that escape to infinity. The lower bound is based on a lower bound on the entropy of a conditionally Poisson random variable in terms of the differential entropy of its conditional mean.

The fading number of single-input multiple-output fading channels with memory

We derive the fading number of stationary and ergodic (not necessarily Gaussian) single-input multiple-output (SIMO) fading channels with memory. This is the second term, after the double-logarithmic term, of the high signal-to-noise ratio (SNR) expansion of channel capacity. The transmitter and receiver are assumed to be cognizant of the probability law governing the fading but not of its realization. It is demonstrated that the fading number is achieved by independent and identically distributed (i.i.d.) circularly symmetric inputs of squared magnitude whose logarithm is uniformly distributed over an SNR-dependent interval. The upper limit of the interval is the logarithm of the allowed transmit power, and the lower limit tends to infinity sublogarithmically in the SNR. The converse relies inter alia on a new observation regarding input distributions that escape to infinity. Lower and upper bounds on the fading number for Gaussian fading are also presented. These are related to the mean squared-errors of the one-step predictor and the one-gap interpolator of the fading process respectively. The bounds are computed explicitly for stationary mth-order autoregressive AR(m) Gaussian fading processes.

Capacity Results of an Optical Intensity Channel With Input-Dependent Gaussian Noise

This paper investigates a channel model describing optical communication based on intensity modulation. It is assumed that the main distortion is caused by additive Gaussian noise, however, with a noise variance depending on the current signal strength. Both the high-power and low-power asymptotic capacities under simultaneously both a peak-power and an average-power constraint are derived. The high-power results are based on a new firm (nonasymptotic) lower bound and a new asymptotic upper bound. The upper bound relies on a dual expression for channel capacity and the notion of capacity-achieving input distributions that escape to infinity. The lower bound is based on a new lower bound on the differential entropy of the channel output in terms of the differential entropy of the channel input. The low-power results make use of a theorem by Prelov and van der Meulen.

Capacity of the Memoryless Additive Inverse Gaussian Noise Channel

The memoryless additive inverse Gaussian noise channel model describing communication based on the exchange of chemical molecules in a drifting liquid medium is investigated for the situation of simultaneously an average-delay and a peak-delay constraint. Analytical upper and lower bounds on its capacity in bits per molecule use are presented. These bounds are shown to be asymptotically tight, i.e., for the delay constraints tending to infinity with their ratio held constant (or for the drift velocity of the fluid tending to infinity), the asymptotic capacity is derived precisely. Moreover, characteristics of the capacity-achieving input distribution are derived that allow accurate numerical computation of capacity. The optimal input appears to be a mixed continuous and discrete distribution.

The Fading Number of Multiple-Input Multiple-Output Fading Channels With Memory

The fading number of a general (not necessarily Gaussian) regular multiple-input multiple-output (MIMO) fading channel with arbitrary temporal and spatial memory is derived. The channel is assumed to be noncoherent, i.e., neither receiver nor transmitter have knowledge about the channel state, but they only know the probability law of the fading process. The fading number is the second term in the asymptotic expansion of channel capacity when the signal-to-noise ratio (SNR) tends to infinity. It is related to the border of the high-SNR region with double-logarithmic capacity growth.

On the capacity of free-space optical intensity channels

Upper and lower bounds are derived on the capacity of the free-space optical intensity channel. This channel has a nonnegative input (representing the transmitted optical intensity), which is corrupted by additive white Gaussian noise. To preserve the battery and for safety reasons, the input is constrained in both its average and its peak power. For a fixed ratio of the allowed average power to the allowed peak power, the difference between the upper and the lower bound tends to zero as the average power tends to infinity and their ratio tends to one as the average power tends to zero. When only an average power constraint is imposed on the input, the difference between the bounds tends to zero as the allowed average power tends to infinity, and their ratio tends to a constant as the allowed average power tends to zero.

Convex-programming bounds on the capacity of flat-fading channels

We propose a technique to derive analytic upper bounds on channel capacity via its dual expression. This is demonstrated on single- and multi-antenna flat fading channels where the receiver has no side information regarding the pathwise realisation of the fading process. The results indicate that the capacity of such channels typically grows double-logarithmically in the SNR and not logarithmically as the piecewise constant fading models predict.

Expectations of a noncentral chi-square distribution with application to IID MIMO Gaussian fading

In this paper closed-form expressions are derived for the expectation of the logarithm and for the expectation of the n-th power of the reciprocal value (inverse moments) of a noncentral chi-square random variable of even degree of freedom. It is shown that these expectations can be expressed by a family of continuous functions gm(middot) and that these families have nice properties (monotonicity, convexity, etc.). Moreover, some tight upper and lower bounds are derived that are helpful in situations where the closed-form expression of gm(middot) is too complex for further analysis. As an example of the applicability of these results, in the second part of this paper an independent and identically distributed (IID) Gaussian multiple-input-multiple-output (MIMO) fading channel with a scalar line-of-sight component is analyzed. Some new expressions are derived for the fading number that describes the asymptotic channel capacity at high signal-to-noise ratios (SNR).

Optimal Ultrasmall Block-Codes for Binary Discrete Memoryless Channels

Optimal block-codes (in the sense of minimum average error probability, using maximum likelihood decoding) with a small number of codewords are investigated for the binary asymmetric channel (BAC), including the two special cases of the binary symmetric channel (BSC) and the Z-channel (ZC), both with arbitrary cross-over probabilities. For the ZC, the optimal code structure for an arbitrary finite blocklength is derived in the cases of two, three, and four codewords and conjectured in the case of five codewords. For the BSC, the optimal code structure for an arbitrary finite blocklength is derived in the cases of two and three codewords and conjectured in the case of four codewords. For a general BAC, the best codebooks under the assumption of a threshold decoder are derived for the case of two codewords. The derivation of these optimal codes relies on a new approach of constructing and analyzing the codebook matrix not rowwise (codewords), but columnwise. This new tool leads to an elegant definition of interesting code families that is recursive in the blocklength n and admits their exact analysis of error performance. This allows for a comparison of the average error probability between all possible codebooks.