Cooperative Symbol-Based Signaling for Networks with Multiple Relays

Wireless channels suffer from severe inherent impairments and hence reliable and high data rate wireless transmission is particularly challenging to achieve. Fortunately, using multiple antennae improves performance in wireless transmission by providing space diversity, spatial multiplexing, and power gains. However, in wireless ad-hoc networks multiple antennae may not be acceptable due to limitations in size, cost, and hardware complexity. As a result, cooperative relaying strategies have attracted considerable attention because of their abilities to take advantage of multi-antenna by using multiple single-antenna relays. This study is to explore cooperative signaling for different relay networks, such as multi-hop relay networks formed by multiple single-antenna relays and multi-stage relay networks formed by multiple relaying stages with each stage holding several single-antenna relays. The main contribution of this study is the development of a new relaying scheme for networks using symbol-level modulation, such as binary phase shift keying (BPSK) and quadrature phase shift keying (QPSK). We also analyze effects of this newly developed scheme when it is used with space-time coding in a multi-stage relay network. Simulation results demonstrate that the new scheme outperforms previously proposed schemes: amplify-and-forward (AF) scheme and decode-and-forward (DF) scheme

Capacity Results for Block-Stationary Gaussian Fading Channels with a Peak Power Constraint

We consider a peak-power-limited single-antenna block-stationary Gaussian fading channel where neither the transmitter nor the receiver knows the channel state information, but both know the channel statistics. This model subsumes most previously studied Gaussian fading models. We first compute the asymptotic channel capacity in the high SNR regime and show that the behavior of channel capacity depends critically on the channel model. For the special case where the fading process is symbol-by-symbol stationary, we also reveal a fundamental interplay between the codeword length, communication rate, and decoding error probability. Specifically, we show that the codeword length must scale with SNR in order to guarantee that the communication rate can grow logarithmically with SNR with bounded decoding error probability, and we find a necessary condition for the growth rate of the codeword length. We also derive an expression for the capacity per unit energy. Furthermore, we show that the capacity per unit energy is achievable using temporal ON-OFF signaling with optimally allocated ON symbols, where the optimal ON-symbol allocation scheme may depend on the peak power constraint.Comment: Submitted to the IEEE Transactions on Information Theor

Mutual Information and Minimum Mean-square Error in Gaussian Channels

This paper deals with arbitrarily distributed finite-power input signals observed through an additive Gaussian noise channel. It shows a new formula that connects the input-output mutual information and the minimum mean-square error (MMSE) achievable by optimal estimation of the input given the output. That is, the derivative of the mutual information (nats) with respect to the signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input statistics. This relationship holds for both scalar and vector signals, as well as for discrete-time and continuous-time noncausal MMSE estimation. This fundamental information-theoretic result has an unexpected consequence in continuous-time nonlinear estimation: For any input signal with finite power, the causal filtering MMSE achieved at SNR is equal to the average value of the noncausal smoothing MMSE achieved with a channel whose signal-to-noise ratio is chosen uniformly distributed between 0 and SNR

Information capacity of genetic regulatory elements

Changes in a cell's external or internal conditions are usually reflected in the concentrations of the relevant transcription factors. These proteins in turn modulate the expression levels of the genes under their control and sometimes need to perform non-trivial computations that integrate several inputs and affect multiple genes. At the same time, the activities of the regulated genes would fluctuate even if the inputs were held fixed, as a consequence of the intrinsic noise in the system, and such noise must fundamentally limit the reliability of any genetic computation. Here we use information theory to formalize the notion of information transmission in simple genetic regulatory elements in the presence of physically realistic noise sources. The dependence of this "channel capacity" on noise parameters, cooperativity and cost of making signaling molecules is explored systematically. We find that, at least in principle, capacities higher than one bit should be achievable and that consequently genetic regulation is not limited the use of binary, or "on-off", components.Comment: 17 pages, 9 figure

Capacity of a Nonlinear Optical Channel with Finite Memory

The channel capacity of a nonlinear, dispersive fiber-optic link is revisited. To this end, the popular Gaussian noise (GN) model is extended with a parameter to account for the finite memory of realistic fiber channels. This finite-memory model is harder to analyze mathematically but, in contrast to previous models, it is valid also for nonstationary or heavy-tailed input signals. For uncoded transmission and standard modulation formats, the new model gives the same results as the regular GN model when the memory of the channel is about 10 symbols or more. These results confirm previous results that the GN model is accurate for uncoded transmission. However, when coding is considered, the results obtained using the finite-memory model are very different from those obtained by previous models, even when the channel memory is large. In particular, the peaky behavior of the channel capacity, which has been reported for numerous nonlinear channel models, appears to be an artifact of applying models derived for independent input in a coded (i.e., dependent) scenario