The "permutation channel" model is a convenient representation of certain communication networks, where packets are not indexed and delivered out-of-order, and closely resembles models of DNA based storage systems. It consists of a standard discrete memoryless channel (DMC) followed by an independent random permutation block that permutes the output codewords of the DMC. In this paper, we present some new general bounds on the so called permutation channel capacity of such channels. Specifically, on the achievability front, we derive a lower bound on the permutation channel capacity of any DMC in terms of the rank of the stochastic matrix of the DMC. On the converse front, we illustrate two complementary upper bounds on the permutation channel capacity of any DMC whose stochastic matrix is entry-wise strictly positive. Together, these bounds characterize the permutation channel capacities of entry-wise strictly positive and "full rank" DMCs. Finally, we also demonstrate two related results concerning the well-known degradation preorder. The first constructs a symmetric channel for any DMC such that the DMC is a degraded version of the symmetric channel, and the second demonstrates the monotonicity of permutation channel capacity.
We evaluate capacity bounds for multiple-input multiple-output (MIMO) additive white Gaussian noise (AWGN) fading channels subject to input amplitude constraints. We focus on two practical cases, in which the transmitter: (i) employs a single antenna amplifier, which induces a constraint on the norm of the input vector, and (ii) it employs multiple amplifiers, one per antenna, which leads to independent constraints on the amplitude of each input vector entry. For both cases, we evaluate the asymptotic capacity gap between upper and lower bounds at high signal-to-noise ratio.
Low-resolution digital-to-analog and analog-to-digital converters (DACs and ADCs) have attracted considerable attention in efforts to reduce power consumption in millimeter wave (mmWave) and massive MIMO systems. This paper presents an information-theoretic analysis with capacity bounds for classes of linear transceivers with quantization. The transmitter modulates symbols via a unitary transform followed by a DAC and the receiver employs an ADC followed by the inverse unitary transform. If the unitary transform is set to a fast Fourier transform (FFT) matrix, the model naturally captures filtering and spectral constraints which are essential to model in any practical transceiver. In particular, this model allows studying the impact of quantization on out-of-band emission constraints. In the limit of a large random unitary transform, it is shown that the effect of quantization can be precisely described via an additive Gaussian noise model. This model in turn leads to simple and intuitive expressions for the power spectrum of the transmitted signal and a lower bound to the capacity with quantization. Comparison with non-quantized capacity and a capacity upper bound that does not make linearity assumptions suggests that while low resolution quantization has minimal impact on the achievable rate at typical parameters in 5-th generation (5G) systems today, satisfying out-of-band emissions are potentially much more of a challenge.
We establish an upper bound on the information-theoretic capacity of line-of-sight (LOS) multiantenna channels with arbitrary antenna arrangements and identify array structures that, properly configured, can attain at least 96.6% of such capacity at every signal-to-noise ratio (SNR). In the process, we determine how to configure the arrays as a function of the SNR. At low- and high-SNR specifically, the configured arrays revert to simpler structures and become capacity-achieving.
The channel capacity of multicarrier faster-than-Nyquist signaling is investigated. We develop a suitable discrete-time channel model and derive an explicit and interpretable channel capacity formula for the multicarrier faster-than-Nyquist signaling under frequency-selective channels. Fundamental capacity benefits of non-orthogonal information packing over time and frequency are discussed.