No Arabic abstract
We introduce a novel mechanism, called timid/bold coding, by which feedback can be used to improve coding performance. For a certain class of DMCs, called compound-dispersion channels, we show that timid/bold coding allows for an improved second-order coding rate compared with coding without feedback. For DMCs that are not compound dispersion, we show that feedback does not improve the second-order coding rate. Thus we completely determine the class of DMCs for which feedback improves the second-order coding rate. An upper bound on the second-order coding rate is provided for compound-dispersion DMCs. We also show that feedback does not improve the second-order coding rate for very noisy DMCs. The main results are obtained by relating feedback codes to certain controlled diffusions.
We provide a practical implementation of the rubber method of Ahlswede et al. for binary alphabets. The idea is to create the skeleton sequence therein via an arithmetic decoder designed for a particular $k$-th order Markov chain. For the stochastic binary symmetric channel, we show that the scheme is nearly optimal in a strong sense for certain parameters.
Integer-forcing source coding has been proposed as a low-complexity method for compression of distributed correlated Gaussian sources. In this scheme, each encoder quantizes its observation using the same fine lattice and reduces the result modulo a coarse lattice. Rather than directly recovering the individual quantized signals, the decoder first recovers a full-rank set of judiciously chosen integer linear combinations of the quantized signals, and then inverts it. It has been observed that the method works very well for most but not all source covariance matrices. The present work quantifies the measure of bad covariance matrices by studying the probability that integer-forcing source coding fails as a function of the allocated rate, %in excess of the %Berger-Tung benchmark, where the probability is with respect to a random orthonormal transformation that is applied to the sources prior to quantization. For the important case where the signals to be compressed correspond to the antenna inputs of relays in an i.i.d. Rayleigh fading environment, this orthonormal transformation can be viewed as being performed by nature. Hence, the results provide performance guarantees for distributed source coding via integer forcing in this scenario.
In this paper, we consider the power allocation (PA) problem in cognitive radio networks (CRNs) employing nonorthogonal multiple access (NOMA) technique. Specifically, we aim to maximize the number of admitted secondary users (SUs) and their throughput, without violating the interference tolerance threshold of the primary users (PUs). This problem is divided into a two-phase PA process: a) maximizing the number of admitted SUs; b) maximizing the minimum throughput among the admitted SUs. To address the first phase, we apply a sequential and iterative PA algorithm, which fully exploits the characteristics of the NOMA-based system. Following this, the second phase is shown to be quasiconvex and is optimally solved via the bisection method. Furthermore, we prove the existence of a unique solution for the second phase and propose another PA algorithm, which is also optimal and significantly reduces the complexity in contrast with the bisection method. Simulation results verify the effectiveness of the proposed two-phase PA scheme.
The performance limits of scalar coding for multiple-input single-output channels are revisited in this work. By employing randomized beamforming, Narula et al. demonstrated that the loss of scalar coding is universally bounded by ~ 2.51 dB (or 0.833 bits/symbol) for any number of antennas and channel gains. In this work, by using randomized beamforming in conjunction with space-time codes, it is shown that the bound can be tightened to ~ 1.1 dB (or 0.39 bits/symbol).
Three areas of ongoing research in channel coding are surveyed, and recent developments are presented in each area: spatially coupled Low-Density Parity-Check (LDPC) codes, non-binary LDPC codes, and polar coding.