An Upper Bound on the Capacity of non-Binary Deletion Channels

We derive an upper bound on the capacity of non-binary deletion channels. Although binary deletion channels have received significant attention over the years, and many upper and lower bounds on their capacity have been derived, such studies for the non-binary case are largely missing. The state of the art is the following: as a trivial upper bound, capacity of an erasure channel with the same input alphabet as the deletion channel can be used, and as a lower bound the results by Diggavi and Grossglauser are available. In this paper, we derive the first non-trivial non-binary deletion channel capacity upper bound and reduce the gap with the existing achievable rates. To derive the results we first prove an inequality between the capacity of a 2K-ary deletion channel with deletion probability $d$, denoted by $C_{2K}(d)$, and the capacity of the binary deletion channel with the same deletion probability, $C_2(d)$, that is, $C_{2K}(d)\leq C_2(d)+(1-d)\log(K)$. Then by employing some existing upper bounds on the capacity of the binary deletion channel, we obtain upper bounds on the capacity of the 2K-ary deletion channel. We illustrate via examples the use of the new bounds and discuss their asymptotic behavior as $d \rightarrow 0$.Comment: accepted for presentation in ISIT 201

A Note on the Deletion Channel Capacity

Memoryless channels with deletion errors as defined by a stochastic channel matrix allowing for bit drop outs are considered in which transmitted bits are either independently deleted with probability $d$ or unchanged with probability $1-d$. Such channels are information stable, hence their Shannon capacity exists. However, computation of the channel capacity is formidable, and only some upper and lower bounds on the capacity exist. In this paper, we first show a simple result that the parallel concatenation of two different independent deletion channels with deletion probabilities $d_1$ and $d_2$, in which every input bit is either transmitted over the first channel with probability of $\lambda$ or over the second one with probability of $1-\lambda$, is nothing but another deletion channel with deletion probability of $d=\lambda d_1+(1-\lambda)d_2$. We then provide an upper bound on the concatenated deletion channel capacity $C(d)$ in terms of the weighted average of $C(d_1)$, $C(d_2)$ and the parameters of the three channels. An interesting consequence of this bound is that $C(\lambda d_1+(1-\lambda))\leq \lambda C(d_1)$ which enables us to provide an improved upper bound on the capacity of the i.i.d. deletion channels, i.e., $C(d)\leq 0.4143(1-d)$ for $d\geq 0.65$. This generalizes the asymptotic result by Dalai as it remains valid for all $d\geq 0.65$. Using the same approach we are also able to improve upon existing upper bounds on the capacity of the deletion/substitution channel.Comment: Submitted to the IEEE Transactions on Information Theor

On LDPC Codes for Gaussian Interference Channels

In this paper, we focus on the two-user Gaussian interference channel (GIC), and study the Han-Kobayashi (HK) coding/decoding strategy with the objective of designing low-density parity-check (LDPC) codes. A code optimization algorithm is proposed which adopts a random perturbation technique via tracking the average mutual information. The degree distribution optimization and convergence threshold computation are carried out for strong and weak interference channels, employing binary phase-shift keying (BPSK). Under strong interference, it is observed that optimized codes operate close to the capacity boundary. For the case of weak interference, it is shown that via the newly designed codes, a nontrivial rate pair is achievable, which is not attainable by single user codes with time-sharing. Performance of the designed LDPC codes are also studied for finite block lengths through simulations of specific codes picked from the optimized degree distributions.Comment: ISIT 201

Linear Precoder Design for Simultaneous Information and Energy Transfer over Two-User MIMO Interference Channels

Communication strategies that utilize wireless media for simultaneous information and power transfer offer a promising perspective for efficient usage of energy resources. With this motivation, we focus on the design of optimal linear precoders for interference channels utilizing such strategies. We formulate the problem of minimizing the total minimum mean-square error while keeping the energy harvested at the energy receivers above given levels. Our framework leads to a non-convex problem formulation. For point-to-point multiple-input multiple-output channels, we provide a characterization of the optimal solutions under a constraint on the number of transmit antennas. For the general interference scenario, we propose two numerical approaches, one for the single antenna information receivers case, and the other for the general case. We also investigate a hybrid signalling scheme, where the transmitter sends a superposition of two signals: a deterministic signal optimized for energy transfer and an information carrying signal optimized for information and energy transfer. It is illustrated that if hybrid signalling is not incorporated into the transmission scheme, interference can be detrimental to the system performance when the number of antennas at the receivers is low.}

Bounds on the Capacity of Random Insertion and Deletion-Additive Noise Channels

We develop several analytical lower bounds on the capacity of binary insertion and deletion channels by considering independent uniformly distributed (i.u.d.) inputs and computing lower bounds on the mutual information between the input and output sequences. For the deletion channel, we consider two different models: independent and identically distributed (i.i.d.) deletion-substitution channel and i.i.d. deletion channel with additive white Gaussian noise (AWGN). These two models are considered to incorporate effects of the channel noise along with the synchronization errors. For the insertion channel case we consider the Gallager's model in which the transmitted bits are replaced with two random bits and uniform over the four possibilities independently of any other insertion events. The general approach taken is similar in all cases, however the specific computations differ. Furthermore, the approach yields a useful lower bound on the capacity for a wide range of deletion probabilities for the deletion channels, while it provides a beneficial bound only for small insertion probabilities (less than 0.25) for the insertion model adopted. We emphasize the importance of these results by noting that 1) our results are the first analytical bounds on the capacity of deletion-AWGN channels, 2) the results developed are the best available analytical lower bounds on the deletion-substitution case, 3) for the Gallager insertion channel model, the new lower bound improves the existing results for small insertion probabilities.Comment: Accepted for publication in IEEE Transactions on Information Theor

An Overview of Physical Layer Security with Finite-Alphabet Signaling

Providing secure communications over the physical layer with the objective of achieving perfect secrecy without requiring a secret key has been receiving growing attention within the past decade. The vast majority of the existing studies in the area of physical layer security focus exclusively on the scenarios where the channel inputs are Gaussian distributed. However, in practice, the signals employed for transmission are drawn from discrete signal constellations such as phase shift keying and quadrature amplitude modulation. Hence, understanding the impact of the finite-alphabet input constraints and designing secure transmission schemes under this assumption is a mandatory step towards a practical implementation of physical layer security. With this motivation, this article reviews recent developments on physical layer security with finite-alphabet inputs. We explore transmit signal design algorithms for single-antenna as well as multi-antenna wiretap channels under different assumptions on the channel state information at the transmitter. Moreover, we present a review of the recent results on secure transmission with discrete signaling for various scenarios including multi-carrier transmission systems, broadcast channels with confidential messages, cognitive multiple access and relay networks. Throughout the article, we stress the important behavioral differences of discrete versus Gaussian inputs in the context of the physical layer security. We also present an overview of practical code construction over Gaussian and fading wiretap channels, and we discuss some open problems and directions for future research.Comment: Submitted to IEEE Communications Surveys & Tutorials (1st Revision

Unsourced Random Access Using Multiple Stages of Orthogonal Pilots: MIMO and Single-Antenna Structures

We study the problem of unsourced random access (URA) over Rayleigh block-fading channels with a receiver equipped with multiple antennas. We propose a slotted structure with multiple stages of orthogonal pilots, each of which is randomly picked from a codebook. In the proposed signaling structure, each user encodes its message using a polar code and appends it to the selected pilot sequences to construct its transmitted signal. Accordingly, the transmitted signal is composed of multiple orthogonal pilot parts and a polar-coded part, which is sent through a randomly selected slot. The performance of the proposed scheme is further improved by randomly dividing users into different groups each having a unique interleaver-power pair. We also apply the idea of multiple stages of orthogonal pilots to the case of a single receive antenna. In all the set-ups, we use an iterative approach for decoding the transmitted messages along with a suitable successive interference cancellation technique. The use of orthogonal pilots and the slotted structure lead to improved accuracy and reduced computational complexity in the proposed set-ups, and make the implementation with short blocklengths more viable. Performance of the proposed set-ups is illustrated via extensive simulation results which show that the proposed set-ups with multiple antennas perform better than the existing MIMO URA solutions for both short and large blocklengths, and that the proposed single-antenna set-ups are superior to the existing single-antenna URA schemes