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

On Asynchronous Communication Systems: Capacity Bounds and Relaying Schemes

abstract: Practical communication systems are subject to errors due to imperfect time alignment among the communicating nodes. Timing errors can occur in different forms depending on the underlying communication scenario. This doctoral study considers two different classes of asynchronous systems; point-to-point (P2P) communication systems with synchronization errors, and asynchronous cooperative systems. In particular, the focus is on an information theoretic analysis for P2P systems with synchronization errors and developing new signaling solutions for several asynchronous cooperative communication systems. The first part of the dissertation presents several bounds on the capacity of the P2P systems with synchronization errors. First, binary insertion and deletion channels are considered where lower bounds on the mutual information between the input and output sequences are computed for independent uniformly distributed (i.u.d.) inputs. Then, a channel suffering from both synchronization errors and additive noise is considered as a serial concatenation of a synchronization error-only channel and an additive noise channel. It is proved that the capacity of the original channel is lower bounded in terms of the synchronization error-only channel capacity and the parameters of both channels. On a different front, to better characterize the deletion channel capacity, the capacity of three independent deletion channels with different deletion probabilities are related through an inequality resulting in the tightest upper bound on the deletion channel capacity for deletion probabilities larger than 0.65. Furthermore, the first non-trivial upper bound on the 2K-ary input deletion channel capacity is provided by relating the 2K-ary input deletion channel capacity with the binary deletion channel capacity through an inequality. The second part of the dissertation develops two new relaying schemes to alleviate asynchronism issues in cooperative communications. The first one is a single carrier (SC)-based scheme providing a spectrally efficient Alamouti code structure at the receiver under flat fading channel conditions by reducing the overhead needed to overcome the asynchronism and obtain spatial diversity. The second one is an orthogonal frequency division multiplexing (OFDM)-based approach useful for asynchronous cooperative systems experiencing excessive relative delays among the relays under frequency-selective channel conditions to achieve a delay diversity structure at the receiver and extract spatial diversity.Dissertation/ThesisPh.D. Electrical Engineering 201