Error Correction for Index Coding With Coded Side Information

Index coding is a source coding problem in which a broadcaster seeks to meet the different demands of several users, each of whom is assumed to have some prior information on the data held by the sender. If the sender knows its clients' requests and their side-information sets, then the number of packet transmissions required to satisfy all users' demands can be greatly reduced if the data is encoded before sending. The collection of side-information indices as well as the indices of the requested data is described as an instance of the index coding with side-information (ICSI) problem. The encoding function is called the index code of the instance, and the number of transmissions employed by the code is referred to as its length. The main ICSI problem is to determine the optimal length of an index code for and instance. As this number is hard to compute, bounds approximating it are sought, as are algorithms to compute efficient index codes. Two interesting generalizations of the problem that have appeared in the literature are the subject of this work. The first of these is the case of index coding with coded side information, in which linear combinations of the source data are both requested by and held as users' side-information. The second is the introduction of error-correction in the problem, in which the broadcast channel is subject to noise. In this paper we characterize the optimal length of a scalar or vector linear index code with coded side information (ICCSI) over a finite field in terms of a generalized min-rank and give bounds on this number based on constructions of random codes for an arbitrary instance. We furthermore consider the length of an optimal error correcting code for an instance of the ICCSI problem and obtain bounds on this number, both for the Hamming metric and for rank-metric errors. We describe decoding algorithms for both categories of errors

Caching in Heterogeneous Networks

A promising solution in order to cope with the massive request of wireless data traffic consists of having replicas of the potential requested content memorized across the network. In cache-enabled heterogeneous networks, content is pre-fetched close to the users during network off-peak periods in order to directly serve the users when the network is congested. In fact, the main idea behind caching is the replacement of backhaul capacity with storage capabilities, for example, at the edge of the network. Caching content at the edge of heterogeneous networks not only leads to significantly reduce the traffic congestion in the backhaul link but also leads to achieve higher levels of energy efficiency. However, the good performance of a system foresees a deep analysis of the possible caching techniques. Due to the physical limitation of the caches’ size and the excessive amount of content, the design of caching policies which define how the content has to be cached and select the likely data to store is crucial. Within this thesis, caching techniques for storing and delivering the content in heterogeneous networks are investigated from two different aspects. The first part of the thesis is focused on the reduction of the power consumption when the cached content is delivered over an Gaussian interference channel and per-file rate constraints are imposed. Cooperative approaches between the transmitters in order to mitigate the interference experienced by the users are analyzed. Based on such approaches, the caching optimization problem for obtaining the best cache allocation solution (in the sense of minimizing the average power consumption) is proposed. The second part of the thesis is focused on caching techniques at packet level with the aim of reducing the transmissions from the core of an heterogeneous network. The design of caching schemes based on rate-less codes for storing and delivering the cached content are proposed. For each design, the placement optimization problem which minimizes the transmission over the backhaul link is formulated

Delay with network coding and feedback

We consider the problem of minimizing delay when broadcasting over erasure channels with feedback. A sender wishes to communicate the same set of μ messages to several receivers over separate erasure channels. The sender can broad- cast a single message or a combination (encoding) of messages at each timestep. Receivers provide feedback as to whether the transmission was received. If at some time step a receiver cannot identify a new message, delay is incurred. Our notion of delay is motivated by real-time applications that request progressively refined input, such as the successive refinement of an image encoded using multiple description coding. Our setup is novel because it combines coding techniques with feedback information to the end of minimizing delay. It allows Θ(μ) benefits as compared to previous approaches for offline algorithms, while feedback allows online algorithms to achieve smaller delay than online algorithms without feedback. Our main complexity results are that the offline minimization problem is NP-hard when the sender only schedules single messages and that the general problem remains N P -hard even when coding is allowed. However we show that coding does offer delay and complexity gains over scheduling. We also discuss online heuristics and evaluate their performance through simulations

Real-time Delay with Network Coding and Feedback

We consider the problem of minimizing delay when broadcasting over erasure channels with feedback. A sender wishes to communicate the same set of m messages to several receivers. The sender can broadcast a single message or a combination (encoding) of messages to all receivers at each timestep, through separate erasure channels. Receivers provide feedback as to whether the transmission was received. If, at some time step, a receiver cannot identify a new message, delay is incurred. Our notion of delay is motivated by real-time applications that request progressively refined input, such as the refinements or different parts of an image. Our setup is novel because it combines coding techniques with feedback information to the end of minimizing delay. Uncoded scheduling or use of multiple description (MDS) codes has been well-studied in the literature. We show that our setup allows O( m ) benefits as compared to both previous approaches for offline algorithms, while feedback allows online algorithms to achieve smaller delay compared to online algorithms without feedback. Our main complexity results are that the offline minimization problem is NP-hard when the sender only schedules single messages and that the general problem remains NP-hard even when coding is allowed. However we show that coding does offer complexity gains by exhibiting specific classes of erasure instances that become trivial under coding schemes. We also discuss online heuristics and evaluate their performance through simulations