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Mamillapalli Venkata Naga Bhavana – ECE

Mamillapalli Venkata Naga Bhavana received her MS in  Electronics and Communication Engineering (ECE). Her research work was supervised by Dr. Prasad krishnan. Here’s a summary of Mamillapalli Venkata Naga Bhavana’s thesis On Index Coding for Broadcast Channels with Receiver Caches:

High demand for reception of content from multiple users simultaneously enforces usage of intelligent transmission techniques in applications like video-on-demand services, satellite communication, interference management etc. Index coding is one such technique introduced by Birk and Kol in 1998 originally to optimize channel efficiency for satellite communication. The index coding framework consists of a source connected via a broadcast channel to multiple receivers, with each receiver storing locally partial information symbols that is available at the source (this is known as cache or side information. The receivers then demand some new information symbols from the source. An index code is an encoding of the symbols those are demanded by the receivers in such a way that everyone of the receivers can decode their own requested symbols. The goal of index coding is to minimize the number of transmitted symbols (the length or rate of the index code) while ensuring decoding by the receivers. To design the index code with reduced rate, the source makes use of the knowledge of the side-information available at the receivers. Index coding techniques received considerable attention as they can be employed in several engineering applications such as content broadcasting, device-to-device relaying, distributed caching etc. It also has interesting relationships to network coding, distributed storage and guessing games. Several approaches for solving index coding problem have been developed using graph theoretical, linear algebraic methods, interference alignment, linear programming etc. Specifically, in the graph theoretic approach, the side-information and demands of the index coding problem are captured in the form of a graph, and certain properties of the graph are used to construct an index code. Albeit the trials being done in this context, optimal solutions for index coding problems are still open. Index coding problems modelled by circular perfect graphs, which form a strict super class of the perfect graphs, are studied in the first part of this thesis. We derive schemes that achieve optimal broadcast rate for a constrained class of index coding problems defined by complements of circular perfect graphs. We also proposed a better lower bound on the rate of a optimal solution for any index coding problem. We present lower and upper bounds on the sum and product of vector linear broadcast rates of a graph and its complement. The second part of this dissertation is in the area of coded caching, Consider a network of clients connected via a broadcast channel to one server node which has a number of files. The clients or receivers have caches which allow them to store some parts of the files at the transmitter. The caching system proceeds in two phases: Caching Phase which occurs in non-peak times, and Delivery phase which occurs in peak hours when each client demands some file from the server. By prefetching some parts of the files from the server to the clients during the non-peak hours, the remainders of the demanded files alone can be sent by the server during the peak hours. Thus, caching allows us to offload some traffic from the network during the peak hours, when each client is demanding some file from the transmitter. The paradigm of Coded Caching introduced by Ali and Niesen further reduces the load during the peak hours by encoding the parts of the files to be communicated. The coded caching problem is similar to the index coding problem in this sense, and hence the goal here also is to minimize the size of the transmissions, i.e., the rate of coded caching. In this thesis, we derive a subpacketization dependent lower bound on the rate of coded caching and compare our results with prior known lower bounds through which we show that our bound performs better than existing lower bounds on the rate of coded caching.