M.Sc Thesis

M.Sc StudentKaspi Yonatan
SubjectError Exponents for Broadcast Channels with Degraded Message
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Neri Merhav


We consider a broadcast channel with a degraded message set, in which, a single transmitter sends a common message to two receivers and a private message only to one of the receivers. The main goal of this work is to find new lower bounds to the error exponents of the strong user, that should decode both messages, and the weak user, that should decode only the common message. Unlike previous works in this field, where in order to avoid the complex analysis of optimal decoding, suboptimal decoders where used, the exponents we derive in this work pertain to optimal decoding and depend on both rates. When using optimal decoding, the hierarchical structure of the codebook makes the derivation of the exponents very difficult. To overcome this difficulty, we take two different approaches.
The first approach is based, in part, on variations of Gallager-type bounding techniques that were presented in a much earlier work on error exponents for erasure/list decoding. Using these techniques, we are able to derive new lower bounds which are quite simple to understand and compute. Numerical results show that the new bounds, obtained by this technique, improve previous results.\\
The second approach is based on a technique that is rooted in statistical physics. This new technique seemed promising as it is exponentially tight after an initial step, and it improved previous results in other cases. Unlike the first approach which is rather algebraic, this technique is based on analyzing the statistics of certain enumerators. This technique also gives us a better understanding of the exponential tightness of known inequalities, such as Jensen's inequality. Although exponentially tight, the derivation is much more complex than the first approach and the retrieved exponents are hard to compute. Numerical results show that this technique improves on our results from the first part of our work.