M.Sc Student | Kaspi Yonatan |
---|---|

Subject | Error Exponents for Broadcast Channels with Degraded Message Sets |

Department | Department of Electrical Engineering |

Supervisor | Professor Neri Merhav |

Full Thesis text |

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.