M.Sc Thesis | |

M.Sc Student | Tamir Ran |
---|---|

Subject | Error Exponents and Universal Decoders for the Asymmetric Broadcast Channel |

Department | Department of Electrical and Computer Engineering |

Supervisor | PROF. Neri Merhav |

This work contains three main contributions concerning the

asymmetric broadcast channel. The first is an analysis of

the exact random coding error exponents

for both users, and the second is the derivation

of universal decoders for both users. These universal decoders are

certain variants of the maximum mutual information (MMI)

universal decoder, which achieve the corresponding random coding

exponents of optimal decoding.

In addition, we introduce some lower bounds,

which involve optimization over very few parameters,

unlike the original, exact error exponents, which involve minimizations over auxiliary probability distributions, which may be computationally painful especially for large alphabets.

Later, we analyze these lower bounds, and derive a phase diagram for the weak user,

which fully describes the functional behavior of the bound

in different regions of the plane of rates.

Numerical results for the binary symmetric broadcast channel show improvements over previously derived error exponents for the same model.

The third contribution of this work concerns the

expurgation of hierarchical ensembles.

Expurgating a code for the asymmetric broadcast channel is not a trivial extension of expurgation in the single-user case, because there might be a conflict from the viewpoints of the two users. Nonetheless, we can define expurgation procedures that guarantee no harm to the performance of either user.

We provide an analysis of the optimal maximum likelihood (ML) decoders via two different methods of code expurgation, which results two competing error exponents.