Ph.D Thesis

Ph.D StudentSason Igal
SubjectUpper Bounds on the Maximum Likelihood Decoding Error
Probability for Block Codes and Turbo-Like Codes
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Shlomo Shamai )Shitz(


Since the error performance of efficiently coded communication

systems rarely admits exact expressions, tight analytical bounds

emerge as a useful theoretical and engineering tool for assessing

performance and for gaining insight into the effect of the main system

parameters. As specific good codes are hard to identify, one

resorts to accurately assessing the performance of ensembles of


In this thesis, the performance of either structured or random

turbo codes and other efficient binary linear block codes is

assessed for certain channel models by upper bounds on the error

performance of maximum likelihood decoding. These bounds on the

block and bit error probability which depend respectively on the

distance spectrum and the input-output weight enumeration of these

codes, are compared for a variety of cases to simulated

performance of iterative decoding. The comparison facilitates to

assess the efficiency (as compared to the optimal maximum

likelihood decoding rule) of iterative decoding on one hand and

the tightness of the examined upper bounds on the other hand. Some

applications of the tangential sphere bound for bounding the

ensemble performance of turbo-like codes over the Gaussian channel

are studied here, and their tightness is demonstrated.

In addressing the Gallager bounding techniques and their

variations, we focus on the Duman and Salehi variation which

originates from the standard 1965 Gallager bound. By generalizing

the framework of the second version of the Duman and Salehi

bounds, we demonstrate its considerable generality.

The analytical and rigorous upper bounds which are derived in this

thesis and their rather good match in many examples with

simulation results of efficient iterative decoding algorithms

(though the bounds refer to ML decoding) makes these bounding

techniques applicable to the design and analysis of efficient

coding schemes.