M.Sc Thesis

M.Sc StudentGoldenberg Idan
SubjectGallager-Type Bounds for Parallel Channels with
Applications to Modern Coding Techniques
DepartmentDepartment of Electrical and Computer Engineering
Supervisor PROF. Igal Sason
Full Thesis textFull thesis text - English Version


Some communication scenarios can be modeled as standard coded transmission over a set of parallel communication channels. These include transmission over block fading channels, rate-compatible puncturing of turbo-like codes, multi-carrier signaling and others. This thesis is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error probability are derived. These bounds include the generalization of the second version of the Duman and Salehi (DS2) bound to the case of parallel channels and a generalization of the classic 1961 Gallager bound to parallel channels. Optimized tilting measures for the new bound are derived. The connection between the generalized DS2 and the 1961 Gallager bounds, which was previously addressed for a single channel, is explored in the case of an arbitrary number of independent parallel channels. The generalization of the DS2 bound for parallel channels enables to rederive specific bounds which were previously derived as special cases of the Gallager bound. The new bounds are applied to various ensembles of turbo-like codes, focusing especially on repeat-accumulate codes and their recent variations which possess low encoding and decoding complexity and exhibit remarkable performance under iterative decoding. In the asymptotic case where we let the block length tend to infinity, the new bounds are used to obtain improved inner bounds on the attainable channel regions under ML decoding. The tightness of the new bounds for independent parallel channels is exemplified for structured ensembles of turbo-like codes. The improved bounds with their optimized tilting measures show, irrespectively of the block length of the codes, an improvement over the union bound and other previously reported bounds for independent parallel channels; this improvement is especially pronounced for moderate to large block lengths.