Off-campus UNL users: To download campus access dissertations, please use the following link to log into our proxy server with your NU ID and password. When you are done browsing please remember to return to this page and log out.
Non-UNL users: Please talk to your librarian about requesting this dissertation through interlibrary loan.
Time-varying and capacity -approaching codes
Abstract
This dissertation tries to unify the three classes of capacity-approaching codes: time-varying convolutional codes, turbo codes, and low-density parity-check codes. The structural properties of periodically time-varying convolutional codes are studied first. It is shown that every periodically time-varying convolutional encoder is equivalent to a time-invariant convolutional encoder. A method to find the time-invariant convolutional encoder with feedback equivalent to a periodically time-varying convolutional encoder with feedback is found. Based on the equivalence between periodically time-varying and time-invariant convolutional encoders, a new catastrophic condition for periodically time-varying convolutional encoders is derived. A new technique to convert a catastrophic periodically time-varying convolutional encoder into a noncatastrophic encoder is also presented. The average transfer functions of periodically time-varying convolutional codes and their relationship to the spectrum-thinning conjecture of periodically time-varying convolutional codes are discussed. Time-varying convolutional codes are found to be compatible with the turbo iterative decoding algorithm and thus can be used to build good turbo codes. A time-varying turbo code, i.e., turbo code with periodically time-varying convolutional component codes, that outperforms some of the well-known turbo codes is constructed. This turbo code is found to have thinner distance spectrum than the other turbo codes. To understand the relationship between turbo and low-density parity-check codes better, a general form of the generator and parity-check matrices of an arbitrary turbo code is derived. Turbo codes are then decoded by the sum-product algorithm based on their parity-check matrices. Guided by the general expression of the parity-check matrix of an arbitrary turbo code, turbo encoders with large memory and selected generator polynomials are used to generate turbo codes with low-density parity-check matrices. These codes can be decoded by the sum-product algorithm, whereas the turbo decoding algorithm is impractical due to the large encoder memory. The bit-error-rate performance of these turbo codes is still worse than that of the conventional low-density parity-check codes. This loss in performance may be justified by the largely decreased encoder complexity.
Subject Area
Electrical engineering
Recommended Citation
Jiang, Fan, "Time-varying and capacity -approaching codes" (2006). ETD collection for University of Nebraska-Lincoln. AAI3215056.
https://digitalcommons.unl.edu/dissertations/AAI3215056