A Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy
in the Centre for Telecommunications Access and Services, School of Electrical and Information Engineering, October 2019 / In the field of forward error correction, the development of decoding algorithms
with a high error correction performance and tolerable complexity has been of
great interest for the reliable transmission of data through a noisy channel. The
focus of the work done in this thesis is to exploit techniques used in forward error
correction in the development of an iterative soft-decision decoding approach
that yields a high performance in terms of error correction and a tolerable computational
complexity cost when compared to existing decoding algorithms. The
decoding technique developed in this research takes advantage of the systematic
structure exhibited by linear block codes to implement an information set decoding
approach to correct errors in the received vector outputted from the channel. The
proposed decoding approach improves the iterative performance of the algorithm
as the decoder is only required to detect and correct a subset of the symbols from
the received vector. These symbols are referred to as the information set. The
information set, which matches the length of the message, is then used decode the
entire codeword.
The decoding approach presented in the thesis is tested on both Reed Solomon
and Low Density Parity Check codes. The implementation of the decoder varies
for both the linear block codes due to the different structural properties of the
codes.
Reed Solomon codes have the advantage of having a row rank inverse property
which enables the construction of a partial systematic structure using any set of
columns in the parity check matrix. This property provides a more direct implementation
for finding the information set required by the decoder based on the soft
reliability information. However, the dense structure of the parity check matrix of
Reed Solomon codes presents challenges in terms of error detection and correction
for the proposed decoding approach. To counter this problem, a bit-level implementation
of the decoding technique for Reed Solomon codes is presented in the
thesis.
The presentation of the parity check matrix extension technique is also proposed
in the thesis. This technique involves the addition of low weight codewords from
the dual code, that match the minimum distance of the code, to the parity check
matrix during the decoding process. This helps add sparsity to the symbol-level
implementation of the proposed decoder. This sparsity helps with the efficient
exchange of the soft information during the message passing stage of the proposed
decoder.
Most high performance Low Density Parity Check codes proposed in literature
lack a systematic structure. This presents a challenge for the proposed decoding
approach in obtaining the information set. A systematic construction for a
Quasi-Cyclic Low Density Parity Check code is also presented in this thesis so as
to allow for the information set decoding. The proposed construction is able to
match the error correction performance of a high performance Quasi-Cyclic Low
Density Parity Check matrix design, while having the benefit of a low complexity
construction for the encoder.
In addition, this thesis also proposes a stopping condition for iterative decoding
algorithms based on the information set decoding technique. This stopping condition
is applied to other high performance iterative decoding algorithms for both
Reed Solomon codes and Low Density Parity Check codes so as to improve the
iterative performance. This improves on the overall efficiency of the decoding algorithms. / PH2020
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/29047 |
| Date | 10 1900 |
| Creators | Genga, Yuval Odhiambo |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | Online resource (192 leaves), application/pdf, application/pdf |
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