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State-independent decodable DC-free codes with complex-valued signalling alphabets
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- Author / Creator
- Jamieson, Craig
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Traditionally, constrained sequence coding has been employed exclusively in codes using binary or multilevel signalling. This thesis extends the procedure for constructing DC-free constrained sequence codes to alphabets that use signalling constellations with complex-valued symbols. In particular, the codes are separated into two types: i) constraints with independent logical signalling dimensions and ii) constraints using dependent logical signalling dimensions. In both cases, constraint modelling for the purpose of the evaluation of capacity is explored. Within the case of dependent signalling dimensions, the state machines can contain a finite or an infinite number of states, depending on the signalling constellation that is used. Evaluation of capacity of these types of constrained systems is considered in detail.
Building upon the capacity analysis and constraint modelling techniques, DC-free codes using complex-valued signalling constellations are constructed. The three constellations that are considered in detail in this thesis are quadrature phase shift keying (QPSK), 8 phase shift keying (PSK), and 16 quadrature amplitude modulation (QAM). A number of codes have been constructed for each of the three types for various RDS spans. Further, it is shown that Justesen's relationship for codes using binary-valued symbols, which relates the value of the sum variance to the width of the spectral notch around DC, also holds for codes using complex-valued symbols.
To complete the code construction procedure for DC-free codes using complex-valued signalling alphabets, which involves state-based encoding and decoding, an algorithm was developed to construct codes that can be decoded at the receiver without requiring state information. This algorithm was designed to execute in polynomial time with respect to the size of the input and to be both general and flexible, so that it can operate on any family of constrained sequence codes. In addition to codes with complex-valued symbols, a number of binary DC-free RLL block codes are constructed using this algorithm, achieving the maximum possible code rates with codeword lengths less than 20. This algorithm is also extended to include the principles of weakly constrained coding.
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- Graduation date
- Fall 2011
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- Type of Item
- Thesis
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- Degree
- Doctor of Philosophy
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- License
- This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.