In this thesis, we consider error-correction codes for systems which have burst erasure channels, but where the packet delay is constrained. The packet delay itself is the time di erence between the arrival of a source packet at the encoder and the reconstruction of that source packet at the decoder. While such a framework was introduced by Martinian (2004) and his co-authors, several problems remain open. We make three contributions in this thesis. First we develop a rigorous converse proof for the point-to-point case and thus complete the result of Martinian (2004). Our proof technique is also applied to a multicast channel model and new results are obtained. Secondly we study the case when there are multiple parallel links between the encoder and decoder and obtain the capacity in some special cases. Finally we study a setup when there are multiple source streams, each with a di erent delay constraint, and obtain capacity results.

In this thesis, we consider error-correction codes for systems which have burst erasure channels, but where the packet delay is constrained. The packet delay itself is the time di erence between the arrival of a source packet at the encoder and the reconstruction of that source packet at the decoder. While such a framework was introduced by Martinian (2004) and his co-authors, several problems remain open. We make three contributions in this thesis. First we develop a rigorous converse proof for the point-to-point case and thus complete the result of Martinian (2004). Our proof technique is also applied to a multicast channel model and new results are obtained. Secondly we study the case when there are multiple parallel links between the encoder and decoder and obtain the capacity in some special cases. Finally we study a setup when there are multiple source streams, each with a di erent delay constraint, and obtain capacity results.

Electronic signal processing techniques have assumed a prominent role in the design of fibre-optic communication systems. However, state-of-the-art systems operate at per-channel data rates of 100 Gb/s, which constrains the class of communication algorithms that can be practically implemented. Relative to LDPC-like codes, product-like codes with syndrome-based decoding have decoder dataflow requirements that are smaller by more than two orders of magnitude, which strongly motivates the search for powerful product-like codes. This thesis presents a new class of high-rate binary error-correcting codes, staircase codes, whose construction combines ideas from convolutional and block coding. A G.709-compliant staircase code is proposed, and FPGA-based simulation results show that performance within 0.5 dB of the Shannon Limit is attained for bit-error-rates below 1E-15. An error-floor analysis technique is presented, and the G.709-compliant staircase code is shown to have an error floor below 1E-20. Using staircase codes, a pragmatic approach for coded modulation in fibre-optic communication systems is presented that provides reliable communications to within 1 bit/s/Hz of the capacity of a QAM-modulated system modeled via the generalized non-linear Schrodinger equation. A system model for a real-world DQPSK receiver with correlated bit-errors is presented, along with an analysis technique to estimate the resulting error floor for the G.709- compliant staircase code. By applying a time-varying pseudorandom interleaver of size 2040 to the output of the encoder, the error floor of the resulting system is shown to be less than 1E-20.

Balanced codes, in which each codeword contains equally many 1's and 0's, are useful in such applications as in optical transmission and optical recording. When balanced codes are used, the same number of 1's and 0's pass through the channel after the transmission of every word, so the channel is in a dc-null state. Optical channels require this property because they employ AC-coupled devices. Line codes, in which codewords may not be balanced, are also used as dc-free codes in such channels. In this thesis we present the research that leads to the following results: 1- Balanced codes These have higher information rate than existing codes yet maintain similar encoding and decoding complexities. 2- Error-correcting balanced codes In many cases, these give higher information rates and more efficient encoding and decoding algorithms than the best-known equivalent codes. 3- DC-Free coset codes A new technique to design dc-free coset codes was developed. These codes have better properties than existing ones. 4- Generalization of balanced codes -- Balanced codes are generalized in three ways among which the first is the most significant: a) Balanced codes with low dc level These codes are designed based on the combined techniques used in (1) and (3) above. A lower dc-level and higher transitions density is achieved at the cost of one extra check bit. These codes are much more attractive, to optical transmission, than the bare-bone balanced codes. b) Non-Binary Balanced Codes Balanced codes over a non-binary alphabet. c) Semi-Balanced Codes -- Codes in which the number of 1's and 0's in every code word differs by at most a certain value. 5- t-EC/AUED coset codes These are t error correcting/all unidirectional error detecting codes. Again the technique in (3) above is used to design t-EC/AUED coset codes. These codes obtain higher information rate than the best-known equivalent codes and yet maintain the same encoding/decoding complexity. / Graduation date: 1990

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Thesis (Ph.D.)--University of Florida, 2005. / Title from title page of source document. Document formatted into pages; contains 101 pages. Includes vita. Includes bibliographical references.

Thesis (Ph. D.)--University of Hong Kong, 2001. / Includes bibliographical references (leaves 317-338).

Thesis (Ph. D.)--University of Washington, 2001. / Vita. Includes bibliographical references (p. 169-184).

Thesis (M.Sc.)--York University, 2008. Graduate Programme in Science. / Typescript. Includes bibliographical references (leaves 223-232). Also available on the Internet. MODE OF ACCESS via web browser by entering the following URL: http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:MR45965