Application of spectral shaping techniques to synchronization error correcting codes

by Willem Adriaan Clarke

Institution: University of Johannesburg
Year: 2015
Keywords: Error-correcting codes (Information theory)
Record ID: 1480138
Full text PDF: http://hdl.handle.net/10210/13365


In this thesis, spectral shaping techniques are applied to the insertion/deletion error correcting codes. Spectral shaping techniques are introduced and applied to insertion/deletion error correcting codes. The attainable rates for subcodes with spectral properties are computed and presented. The theory of comma-free codes is briefly reviewed and a new construction method is given : for comma-free insertion/deletion correcting codes. This method serves as a lower bound on the cardinality of comma-free insertion/deletion codes. The idea of a marker is introduced as an alternative method of finding word boundaries. Rules are given for governing the construction of marker code books that can differentiate between additive and insertion/deletion errors. The marker code books are then used in such: a way as not to violate the spectral properties of the abovementioned insertion/deletion correcting codes. A new class of codes is presented that has higher order spectral zeros at both DC and the Nyquist frequency. It is shown that these codes are insertion/deletion and additive error correcting. Besides this, it is shown that the abovementioned class of codes can correct two adjacent additive errors.