Constrained sequences and coding for spectral and error control

D.Ing.When digital information is to be transmitted over a communications channel or stored in a data recording system, it is first mapped onto a code sequence by an encoder. The code sequence has certain properties which makes it suitable for use on the channel, ie the sequence complies to the channel input restrictions. These input restrictions are often described in terms of a required power spectral density of the code sequence. In addition, the code sequence can also be chosen in such a way as to enable the receiver to correct errors which occur in the channel. The set of rules which governs the encoding process is referred to as a line code or a modulation code for the transmission or storage of data, respectively. Before a new line code or modulation code can be developed, the properties that the code sequence should have for compliance to the channel input, restrictions and possession of desired error correction capabilities have to be established. A code' construction algorithm, which is often time consuming and difficult to apply, is then used to obtain the new code. In this dissertation, new classes of sequences which comply to the input restrictions and error correction requirements of practical channels are defined, and new line codes and recording codes are developed for mapping data onto these sequences. Several theorems which show relations between' information theoretical aspects of different classes of code sequences are presented. Algorithms which can be used to transform an existing line code or modulation code into a new code for use on another channel are introduced. These algorithms are systematic and easy to apply, and precludes the necessity of applying a code construction algorithm