A simulation and graph theoretical analysis of certain properties of spectral null codebooks

The spectral shaping technique and the design of codes providing nulls at rational sub-multiples of the symbol frequency, as the case with spectral null (SN) codes, have enhanced digital signaling over communication channels as digital mass recorders and metallic cables. The study of the special structure of these codes helps in investigating and analyzing certain of their properties which have been proved and emphasized from a mathematical perspective using graph theory. The cardinality of spectral null codebooks reflects the rate of spectral null codes and therefore the amount of transmitted information data. The rate of these codes can also play a role in their error correction capability. The paper presents in different ways the special structure of spectral null codebooks and analyze better their properties. A possible link between these codes and other error correcting codes as the case of Low Density Parity Check (LDPC) is presented and discussed in this paper.