Permutation sequences and coded PAM signals with spectral nulls at rational submultiples of the symbol frequency

Coded PAM signals with spectral nulls at rational submultiples of the symbol frequency are presented. Spectral shaping using permutation symbols and distance-preserving mappings (DPMs) are two techniques presented in this paper to design codes with better error correction capability, which make them achieve a significant decoding gain compared to other published codes. The use of Viterbi decoding algorithm, gives these new codes an advantage with their property of no error propagation. The well shaped power spectral densities of these new codes may overcome some communications problem like zero frequency components.