Injection Coding with Spectral Nulls for Even Codeword Lengths

With a view to adapting information signals to suit the frequency characteristics of digital transmission channels, it is pertinent to design channel coding schemes that can exhibit spectral shaping capabilities after being processed with a suitable modulation technique. This involves concentrating the frequency energy of the coded and modulated information signal towards a predetermined range of the frequency spectrum, or making it have low power content at such frequencies. One modulation scheme that is suitable for achieving this is pulse amplitude modulation (PAM). We thus present a permutation coding (PC) system with injections that can exhibit spectral nulls at rational sub-multiples of the symbol frequency. Such injections are achieved by strategically removing δ columns from the source PC. We also present a mathematical expression that allows for the prediction of zero energy positions in the codebook’s spectrum. Due to the way the injections are introduced, it gives the scheme an advantage of achieving higher symbol rate, when compared with conventional PC systems. The work is however limited to cases where δ =2 and the lengths of the codewords involved are even numbers.