Extended Permutation Coding with Spectral Shaping Capability

Abstract

Considerable effort has been focused on efficient error correction schemes in digital communications where the medium of transmission is unfriendly for information transmission. Also, some of such channels have certain frequency characteristics that should be considered during system designs. Permutation coding (PC) has been reported as being capable of spectral shaping, by manipulating channel symbols in such a way that the frequency energy of the transmitted signal is concentrated towards certain areas of the frequency spectrum. We, therefore, report an extension operation that enables the generation of a new PC from a source PC that is capable of spectrum shaping, while still maintaining its spectral shaping capability. A mathematical expression that can predict the low energy sections of the codebook's spectrum is also presented, together with their lower and upper bounds. An added advantage of the proposed scheme is that better error correction is attainable due to the way the extension is introduced.