Spectrum shaping codes

The first application of spectrum shaping codes was related to digital communication systems that used transformers to connect two communication lines. Because transformers do not convey dc-component, and suppress low frequency components, direct transmission of source signals whose power spectral densities contain these frequency components were not possible without significant distortion. That is why dc-free or dc-balanced codes were devised [1-3, 10-13]. Their role is to transform a source sequence into a channel sequence whose spectral characteristic corresponds to spectral characteristic of communication channel. At the end of communication line, the sequence is received by the decoder that generates original sequence without errors in the case of noiseless channel. In recording systems that can be modeled as any communication system, this kind of codes have been widely used. For instance in digital audio tape systems, they prevent write signal distortion that can occur due to transformer-coupling in write electronics [2]. In optical recording systems they are used to circumvent the interference between recorded signal and servo tracking system. Further development of spectrum shaping codes for recording systems was driven by requirements for better codes in the sense of larger rejection of low frequency components. The codes providing this feature are codes with higher order spectral zero at f = 0, and can be found in [14, 16, 17]. Although thewidth of suppressed frequencies of these codes is smaller than in the case of dc-balanced codes, the rejection in the vicinity of f = 0 is significantly larger. Another class of spectrum shaping codes were invented in order to support the use of frequencymultiplexing technique for track following [1], and partial response technique for high density data storage [15]. Both techniques require the spectral nulls of the recorded signal at frequencies that can be different than f = 0 in order to enable reliable data storage. The typical example of such codes are codes that have spectral zeros at submultiple of channel symbol frequency.