Spectral Shaping Codes

We investigate a new approach for designing spectral shaping block codes with a target spectrum, <inline-formula> <tex-math notation="LaTeX">$H_{t}(f)$ </tex-math></inline-formula>, that has been specified at a plurality of frequencies. We analyze the probability density function of the spectral power density function of uncoded <inline-formula> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula>-symbol bipolar codewords. We present estimates of the redundancy and the spectrum of spectral shaping codes with specified target spectral densities <inline-formula> <tex-math notation="LaTeX">$H_{t}(f_{i})$ </tex-math></inline-formula> at frequencies <inline-formula> <tex-math notation="LaTeX">$f_{i}$ </tex-math></inline-formula>. Constructions of low-redundancy codes with suppressed low-frequency content are presented that compare favorably with conventional dc-balanced codes currently used in data transmission and data storage devices with applications in consumer electronics.

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