The amount of information in the human genome is not as large as you seem to think. All of it can be compressed to only about 4MB.
quote:
The inherent structure of genome data allows for more efficient lossless compression than can be obtained through the use of generic compression programs. We apply a series of techniques to James Watson's genome that in combination reduce it to a mere 4MB, small enough to be sent as an email attachment.
(Human genomes as email attachments, Scott Christley, Yiming Lu, Chen Li, and Xiaohui Xie, Bioinformatics Volume 25, Number 2 Pp. 274-275)
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