  We provide a novel achievability proof of the Slepian-Wolf theorem for i.i.d.
sources over finite alphabets. We demonstrate that random codes that are linear
over the real field achieve the classical Slepian-Wolf rate-region. For finite
alphabets we show that typicality decoding is equivalent to solving an integer
program. Minimum entropy decoding is also shown to achieve exponentially small
probability of error. The techniques used may be of independent interest for
code design for a wide class of information theory problems, and for the field
of compressed sensing.
