  An interference-limited noise-free CDMA downlink channel operating under a
complexity constraint on the receiver is introduced. According to this
paradigm, detected bits, obtained by performing hard decisions directly on the
channel's matched filter output, must be the same as the transmitted binary
inputs. This channel setting, allowing the use of the simplest receiver scheme,
seems to be worthless, making reliable communication at any rate impossible. We
prove, by adopting statistical mechanics notion, that in the large-system limit
such a complexity-constrained CDMA channel gives rise to a non-trivial
Shannon-theoretic capacity, rigorously analyzed and corroborated using
finite-size channel simulations.
