A Poltyrev outage limit for lattices

Nonergodic fading is a useful model for various wireless communication channels in both indoor and outdoor environments. With this model, a codeword is divided into multiple blocks such that fading is constant within a block and independent across blocks. Building on Poltyrev´s work on infinite lattice constellations for the Gaussian channel, we derive a Poltyrev outage limit for lattice constellations transmitted over a block-faded channel. We prove that the diversity order of this Poltyrev outage limit is equal to the number of degrees of freedom in the channel. An important application is in decoding low-density lattice codes. With block fading, the presence of an outage may dramatically increase the runtime of both sphere and iterative decoders. Using our newly defined Poltyrev outage limit, decoding is not performed whenever an outage is declared, which drastically reduces the overall decoding time.