Lattice-based WOM codebooks that allow two writes

The continuous approximation is a technique to separate the shaping gain and coding gain of a channel code. In this paper, this technique is applied to codes for write-once memories (WOM codes) based upon lattices. For a lattice of arbitrary dimension n, a hyperbolic shaping region is optimal in the sense of maximizing the sum rate in the worst case, when there are two writes. Then, asymptotic results are obtained when the rates for two writes are equal. Under this condition, the sum rate assuming two equal rates closely approaches, but not achieve, the capacity which allows two unequal rates.