Low-complexity channel resolvability codes for the symmetric multiple-access channel

We investigate channel resolvability for the l-user multiple-access channel (MAC) with two different families of encoders. The first family consists of invertible extractors, while the second one consists of injective group homomorphisms, and was introduced by Hayashi for the point-to-point channel resolvability. The main benefit of these two families is to provide explicit low-complexity channel resolvability codes in the case of symmetric MACs. Specifically, we provide two examples of families of invertible extractors suitable for MAC resolvability with uniform input distributions, one based on finite-field multiplication, which can be implemented in O(n log n) for a limited range of values of the encoding blocklength n, and a second based on modified Toeplitz matrices, which can be implemented in O(n log n) for a wider range of values of n. We also provide an example of family of injective group homomorphisms based on finite-field multiplication suitable for MAC resolvability with uniform input distributions, which can be implemented in O(n log n) for some values of n.