Techniques for polar coding over multiple access channels

The problem of channel polarization and polar code construction for two-user multiple access channels is considered. The well-known method of time sharing is discussed first, where the underlying codes are point to point polar codes. We explain how to improve the performance in time sharing using the recently proposed compound polar codes. Then we propose a new scheme in which both users encode their messages using a polar encoder, while a joint successive cancellation decoder is used at the decoder. The polar codes for both users is constructed jointly by treating the whole polar transformation on both users as a single polar transformation, wherein the multiple access channel (MAC) is regarded as one more level of polarization. We prove that our scheme achieves the whole uniform rate region by changing the decoding order in the joint successive cancellation decoder, where the uniform rate region of a MAC is the set of achievable rates assuming that the input distributions are uniform. Some simulation results over binary-additive Gaussian noise MAC are provided. The proposed scheme is compared with the existing results on polar codes for multiple access channels to emphasize the differences and the main advantages of our scheme.