On carrier-cooperation in parallel Gaussian MIMO relay channels with partial decode-and-forward

It is known that parallel relay channels are not separable, i.e., the capacity with joint processing of the subchannels can be higher than the sum of the individual capacities. The same holds for the data rates achievable using partial decode-and-forward in parallel Gaussian MIMO relay channels. However, in this paper, we show that it is sufficient to allow the relay to remap information from one subchannel to another between the decoding and the re-encoding. A carrier-cooperative transmission in the sense of spreading transmit symbols over several subchannels does not bring advantages in terms of achievable rate.