Error protection based on a nonlinear code set may be used in a multiple input multiple output (MIMO) radio communications system. A decoder decodes received MIMO data streams and generates an automatic repeat request (ARQ) message for data units received for the MIMO data streams for each transmission time interval. An encoder codes the ARQ message using a code word from a nonlinear code set. At the data transmitter, which transmits one or more data units in transmission time intervals from two or more MIMO data streams, the ARQ message associated with the transmitted data units is decoded using a code word from the nonlinear code set.