Methods of mapping, indicating, encoding and transmitting uplink (UL) grants and downlink (DL) assignments for wireless communications for carrier aggregation are disclosed. Methods to encode and transmit DL assignments and UL grants and map and indicate the DL assignments to DL component carriers and UL grants to UL component carriers are described. Methods include specifying the mapping rules for DL component carriers that transmit DL assignment and DL component carriers that receive physical downlink shared channel (PDSCH), and mapping rules for DL component carriers that transmit UL grants and UL component carriers that transit physical uplink shared channel (PUSCH) when using separate coding/separate transmission schemes.