Hierarchical coding for a MIMO channel

The single-user (SU) broadcast transmission strategy (Shamai S., IEEE ISIT´97. p.150, 1997) is extended for the multiple input single output (MISO) channel. A derivation of the maximal achievable rate with layered coding for M transmit antennas is obtained, when perfect channel state information (CSI) is assumed at the receiver front end only. We consider also a two level code layering, and derive single integral expressions for probabilities of joint and successive decoding. The maximal achievable rate shows small improvement in two level layering relative to the single level layering (outage). In another setting, a multiple access channel (MAC) approach for the MIMO channel is discussed. In this approach, instead of performing joint encoding for all transmit antennas, each antenna has an independent encoder, thus the receiver views a MAC. Closed form expressions for the probabilities of the decoding regions in the MAC outage scheme are derived, under the optimal and successive decoding rules. We further consider some space-time coding schemes, namely multi-access permutation codes (MAPC). A Hadamard transformation is compared with a suggested diagonal permutation code. It is shown that diagonal permutation codes with single layer coding, achieve the outage capacity when employing SU decoders for each code.