Incremental coding over MIMO channels

The problem of multicasting common data to several users over multiple-input multiple-output (MIMO) Gaussian channels is studied. A closed-loop setup is considered where the channel matrices are known to the transmitter and respective receivers. An incremental-redundancy (rateless) scenario is considered, where the effective rate is measured by the time that each user needs to stay online until it is able to decode the message. A practical transmission scheme for the two-user case is proposed which, by linear pre - and post-processing combined with successive decoding and interference cancellation, transforms the two MIMO channels into a set of parallel channels with no loss of mutual information, where each user needs to tune in for a duration of time proportional to its individual capacity. This scheme is used for designing a practical transmission scheme for the Gaussian MIMO half-duplex relay channel. We then turn to the related scenario of transmission to a single user over a MIMO channel with unknown but constant signal-to-noise ratio (SNR), for which we develop an optimal low-complexity hybrid ARQ coding scheme, which is optimal for two SNRs and propose a scheme for more SNRs, the loss of which vanishes when the SNRs are high. Finally, we show that even when applied to single-input single-output (“scalar”) channels, the scheme provides a practical solution for cases not covered by previous work.