The Streaming-DMT of Fading Channels

We consider the sequential transmission of a stream of messages over a block-fading multi-input-multi-output channel. A new message arrives at the beginning of each coherence block, and the decoder is required to output each message sequentially, after a delay of T coherence blocks. In the special case when T = 1, the setup reduces to the quasi-static fading channel. We establish the optimal diversity-multiplexing tradeoff (DMT) in the high signal-to-noise-ratio (SNR) regime, and show that it equals T times the DMT of the quasi-static channel. The converse is based on utilizing the delay constraint to amplify a local outage event associated with a message, globally across all the coherence blocks. This approach appears to be new. We propose two coding schemes that achieve the optimal DMT. The first scheme involves interleaving of messages, such that each message is transmitted across T consecutive coherence blocks. This scheme requires the knowledge of the delay constraint at both the encoder and decoder. Our second coding scheme involves a sequential tree code and is delay universal, i.e., the knowledge of the decoding delay is not required by the encoder. However, in this scheme, we require the coherence block length to increase as log (SNR), in order to attain the optimal DMT. Finally, we discuss the case when multiple messages arrive at uniform intervals within each coherence period. Through a simple example, we exhibit the suboptimality of interleaving and propose another scheme that achieves the optimal DMT.