We consider streaming data transmission over a discrete memoryless channel. A new message is given to the encoder at the beginning of each block and the decoder decodes each message sequentially, after a delay of T blocks. In this streaming setup, we study the fundamental interplay between the rate and error probability in the central limit and moderate deviations regimes and show the following achievability results: i) in the moderate deviations regime, the moderate deviations constant improves over the block coding or non-streaming setup at least by a factor of T and ii) in the central limit regime, the second-order coding rate improves at least by a factor of approximately √T for a wide range of channel parameters. For both the regimes, we propose coding techniques that incorporate a joint encoding of fresh and previous messages. Furthermore, we show that the exponent of the error probability can be improved tremendously by allowing variable decoding delay in the moderate deviations regime.
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