Streaming Data Transmission in the Moderate Deviations and Central Limit\n Regimes

We consider streaming data transmission over a discrete memoryless channel. A\nnew message is given to the encoder at the beginning of each block and the\ndecoder decodes each message sequentially, after a delay of $T$ blocks. In this\nstreaming setup, we study the fundamental interplay between the rate and error\nprobability in the central limit and moderate deviations regimes and show that\ni) in the moderate deviations regime, the moderate deviations constant improves\nover the block coding or non-streaming setup by a factor of $T$ and ii) in the\ncentral limit regime, the second-order coding rate improves by a factor of\napproximately $\\sqrt{T}$ for a wide range of channel parameters. For both\nregimes, we propose coding techniques that incorporate a joint encoding of\nfresh and previous messages. In particular, for the central limit regime, we\npropose a coding technique with truncated memory to ensure that a summation of\nconstants, which arises as a result of applications of the central limit\ntheorem, does not diverge in the error analysis.\n Furthermore, we explore interesting variants of the basic streaming setup in\nthe moderate deviations regime. We first consider a scenario with an erasure\noption at the decoder and show that both the exponents of the total error and\nthe undetected error probabilities improve by factors of $T$. Next, by\nutilizing the erasure option, we show that the exponent of the total error\nprobability can be improved to that of the undetected error probability (in the\norder sense) at the expense of a variable decoding delay. Finally, we also\nextend our results to the case where the message rate is not fixed but\nalternates between two values.\n

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