Streaming Data Transmission in the Moderate Deviations and Central Limit Regimes

Abstract

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 that i) in the moderate deviations regime, the moderate deviations constant improves over the block coding or non-streaming setup by a factor of T and ii) in the central limit regime, the second-order coding rate improves by a factor of approximately √ T for a wide range of channel parameters. For both regimes, we propose coding techniques that incorporate a joint encoding of fresh and previous messages. In particular, for the central limit regime, we propose a coding technique with truncated memory to ensure that a summation of constants, which arises as a result of applications of the central limit theorem, does not diverge in the error analysis.Furthermore, we explore interesting variants of the basic streaming setup in the moderate deviations regime. We first consider a scenario with an erasure option at the decoder and show that both the exponents of the total error and the undetected error probabilities improve by factors of T . Next, by utilizing the erasure option, we show that the exponent of the total error probability can be improved to that of the undetected error probability (in the order sense) at the expense of a variable decoding delay.Finally, we also extend our results to the case where the message rate is not fixed but alternates between two values.

Moderate deviation analysis for classical communication over quantum channels

“…However, our approach differs from that in Ref. [51] because we do not want to assume that the average variance, V n , is bounded away from zero.…”

Moderate Deviation Asymptotics for Variable-Length Codes With Feedback

“…Note that the "exponent" here contains ρ N instead of ρ 2 n (for fixed-length codes as discussed in Section I-A) so this is further evidence that variable-length codes dramatically improve the error probability performance over fixed-length codes. This phenomenon has also been observed in other contexts such as decoding with the erasure option [23,Theorems 1 & 3] and streaming communications with variable decoding delay [24,Theorem 7]. This derivation in (2) is, of course, heuristic and non-rigorous.…”

“…and (24) is replaced by (19) for some T ≥ T 0 (where T 0 ∈ R is mentioned in Lemma 2). Then, (25) also holds.…”

Achievable Moderate Deviations Asymptotics for Streaming Compression of Correlated Sources

“…The papers that are most related to the present one are those by Lee, Tan and Khisti [19] and Draper, Chang and Sahai [10]. In [19], the authors study the information-theoretic limits of the blockwise streaming version of channel coding in the moderate deviations and central limit regimes.…”

“…The proof of our main result involves the use of various analytical tools and amalgamates several ideas from the recent information-theoretic streaming literature. We adapt the so-called truncated memory encoding idea from Khisti (2011) andKhisti (2016) to ensure that the effect of error accumulation is nullified in the limit of large blocklengths. We also adapt the use of the so-called minimum weighted empirical suffix entropy decoder which was used by Draper, Chang, and Sahai (2014) to derive achievable error exponents for symbolwise streaming Slepian-Wolf coding.…”