Moderate Deviations in Channel Coding

IEEE Trans. Inform. Theory

Motani

2017

We derive the optimal second-order coding region and moderate deviations constant for successive refinement source coding with a joint excess-distortion probability constraint. We consider two scenarios: (i) a discrete memoryless source (DMS) and arbitrary distortion measures at the decoders and (ii) a Gaussian memoryless source (GMS) and quadratic distortion measures at the decoders. For a DMS with arbitrary distortion measures, we prove an achievable second-order coding region, using type covering lemmas by Kanlis and Narayan and by No, Ingber and Weissman. We prove the converse using the perturbation approach by Gu and Effros. When the DMS is successively refinable, the expressions for the second-order coding region and the moderate deviations constant are simplified and easily computable. For this case, we also obtain new insights on the second-order behavior compared to the scenario where separate excess-distortion proabilities are considered. For example, we describe a DMS, for which the optimal second-order region transitions from being characterizable by a bivariate Gaussian to a univariate Gaussian, as the distortion levels are varied. We then consider a GMS with quadratic distortion measures. To prove the direct part, we make use of the sphere covering theorem by Verger-Gaugry, together with appropriately-defined Gaussian type classes. To prove the converse, we generalize Kostina and Verdú's one-shot converse bound for point-to-point lossy source coding. We remark that this proof is applicable to general successively refinable sources. In the proofs of the moderate deviations results for both scenarios, we follow a strategy similar to that for the second-order asymptotics and use the moderate deviations principle.

Section: B Related Workmentioning

confidence: 99%

Second-Order and Moderate Deviation Asymptotics for Successive Refinement

Zhou

IEEE Trans. Inform. Theory

Motani

2017

“…Shortly after the conference version of Ref. [12], Polyanskiy and Verdú [13] relaxed some of the conditions on the class of DMCs and also established the moderate deviations asymptotics for other important classical channels such as the additive white Gaussian noise channel. The other main contributions to the analysis of hypothesis testing, channel coding, quantum hypothesis testing, and c-q channel coding in the different parameter regimes are summarised in Table 1.…”

Section: Introductionmentioning

confidence: 99%

“…For classical channels, Altȗg and Wagner [12] first established the best decay rate of the average error probability for a class of discrete memoryless channels (DMCs) when the code rate approaches capacity at a rate slower than Θ(n −1/2 ). Shortly after the conference version of Ref.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Moderate Deviation Analysis for Classical Communication over Quantum Channels

Chubb

Tomamichel

2017

Commun. Math. Phys.

We analyse families of codes for classical data transmission over quantum channels that have both a vanishing probability of error and a code rate approaching capacity as the code length increases. To characterise the fundamental tradeoff between decoding error, code rate and code length for such codes we introduce a quantum generalisation of the moderate deviation analysis proposed by Altȗg and Wagner as well as Polyanskiy and Verdú. We derive such a tradeoff for classical-quantum (as well as image-additive) channels in terms of the channel capacity and the channel dispersion, giving further evidence that the latter quantity characterises the necessary backoff from capacity when transmitting finite blocks of classical data. To derive these results we also study asymmetric binary quantum hypothesis testing in the moderate deviations regime. Due to the central importance of the latter task, we expect that our techniques will find further applications in the analysis of other quantum information processing tasks.

“…Alternatively, one could attempt to derive the sphere-packing bound directly as in [8] for block channel coding. In this approach, we first assume by using some standard arguments that the channel input sequences over T S * n blocks are constant composition, say type P , and then choose the auxiliary channel V * n as follows instead of (32):…”

Section: Discussionmentioning

confidence: 99%

Exact moderate deviation asymptotics in streaming data transmission

Lee

2017 IEEE International Symposium on Information Theory (ISIT)

Khisti

2017

In this paper, a streaming transmission setup is considered where an encoder observes a new message in the beginning of each block and a decoder sequentially decodes each message after a delay of T blocks.In this streaming setup, the fundamental interplay between the coding rate, the error probability, and the blocklength in the moderate deviations regime is studied. For output symmetric channels, the moderate deviations constant is shown to improve over the block coding or non-streaming setup by exactly a factor of T for a certain range of moderate deviations scalings. For the converse proof, a more powerful decoder to which some extra information is fedforward is assumed. The error probability is bounded first for an auxiliary channel and this result is translated back to the original channel by using a newly developed change-of-measure lemma, where the speed of decay of the remainder term in the exponent is carefully characterized. For the achievability proof, a known coding technique that involves a joint encoding and decoding of fresh and past messages is applied with some manipulations in the error analysis.