A Beta-Beta Achievability Bound with Applications

A channel coding achievability bound expressed in terms of the ratio between two Neyman-Pearson $\beta$ functions is proposed. This bound is the dual of a converse bound established earlier by Polyanskiy and Verd\'{u} (2014). The new bound turns out to simplify considerably the analysis in situations where the channel output distribution is not a product distribution, for example due to a cost constraint or a structural constraint (such as orthogonality or constant composition) on the channel inputs. Connections to existing bounds in the literature are discussed. The bound is then used to derive 1) an achievability bound on the channel dispersion of additive non-Gaussian noise channels with random Gaussian codebooks, 2) the channel dispersion of the exponential-noise channel, 3) a second-order expansion for the minimum energy per bit of an AWGN channel, and 4) a lower bound on the maximum coding rate of a multiple-input multiple-output Rayleigh-fading channel with perfect channel state information at the receiver, which is the tightest known achievability result.Comment: extended version of a paper submitted to ISIT 201

Towards fundamental limits of bursty multi-user communications in wireless networks

International audienceConsidering an isolated wireless cell containing a high density of nodes, the fundamental limit can be defined as the maximal number of nodes the associate base station can serve under some system level constraints including maximal rate, reliability, latency and transmission power. This limit can be investigated in the downlink, modeled as a spatial continuum broadast channel (SCBC) as well as in the uplink modeled as a spatial continuum multiple access channel (SCMAC). In this short paper, we summarize the different steps towards the characterization of this fundamental limit, considering four figures of merit: energy efficiency, spectral efficiency, latency, reliabilty

The Dispersion of Nearest-Neighbor Decoding for Additive Non-Gaussian Channels

We study the second-order asymptotics of information transmission using random Gaussian codebooks and nearest neighbor (NN) decoding over a power-limited stationary memoryless additive non-Gaussian noise channel. We show that the dispersion term depends on the non-Gaussian noise only through its second and fourth moments, thus complementing the capacity result (Lapidoth, 1996), which depends only on the second moment. Furthermore, we characterize the second-order asymptotics of point-to-point codes over $K$-sender interference networks with non-Gaussian additive noise. Specifically, we assume that each user's codebook is Gaussian and that NN decoding is employed, i.e., that interference from the $K-1$ unintended users (Gaussian interfering signals) is treated as noise at each decoder. We show that while the first-order term in the asymptotic expansion of the maximum number of messages depends on the power of the interferring codewords only through their sum, this does not hold for the second-order term.Comment: 12 pages, 3 figures, IEEE Transactions on Information Theor

Exact Moderate Deviation Asymptotics in Streaming Data Transmission

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.Comment: 23 pages, 1 figure, 1 table, Submitted to IEEE Transactions on Information Theor

Random Access Channel Coding in the Finite Blocklength Regime

Consider a random access communication scenario over a channel whose operation is defined for any number of possible transmitters. Inspired by the model recently introduced for the Multiple Access Channel (MAC) with a fixed, known number of transmitters by Polyanskiy, we assume that the channel is invariant to permutations on its inputs, and that all active transmitters employ identical encoders. Unlike Polyanskiy, we consider a scenario in which neither the transmitters nor the receiver know which or how many transmitters are active. We refer to this agnostic communication setup as the Random Access Channel, or RAC. Limited feedback is used to ensure that the collection of active transmitters remains fixed during each epoch. The decoder is tasked with determining from the channel output the number of active transmitters (k) and their messages but not which transmitter sent which message. The central result of this work demonstrates the achievability on a RAC of performance that is first-order optimal for the MAC in operation during each coding epoch. While prior multiple access schemes for a fixed number of transmitters require 2^k - 1 simultaneous threshold rules, the proposed scheme uses a single threshold rule and achieves the same dispersion

Beta-Beta Bounds: Finite-Blocklength Analog of the Golden Formula

It is well known that the mutual information between two random variables can be expressed as the difference of two relative entropies that depend on an auxiliary distribution, a relation sometimes referred to as the golden formula. This paper is concerned with a finite-blocklength extension of this relation. This extension consists of two elements: 1) a finite-blocklength channel-coding converse bound by Polyanskiy and Verd\'{u} (2014), which involves the ratio of two Neyman-Pearson $\beta$ functions (beta-beta converse bound); and 2) a novel beta-beta channel-coding achievability bound, expressed again as the ratio of two Neyman-Pearson $\beta$ functions. To demonstrate the usefulness of this finite-blocklength extension of the golden formula, the beta-beta achievability and converse bounds are used to obtain a finite-blocklength extension of Verd\'{u}'s (2002) wideband-slope approximation. The proof parallels the derivation of the latter, with the beta-beta bounds used in place of the golden formula. The beta-beta (achievability) bound is also shown to be useful in cases where the capacity-achieving output distribution is not a product distribution due to, e.g., a cost constraint or structural constraints on the codebook, such as orthogonality or constant composition. As an example, the bound is used to characterize the channel dispersion of the additive exponential-noise channel and to obtain a finite-blocklength achievability bound (the tightest to date) for multiple-input multiple-output Rayleigh-fading channels with perfect channel state information at the receiver.Comment: to appear in IEEE Transactions on Information Theor

Random Access Channel Coding in the Finite Blocklength Regime

Consider a random access communication scenario over a channel whose operation is defined for any number of possible transmitters. Inspired by the model recently introduced for the Multiple Access Channel (MAC) with a fixed, known number of transmitters by Polyanskiy, we assume that the channel is invariant to permutations on its inputs, and that all active transmitters employ identical encoders. Unlike Polyanskiy, we consider a scenario in which neither the transmitters nor the receiver know which or how many transmitters are active. We refer to this agnostic communication setup as the Random Access Channel, or RAC. Limited feedback is used to ensure that the collection of active transmitters remains fixed during each epoch. The decoder is tasked with determining from the channel output the number of active transmitters (k) and their messages but not which transmitter sent which message. The central result of this work demonstrates the achievability on a RAC of performance that is first-order optimal for the MAC in operation during each coding epoch. While prior multiple access schemes for a fixed number of transmitters require 2^k - 1 simultaneous threshold rules, the proposed scheme uses a single threshold rule and achieves the same dispersion