Probabilistic Shaping for Finite Blocklengths: Distribution Matching and Sphere Shaping

In this paper, we provide for the first time a systematic comparison of distribution matching (DM) and sphere shaping (SpSh) algorithms for short blocklength probabilistic amplitude shaping. For asymptotically large blocklengths, constant composition distribution matching (CCDM) is known to generate the target capacity-achieving distribution. As the blocklength decreases, however, the resulting rate loss diminishes the efficiency of CCDM. We claim that for such short blocklengths and over the additive white Gaussian channel (AWGN), the objective of shaping should be reformulated as obtaining the most energy-efficient signal space for a given rate (rather than matching distributions). In light of this interpretation, multiset-partition DM (MPDM), enumerative sphere shaping (ESS) and shell mapping (SM), are reviewed as energy-efficient shaping techniques. Numerical results show that MPDM and SpSh have smaller rate losses than CCDM. SpSh--whose sole objective is to maximize the energy efficiency--is shown to have the minimum rate loss amongst all. We provide simulation results of the end-to-end decoding performance showing that up to 1 dB improvement in power efficiency over uniform signaling can be obtained with MPDM and SpSh at blocklengths around 200. Finally, we present a discussion on the complexity of these algorithms from the perspective of latency, storage and computations.Comment: 18 pages, 10 figure

Partial Enumerative Sphere Shaping

The dependency between the Gaussianity of the input distribution for the additive white Gaussian noise (AWGN) channel and the gap-to-capacity is discussed. We show that a set of particular approximations to the Maxwell-Boltzmann (MB) distribution virtually closes most of the shaping gap. We relate these symbol-level distributions to bit-level distributions, and demonstrate that they correspond to keeping some of the amplitude bit-levels uniform and independent of the others. Then we propose partial enumerative sphere shaping (P-ESS) to realize such distributions in the probabilistic amplitude shaping (PAS) framework. Simulations over the AWGN channel exhibit that shaping 2 amplitude bits of 16-ASK have almost the same performance as shaping 3 bits, which is 1.3 dB more power-efficient than uniform signaling at a rate of 3 bit/symbol. In this way, required storage and computational complexity of shaping are reduced by factors of 6 and 3, respectively.Comment: 6 pages, 6 figure

Information Theoretical Analysis of Identification based on Active Content Fingerprinting

Content fingerprinting and digital watermarking are techniques that are used for content protection and distribution monitoring. Over the past few years, both techniques have been well studied and their shortcomings understood. Recently, a new content fingerprinting scheme called {\em active content fingerprinting} was introduced to overcome these shortcomings. Active content fingerprinting aims to modify a content to extract robuster fingerprints than the conventional content fingerprinting. Moreover, contrary to digital watermarking, active content fingerprinting does not embed any message independent of contents thus does not face host interference. The main goal of this paper is to analyze fundamental limits of active content fingerprinting in an information theoretical framework.Comment: 35th WIC Symposium on Information Theory in the Benelu

Achievable Information Rates for Probabilistic Amplitude Shaping: An Alternative Approach via Random Sign-Coding Arguments

Probabilistic amplitude shaping (PAS) is a coded modulation strategy in which constellation shaping and channel coding are combined. PAS has attracted considerable attention in both wireless and optical communications. Achievable information rates (AIRs) of PAS have been investigated in the literature using Gallager's error exponent approach. In particular, it has been shown that PAS achieves the capacity of the additive white Gaussian noise channel (B\"ocherer, 2018). In this work, we revisit the capacity-achieving property of PAS and derive AIRs using weak typicality. Our objective is to provide alternative proofs based on random sign-coding arguments that are as constructive as possible. Accordingly, in our proofs, only some signs of the channel inputs are drawn from a random code, while the remaining signs and amplitudes are produced constructively. We consider both symbol-metric and bit-metric decoding.Comment: 19 pages, 6 figures (v3: proofs of Theorems 3 and 4 are generalized for M-ASK.

Enumerative Sphere Shaping for Rate Adaptation and Reach Increase in WDM Transmission Systems

The performance of enumerative sphere shaping (ESS), constant composition distribution matching (CCDM), and uniform signalling are compared at the same forward error correction rate. ESS is shown to offer a reach increase of approximately 10% and 22% compared to CCDM and uniform signalling, respectively.Comment: 4 Pages, 4 figure

First Experimental Demonstration of Probabilistic Enumerative Sphere Shaping in Optical Fiber Communications

We transmit probabilistic enumerative sphere shaped dual-polarization 64-QAM at 350Gbit/s/channel over 1610km SSMF using a short blocklength of 200. A reach increase of 15% over constant composition distribution matching with identical blocklength is demonstrated

Thrombolysis with tissue plasminogen activator in acute myocardial infarction: no additional benefit from immediate percutaneous coronary angioplasty

A randomised trial of 367 patients with acute myocardial infarction was performed to determine whether an invasive strategy combining thrombolysis with recombinant tissue-type plasminogen activator (rTPA), heparin, and acetylsalicylic acid, and immediate percutaneous transluminal coronary angioplasty (PTCA) would be superior to a noninvasive strategy with the same medical treatment but without immediate angiography and PTCA. Intravenous infusion of 100 mg rTPA was started within 5 h after onset of symptoms (median 156 min). Angiography was performed 6-165 min later in 180 out of 183 patients allocated to the invasive strategy; 184 patients were allocated to the non-invasive strategy. Immediate PTCA reduced the percentage stenosis of the infarc