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

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

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

Wealth Dynamics in the 1980’s and 1990’s: Sweden and the U.S.

Given differences in public saving programs between Sweden and the United States, an examination of household private wealth accumulation in these two countries can be enlightening. In this paper we examine wealth inequality and mobility in Sweden and the United States over the past decade. We show that wealth inequality has been significantly greater in the U.S. than in Sweden and, while remaining relatively constant since the mid-1980’s in Sweden, has increased in the United States. In addition to less inequality and a higher median wealth, we also show that wealth quintile mobility in the 1990’s has been 25.7% higher in Sweden, as measured by Shorrocks’ index. Noting the role of various demographic components in shaping the patterns of wealth mobility as well as the importance of the initial wealth distribution, we utilize a matching algorithm that controls for these differences. Matching on the initial wealth distribution alone accounts for most of the mobility difference between the two countries and yields a Shorrocks’ index in the U.S. 11.1% less than that in Sweden. Adjusting for the large degree of imputation in the Swedish data, the U.S. index is only 3.4% to 6.1% less than that of Sweden. Along with exploring the role of racial composition differences, we conclude tha demographic variation between Sweden and the U.S. play very little role in explaining wealth mobility beyond that explained by the initial wealth distribution. Despite the higher quintile mobility in Sweden, dollar mobility is still high in the United States.Mobility; Wealth; Panel data; Statistical matching; Comparison U.S. - Sweden

Design and Analysis of a Trellis-Based Syndrome Distribution Matching Algorithm

Negli ultimi anni, la tecnica di modulazione chiamata "probabilistic shaping" ha assunto grande interesse sia in ambito accademico che industriale. Quando i bit vengono modulati e trasmessi come simboli di canale di comunicazione, è necessario tenere in considerazione che distribuzioni di ingresso uniformi non consentono in molti casi di avvicinarsi alla capacità. La tecnica di probabilistic shaping consente quindi di sfruttare in modo più efficiente il canale di trasmissione. L'elemento fondamentale che consente di implementare il probabilistic shaping è noto come "distribution matcher". Nel capitolo 1 viene presentata una panoramica generale sul modello di un sistema di comunicazione digitale. Nel capitolo 2 viene discusso il distribution matching e viene introdotta la tecnica constant composition distribution matcher (CCDM). Nel capitolo 3 si descrive l’algoritmo di distribution matching proposto nella tesi. Nei capitoli 4 e 5 si presentano i risultati di due scenari differenti, proponendo anche possibili applicazioni in cui risulta utile l’algoritmo. In conclusione, si forniscono osservazioni e possibili miglioramenti