Finite codelength analysis of the sequential waveform nulling receiver for M-ary PSK

Si Hui Tan, Zachary Dutton, Ranjith Nair, Saikat Guha

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations


The conditions for a quantum measurement to discriminate a set of states with the minimum probability of error were specified by Yuen, Kennedy and Lax, and are often termed the YKL conditions [1]. Since light is quantum mechanical, the ultimate limit on minimum-error discrimination of an optical modulation constellation is determined by the YKL bound. Standard optical receivers (i.e., direct, homodyne or heterodyne detection) - even at their respective ideal operation limits - cannot achieve this performance. Recently, it was shown that a 'sequential waveform nulling' (SWN) receiver can, not only discriminate an arbitrary M-ary coherent-state (ideal laser-light) constellation asymptotically at the YKL bound in the high-power limit, but that it achieves a factor of 4 better in the asymptotic error-probability exponent compared with heterodyne detection - the only conventional optical receiver that can in principle be employed for detecting an arbitrary phase-and-amplitude modulated constellation [2]. The SWN receiver can be built with standard optical components; i.e., beamsplitters, local-oscillator lasers, delay loops and single-photon detectors. However on the other hand, in the high power regime, heterodyne detection is known to achieve a reliable communication rate that asymptotically approaches the Holevo capacity of a lossy-noisy optical channel (the ultimate limit to the classical capacity of a quantum channel) [3]. In fact, in the high power regime, heterodyne detection was also shown recently to achieve the optimal second-order coding rate, when using the optimal (Gaussian) input distribution [4]. In this paper, we show that when restricted to the M-ary phase-shift keying (PSK) ensemble, that the SWN receiver's superiority over heterodyne detection in its asymptotic error exponent of the demodulation error probability, translates to a slightly higher capacity and a pronouncedly higher finite blocklength reliable-communication rate. We also quantify, via a numerical calculation, the dependence of the SWN receiver's capacity on the order in which the PSK constellation points are nulled. Our results suggest that for short-latency PSK-modulated optical communication in the high spectral efficiency regime - for which heterodyne detection is the conventional receiver choice - that it may be beneficial to employ the SWN receiver, despite the widely-regarded capacity optimality of heterodyne detection in this operating regime.

Original languageEnglish (US)
Title of host publicationProceedings - 2015 IEEE International Symposium on Information Theory, ISIT 2015
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781467377041
StatePublished - Sep 28 2015
EventIEEE International Symposium on Information Theory, ISIT 2015 - Hong Kong, Hong Kong
Duration: Jun 14 2015Jun 19 2015

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
ISSN (Print)2157-8095


OtherIEEE International Symposium on Information Theory, ISIT 2015
Country/TerritoryHong Kong
CityHong Kong

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modeling and Simulation
  • Applied Mathematics


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