The DOI matches its Crossref record; 16 of the 16 references it cites were found in a registry or an index.
Optimal nonuniform signaling for Gaussian channels
Abstract
Variable-rate data transmission schemes in which constellation points are selected according to a nonuniform probability distribution are studied. When the criterion is one of minimizing the average transmitted energy for a given average bit rate, the best possible distribution with which to select constellations points is a Maxwell-Boltzmann distribution. In principle, when constellation points are selected according to a Maxwell-Boltzmann distribution, the ultimate shaping gain ( pi e/6 or 1.53 dB) can be achieved in any dimension. Nonuniform signaling schemes can be designed by mapping simple variable-length prefix codes onto the constellation. Using the Huffman procedure, prefix codes can be designed that approach the optimal performance. These schemes provide a fixed-rate primary channel and a variable-rate secondary channel, and are easily incorporated into standard lattice-type coded modulation schemes.>
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
Optimization by Simulated Annealing
Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983) · Science · doi:10.1126/science.220.4598.671 · Cited by 45,134
Handbook of Mathematical Functions
McQuarrie, D. A. (1966) · American Journal of Physics · doi:10.1119/1.1972842 · Cited by 40,433
Elements of Information Theory
Cover, T. M., & Thomas, J. A. (2001) · Wiley eBooks · doi:10.1002/0471200611 · Cited by 36,808
Handbook of Mathematical Functions.
Florentin, J. J., Abramowitz, M., & Stegun, I. A. (1966) · The American Mathematical Monthly · doi:10.2307/2314682 · Cited by 7,560
Introduction to the theory of neural computation
(1994) · Neural Networks · doi:10.1016/0893-6080(94)90014-0 · Cited by 6,401
A Method for the Construction of Minimum-Redundancy Codes
Huffman, D. (1952) · Proceedings of the IRE · doi:10.1109/jrproc.1952.273898 · Cited by 6,334
Channel coding with multilevel/phase signals
Ungerboeck, G. (1982) · IEEE Transactions on Information Theory · doi:10.1109/tit.1982.1056454 · Cited by 3,751
Sphere Packings, Lattices and Groups.
Coxeter, H. S. M., Conway, J. H., & Sloane, N. J. A. (1989) · The American Mathematical Monthly · doi:10.2307/2323992 · Cited by 3,377
Principles of Communication Engineering
Jacobs, I. M., & Wozencraft, J. M. (1965) · CERN Document Server (European Organization for Nuclear Research) · Cited by 1,912
Sphere Packings, Lattices and Groups
Conway, J. H., & Sloane, N. J. A. (1988) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-1-4757-2016-7 · Cited by 1,532
Cited by
Probabilistic Constellation Shaping for Optical Fiber Communications
Cho, J., & Winzer, P. J. (2019) · Journal of Lightwave Technology · doi:10.1109/jlt.2019.2898855 · Cited by 438
Metadata
- Authors
- Kschischang, F. R., & Pasupathy, S.
- Venue
- IEEE Transactions on Information Theory
- Published
- 1993-05
- Volume
- 39
- Issue
- 3
- Pages
- 913-929
- ISSN
- 0018-9448 (ISSN-L)
- 1557-9654
- OpenAlex
- W2115001548
- Cited by
- 503
- References
- 16
- FWCI
- 2.96
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
How to cite
Cite CoChat for the checks on this page, and the paper for its own findings.
- This page
- CoChat. (2026). Citation check: Optimal nonuniform signaling for Gaussian channels. https://app.cochat.ai/papers/10.1109/18.256499
- The paper
- Kschischang, F. R., & Pasupathy, S. (1993). Optimal nonuniform signaling for Gaussian channels. IEEE Transactions on Information Theory. https://doi.org/10.1109/18.256499
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
