Pith. Sign in

RECORD

Matching Dyadic Distributions to Channels

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Georg Böcherer, Rudolf Mathar

Information Theory · Submitted 20 Sep 2010

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Furthermore, we prove that by generating dyadic PMFs of blocks of consecutive input symbols, GHC achieves capacity when the block length goes to infinity.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1009.3751 (version 4)
Pith IDEUOQQU2S, Pith's permanent record of this paper and its review
CitationGeorg B\"ocherer, Rudolf Mathar. "Matching Dyadic Distributions to Channels." arXiv:1009.3751 (2010). https://pith.science/paper/EUOQQU2S
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,382 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.29 · human participants 0.02 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.75 · compares with prior results 0.15 · mentions code or data availability 0.03.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

Many communication channels with discrete input have non-uniform capacity achieving probability mass functions (PMF). By parsing a stream of independent and equiprobable bits according to a full prefix-free code, a modu-lator can generate dyadic PMFs at the channel input. In this work, we show that for discrete memoryless channels and for memoryless discrete noiseless channels, searching for good dyadic input PMFs is equivalent to minimizing the Kullback-Leibler distance between a dyadic PMF and a weighted version of the capacity achieving PMF. We define a new algorithm called Geometric Huffman Coding (GHC) and prove that GHC finds the optimal dyadic PMF in O(m \log m) steps where m is the number of input symbols of the considered channel. Furthermore, we prove that by generating dyadic PMFs of blocks of consecutive input symbols, GHC achieves capacity when the block length goes to infinity.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Many communication channels with discrete input have non-uniform capacity achieving probability mass functions (PMF). background 1.00 0.06 0.02 asserted 0.98
s1 By parsing a stream of independent and equiprobable bits according to a full prefix-free code, a modu-lator can generate dyadic PMFs at the channel input. background 0.86 0.14 0.03 asserted 0.91
s2 In this work, we show that for discrete memoryless channels and for memoryless discrete noiseless channels, searching for good dyadic input PMFs is equivalent to minimizing the Kullback-Leibler distance between a dyadic PMF and a weighted version of the capacity achieving PMF. result 0.74 0.91 0.49 asserted 1.00
s3 We define a new algorithm called Geometric Huffman Coding (GHC) and prove that GHC finds the optimal dyadic PMF in O(m \log m) steps where m is the number of input symbols of the considered channel. contribution 0.82 0.96 0.29 asserted 1.00
s4 Furthermore, we prove that by generating dyadic PMFs of blocks of consecutive input symbols, GHC achieves capacity when the block length goes to infinity. result 0.97 0.93 0.37 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.85 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v4
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Many communication channels with discrete input have non-uniform capacity achieving probability mass functions (PMF). By parsing a stream of independent and equiprobable bits according to a full prefix-free code, a modu-lator can generate dyadic PMFs at the channel input. In this work, we show that for discrete memoryless channels and for memoryless discrete noiseless channels, searching for good dyadic input PMFs is equivalent to minimizing the Kullback-Leibler distance between a dyadic PMF and a weighted version of the capacity achieving PMF. We define a new algorithm called Geometric Huffman Coding (GHC) and prove that GHC finds the optimal dyadic PMF in O(m \log m) steps where m is the number of input symbols of the considered channel. Furthermore, we prove that by generating dyadic PMFs of blocks of consecutive input symbols, GHC achieves capacity when the block length goes to infinity.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.