Interactive Encoding and Decoding Based on Binary LDPC Codes with Syndrome Accumulation
Bibliographic record
Abstract
Interactive encoding and decoding based on binary low-density parity-check codes with syndrome accumulation (SA-LDPC-IED) is proposed and investigated. Assume that the source alphabet is $\mathbf{GF}(2)$, and the side information alphabet is finite. It is first demonstrated how to convert any classical universal lossless code $\mathcal{C}_n$ (with block length $n$ and side information available to both the encoder and decoder) into a universal SA-LDPC-IED scheme. It is then shown that with the word error probability approaching 0 sub-exponentially with $n$, the compression rate (including both the forward and backward rates) of the resulting SA-LDPC-IED scheme is upper bounded by a functional of that of $\mathcal{C}_n$, which in turn approaches the compression rate of $\mathcal{C}_n$ for each and every individual sequence pair $(x^n,y^n)$ and the conditional entropy rate $\mathrm{H}(X |Y)$ for any stationary, ergodic source and side information $(X, Y)$ as the average variable node degree $\bar{l}$ of the underlying LDPC code increases without bound. When applied to the class of binary source and side information $(X, Y)$ correlated through a binary symmetrical channel with cross-over probability unknown to both the encoder and decoder, the resulting SA-LDPC-IED scheme can be further simplified, yielding even improved rate performance versus the bit error probability when $\bar{l}$ is not large. Simulation results (coupled with linear time belief propagation decoding) on binary source-side information pairs confirm the theoretic analysis, and further show that the SA-LDPC-IED scheme consistently outperforms the Slepian-Wolf coding scheme based on the same underlying LDPC code. As a by-product, probability bounds involving LDPC established in the course are also interesting on their own and expected to have implications on the performance of LDPC for channel coding as well.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".