Towards an Algebraic Network Information Theory: Simultaneous Joint\n Typicality Decoding
Bibliographic record
Abstract
Consider a receiver in a multi-user network that wishes to decode several\nmessages. Simultaneous joint typicality decoding is one of the most powerful\ntechniques for determining the fundamental limits at which reliable decoding is\npossible. This technique has historically been used in conjunction with random\ni.i.d. codebooks to establish achievable rate regions for networks. Recently,\nit has been shown that, in certain scenarios, nested linear codebooks in\nconjunction with "single-user" or sequential decoding can yield better\nachievable rates. For instance, the compute-forward problem examines the\nscenario of recovering $L \\le K$ linear combinations of transmitted codewords\nover a $K$-user multiple-access channel (MAC), and it is well established that\nlinear codebooks can yield higher rates. Here, we develop bounds for\nsimultaneous joint typicality decoding used in conjunction with nested linear\ncodebooks, and apply them to obtain a larger achievable region for\ncompute-forward over a $K$-user discrete memoryless MAC. The key technical\nchallenge is that competing codeword tuples that are linearly dependent on the\ntrue codeword tuple introduce statistical dependencies, which requires careful\npartitioning of the associated error events.\n
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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 | 0.003 | 0.014 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.004 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.002 | 0.004 |
| Research integrity | 0.002 | 0.005 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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".