Upper Bound for Uniquely Decodable Codes in a Binary Input N-User Adder Channel
Bibliographic record
Abstract
The binary input N-user adder channel models a communicant ion media accessed simultaneously by N users. In this model each user transmits binary sequences and the channel's output on each bit slot equals the sum of the corresponding N inputs. A uniquely decodable code for this channel is a set of N codes - a code for each of the N users - such that the receiver can determine all possible combinations of transmitted codewords from their sum. Van-Tilborg presented a method for determining an upper bound on the size of a uniquely decodable code for the two-user binary adder channel. He showed that for sufficiently large block length this combinatorial bound converges to the corresponding capacity region boundary. In the present work we use a similar method to derive an upper bound on the size of a uniquely decodable code for the binary input N-user adder channel. The new combinatorial bound is iterative - i.e., the bound for the (N - I)-user case can be obtained by projecting the N-user bound on (N - 1) combinatorial variables and in particular it subsumes the two-user result. For sufficiently large block length the N-user bound converges to the capacity region boundary of the binary input N-user adder channel.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.022 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.004 | 0.008 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.004 |
| Insufficient payload (model declined to judge) | 0.008 | 0.002 |
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".