Design and Practical Decoding of Full-Diversity Construction A Lattices\n for Block-Fading Channels
Bibliographic record
Abstract
Block-fading channel (BF) is a useful model for various wireless\ncommunication channels in both indoor and outdoor environments. The design of\nlattices for BF channels offers a challenging problem, which differs greatly\nfrom its counterparts like AWGN channels. Recently, the original binary\nConstruction A for lattices, due to Forney, has been generalized to a lattice\nconstruction from totally real and complex multiplication (CM) fields. This\ngeneralized algebraic Construction A of lattices provides signal space\ndiversity, intrinsically, which is the main requirement for the signal sets\ndesigned for fading channels. In this paper, we construct full-diversity\nalgebraic lattices for BF channels using Construction A over totally real\nnumber fields. We propose two new decoding methods for these lattices which\nhave complexity that grows linearly in the dimension of the lattice. The first\ndecoder is proposed for generalized Construction A lattices with a binary LDPC\ncode as underlying code. This decoding method contains iterative and\nnon-iterative phases. In order to implement the iterative phase, we propose the\ndefinition of a parity-check matrix and Tanner graph for Construction A\nlattices. We also prove that using an underlying LDPC code that achieves the\noutage probability limit over one-BF channel, the constructed algebraic LDPC\nlattices together with the proposed decoding method admit diversity order n.\nThen, we modify the proposed algorithm by removing its iterative phase which\nenables full-diversity practical decoding of all generalized Construction A\nlattices without any assumption about their underlying code. We provide some\ninstances showing that algebraic Construction A lattices obtained from binary\ncodes outperform the ones based on non-binary codes in BF channels. We\ngeneralize algebraic Construction A lattices over a wider family of number\nfields namely monogenic number fields.\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 | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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".