Error Floor Estimation of LDPC Coded Modulation Systems Using Importance Sampling
Bibliographic record
Abstract
One of the key weaknesses of low-density parity-check (LDPC) codes is the error floor that they typically exhibit at high signal-to-noise ratios (SNRs). Such an error floor is usually attributed to problematic structures known as trapping sets (TSs). The overwhelming majority of existing error floor estimation schemes consider the case of binary phase shift keying (BPSK) signalling. Unfortunately, these schemes are not readily extensible to estimate the error floor of high order LDPC coded modulation systems considered herein. To provide such a scheme, in this work, we use mean-shift importance sampling (MS-IS) to develop a novel error floor estimation methodology for high-order pulse amplitude modulation (PAM) and quadrature amplitude modulation (QAM) LDPC coded systems. First, a computationally efficient graphical-based approach is used to identify the TSs of a given LDPC code. Subsequently, a novel analytical approach is devised to identify the TSs that are likely to have a higher contribution in the error floor. These TSs are referred to as potentially dominant TSs (PDTSs). Finally, a new methodology for categorizing the PDTSs into equivalence classes is developed. A representative PDTS of each equivalence class is chosen and an MS-IS framework is devised to obtain the error rate corresponding to each equivalence class. To arrive at the desired MS-IS scheme, we develop an algorithm that invokes the geometry of the constellation to determine the MS value. In contrast with the conventional MS-IS method used in BPSK signalling, in the proposed MS-IS scheme, the MS value is a variable that is determined based on the TS and the transmitted codeword. The computational complexity of the three main steps of our methodology, viz. extracting the PDTSs, determining the MS values, and applying the MS-IS scheme, depends merely on the size of the constellation and the structure of the code, but not on the SNR. Numerical simulations confirm the efficacy and accuracy of the proposed technique at different SNRs.
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 distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".