Estimating Word Lengths for Fixed-Point DSP Implementations Using Polynomial Chaos Expansions
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Bibliographic record
Abstract
Efficient custom hardware motivates the use of fixed-point arithmetic in the implementation of digital signal-processing (DSP) algorithms. This conversion to finite precision arithmetic introduces quantization noise in the system, which affects the system’s performance. As a result, characterizing quantization noise and its effects within a DSP system is a challenge that must be addressed to avoid over-allocating hardware resources during implementation. Polynomial chaos expansion (PCE) is a method used to model uncertainty in engineering systems. Although it has been employed to analyze quantization effects in DSP systems, previous investigations have been limited in scope and scale. This paper introduces new techniques that allow the application of PCE to be scaled up to larger DSP blocks with many noise sources, as needed for building blocks in software-defined radios (SDRs). Design space exploration algorithms that leverage the accuracy of PCE to estimate bit widths for fixed-point implementations of DSP blocks in an SDR system are explored, and their advantages will be presented.
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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 | 0.000 |
| Open science | 0.000 | 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 it