On the complexity of joint source-channel decoding of markov sequences over memoryless channels
Bibliographic record
Abstract
We investigate the complexity of joint source-channel maximum a posteriori (MAP) decoding of a Markov sequence which is first encoded by a source code, then encoded by a convolutional code, and sent through a noisy memoryless channel. As established previously the MAP decoding can be performed by a Viterbi-like algorithm on a trellis whose states are triples of the states of the Markov source, the source coder and convolutional coder. The large size of the product space (in the order of K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> N, where K is the number of source symbols and N is the number of states of the convolutional coder) appears to prohibit such a scheme. We show that in the case of finite impulse response convolutional codes the state space size can be reduced to O(K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2 </sup> + NlogN), hence the decoding time becomes O(TK <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> + TNlogN), where T is the length in bits of the decoded bitstream. We further show that an additional complexity reduction can be achieved when K > N, if the source satisfies a certain property, which is the case for a scalar quantized Gaussian-Markov source. This decrease becomes more significant as the tree structure of the source code is more unbalanced. The reduction factor ranges between O(K/N) (for a fixed-length source code) and O(K/logN) (for Golomb-Rice code)
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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 | 0.001 | 0.000 |
| 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 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| 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".