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Feedback over finite-state channels, and the zero-error trapdoor code - #36
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Co-authored-by: Cursor <cursoragent@cursor.com>
feedback_initial / feedback_step use the normalized forward vector as the transmitter's belief, and feedback_capacity brackets the capacity with feedback. Horstein's scheme on the trapdoor channel beats the no-feedback upper bound. Co-authored-by: Cursor <cursoragent@cursor.com>
Actions relative to the known ball, enumerative coding into words with no two 1s, and backward decoding from output differences; the rate approaches log2(phi), the trapdoor's feedback capacity. Co-authored-by: Cursor <cursoragent@cursor.com>
Co-authored-by: Cursor <cursoragent@cursor.com>
Co-authored-by: Cursor <cursoragent@cursor.com>
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Re-lands #35, which was merged into
dit-channel-adapterafter #34 had already merged, so it never reachedmain. Same five commits, cherry-picked onto currentmain, including a ty fix for #34's test imports. Needs dit's feedback codes (dit/dit#304).Summary
FiniteStateChannelfeedback methods:feedback_initial/feedback_stepstep the channel one use at a time, with the normalized forward vector as the transmitter's belief.feedback_capacitybrackets the capacity with feedback. dit's feedback codes now run over Mealy-machine channels.sofic.generators.trapdoor_code.trapdoor_code(k): the zero-error feedback code of Permuter, Cuff, Van Roy & Weissman (2008, Sec. VII) for the trapdoor channel.sofic.generators, so sofic still imports with older dit.trapdoor():E[N] = N + 3.5and reaches about 0.663 at k = 64, approaching log2(phi) ≈ 0.694.docs/generators/channel_coding.rst, aHorstein1963bib entry, and changelog entries.Test plan
tests/test_channel_feedback.py: 12 tests. They check thatfeedback_stepreproduceslog_likelihood(hypothesis), that a one-state channel matches dit's BSC, that exact matches Monte Carlo on the trapdoor, and that the feedback-capacity bracket contains log2(phi). Horstein must beat 0.584. The enumerative code must be a bijection (hypothesis), and the trapdoor code must be exactly zero-error withE[N] = N + 3.5. The tests skip when the installed dit lacks feedback codes.ruff check/ruff formatare clean.