[Autoplectic]

Summary

Makes every stochastic MealyMachine, and so every ε-transducer, usable as a channel for dit.coding channel codes. It implements dit's duck-typed channel protocol from dit/dit#301, so dit needs no knowledge of sofic.

from dit.coding import hamming
from sofic.examples.processes import trapdoor

code = hamming(3)
code.probability_of_error(trapdoor(), method="exact")
code.capacity_gap(trapdoor())  # (lower, upper)

• MealyMachine.__dit_channel__() returns a new FiniteStateChannel. It is exported from sofic.generators and sofic.
• FiniteStateChannel provides:
  • log_likelihood: the scaled forward algorithm. It is exact for any finite-state channel, unifilar or not.
  • sample: draws a state path from the initial law.
  • symbol_log_likelihoods: forward-backward (BCJR) under uniform i.i.d. inputs. dit's LDPC, polar, and soft-Viterbi decoders use these values.
  • capacity(**kw): the (lower, upper) no-feedback bracket from sofic.generators.capacity.capacity. The codes don't use feedback.
  • Symbol maps: by default digit strings become ints ("0" becomes 0); input_map and output_map override this.
• Refactor: the initial-state law is factored out of channel_tensors into initial_law, which both use.
• Docs: a new docs/generators/channel_coding.rst page, Bahl1974 added to docs/references.bib, and a CHANGELOG entry.

Depends on dit/dit#301. The new tests skip themselves when the installed dit has no dit.coding.as_channel. Raise the dit>=2.3 floor once a dit release includes that PR.

Test plan

• New tests/test_channel_coding.py:
  • trapdoor and ising_channel likelihoods and BCJR symbol likelihoods match brute-force sums over state paths.
  • Sampled frequencies match the likelihoods.
  • Exact error probability matches a direct sum.
  • A one-state binary_channel(p, p) matches dit's binary symmetric channel.
  • capacity_gap returns a bracket that contains the binary symmetric channel's gap.
  • Custom symbol maps work.
• Full suite passes against a local checkout of Channel protocol: attach channels with memory to channel codes dit#301 (2189 passed, 11 skipped).
• ruff check / ruff format --check clean.

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