Certified Adaptive List Decoding for Error-Correcting Codes

Key points

• We observe that proving a candidate optimal can be far easier than finding it, and build a decoder that does both.1
• We cast decoding as a search over an absorbing-state discrete diffusion model, whose sequential commitment of coordinates turns generation into a tree, and run a probability beam search over it.1
• A dual bound from a linear-programming relaxation and a distance-based test, both derived from the code, then certify per frame that the current candidate is the global ML solution; because both are theorems, certified frames incur no accuracy-computation trade-off.1
• Against an exact ML reference at $5$ dB the decoder is within one standard deviation on three of the four codes where the reference is uncensored, and against four neural baselines it attains the best bit-error rate in $71$ of $75$ cells.1

Sources (1)

• [1]Certified Adaptive List Decoding for Error-Correcting Codes
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 20, 08:03 AM

  Maximum-likelihood (ML) decoding of linear block codes is NP-hard, so neural decoders are evaluated by how closely they approach it.

  We observe that proving a candidate optimal can be far easier than finding it, and build a decoder that does both.

Extractive summary: sentences quoted from the sources.