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ECoG Speech, 50 words (Moses et al., 2021)

Measured by Moses, Metzger, Liu, Anumanchipalli, Chang et al. · N. Engl. J. Med. 385 (2021)

ECoG Speech invasive 2021

Inputs

The measured or assumed values behind the calculations, each with its source.

N = 50
50-word vocabulary the participant attempted to say (Abstract; Methods)
rate = 15.2 word/min
Median decoding rate (Abstract)
P = 0.744
1 − 25.6% median word error rate, with the natural-language model (Abstract). Without the model, WER was 47.1%.

Strictest ITR

Each scoring method is an upper bound on the channel, so the headline is the strictest (smallest) one for this entry. Use the score selector on the home page to view any single method across entries.

Strictest Wolpaw Recomputed
Wolpaw bitrate over N = 50 words
Uniform-prior selection bound over the 50-word vocabulary
0.858 bits/s

  1. Bits per selection (Wolpaw formula)

    B = log2(N) + P*log2(P) + (1-P)*log2((1-P)/(N-1))
  = log2(50) + 0.744*log2(0.744) + 0.256*log2(0.256/49)
  = 3.386 bits / selection

    Term 1 is the information if every choice were correct; terms 2-3 subtract the bits lost to the error rate, assumed spread evenly over the other N-1 targets.

  2. Selections per second

    T = 3.94737 s/selection  ->  1 / 3.94737 = 0.253 selections/s

  3. Information transfer rate

    ITR = B * selections/s = 3.386 * 0.253 = 0.858 bits/s

What counts as a bit depends on the action space. The number of distinguishable actions and how likely each one is are design choices of the task, not the sensing hardware. The same modality can present a fixed set of targets, a set pruned per step by a grammar or language model, or a continuous control space. Each of these changes how many actions are live and how the probability mass is spread, and therefore the information per selection. Read the action space below before comparing headline numbers across entries.

Action space

What the user can produce at each step, and how those options are distributed.

Structure
Fixed set of targets
Size
50 distinguishable actions
Prior
Context-conditioned: likelihoods depend on prior actions
Notes
A 50-word vocabulary, but decoding ran through a Viterbi/HMM language model over sentence sequences, so successive words are not independent and the effective prior is context-conditioned. Treating the 50 words as an equiprobable set is an idealization.

Comparability The strictest bound here is the Wolpaw selection rate: log₂(N) over the real action set, discounted by accuracy. This fits because the output is a closed command set, not free English, so no language predictor applies. Comparable to the other command-and-control entries; against the text entries it reads high per selection, since a few large choices carry more raw bits than the ~1 bit/character of natural language.

Other bounds considered for the headline

Also valid upper bounds for this entry and eligible to be the headline. They just came out looser than the strictest above. Pick any of these in the home-page score selector.

Shannon (text) Recomputed
Word-entropy throughput
Effective bits actually transmitted as English
0.94 bits/s

  1. Error-corrected words per minute

    (1 − WER) × rate = 0.744 × 15.2 = 11.3 net word/min

  2. Shannon per-word entropy of English

    H ≈ 5.0 bits/word

    Credits only the information in the English produced, independent of vocabulary size.

  3. Information transfer rate

    11.3 word/min × 5.0 bits/word ÷ 60 s/min = 0.94 bits/s

Other score types

Bounds the atlas keeps out of the default strictest headline: as-reported figures, alternate task conditions, or raw-channel ceilings that shouldn't win the headline by default. Each still carries a score type, so the home-page selector ranks this entry on it when you choose that type. Read its derivation before comparing across entries.

Nuyujukian Recomputed
Nuyujukian achieved bitrate over N = 50 words
Achieved-bitrate view of the closed-vocabulary channel, shown for comparison
0.69 bits/s

  1. Achieved-bitrate credit per net-correct word

    N = 50 → log2(N − 1) = log2(49) = 5.61 bits per net-correct selection (field-standard achieved bitrate, e.g. Webgrid; Nuyujukian 2015, which introduced the metric, used log2(N)).

  2. Net-correct word rate

    net-correct = 2P − 1 = 2(0.744) − 1 = 0.488 of words. At 15.2 word/min (3.95 s/word) → 0.488 × 15.2 / 60 = 0.124 correct/s.

    A word error commits the wrong word rather than timing out, so incorrect = 1 − P. Same N (50), word accuracy (74.4%, with language model) and rate (15.2 wpm) as the entry's Wolpaw selection bound. At this comparatively low accuracy the 2P − 1 netting bites hard: achieved (0.69) falls below both the Wolpaw bound (~0.86) and the ranked Shannon figure (0.94) — an error-netting artifact, which is exactly why achieved is never used for ranking.

  3. Achieved bitrate

    5.61 bits × 0.124 correct/s = 0.69 bits/s.

Source

Authors
Moses, Metzger, Liu, Anumanchipalli, Chang et al.
Publication
N. Engl. J. Med. 385, 2021
Paper
10.1056/NEJMoa2027540