Checkerboard P300 Speller (Townsend et al., 2010)
Measured by Townsend, LaPallo, Boulay et al. · Clinical Neurophysiology 121(7) (2010)
Inputs
The measured or assumed values behind the calculations, each with its source.
- N = 72
- 8×9 character matrix. The checkerboard paradigm (CBP) reshuffles which items flash together, avoiding the adjacency and double-flash problems of the classic row/column paradigm (RCP).
- rate = 4.4 char/min
- Back-derived from the reported 0.38 bits/s Wolpaw ITR at N=72, 92% accuracy (≈5.28 bits/selection → ~4.4 selections/min); P300 spellers are slow because each selection needs many flash repetitions averaged.
- P = 0.92
- Mean online selection accuracy across 18 subjects with the checkerboard paradigm (vs the row/column paradigm in the same study).
- H = 1.0 bits/char
- English-text entropy (Shannon); the same ~1 bit/char standard applied to QWERTY and every other text entry.
- ITR_reported = 23 bits/s
- Authors' mean Wolpaw bit rate for the checkerboard paradigm (up from 0.32 bits/s for row/column). Counts log2(N) per selection.
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.
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Correct characters per minute
≈ 4.4 selections/min × 0.92 accuracy ≈ 4.0 correct char/min
Each selection emits one character of English; the slow rate is the cost of averaging many P300 flash repetitions per selection.
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Bits per character
H(English) ≈ 1.0 bit/char (Shannon)
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Information transfer rate
4.0 char/min × 1.0 bit/char ÷ 60 s/min = 0.067 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
- 72 distinguishable actions
- Prior
- Context-conditioned: likelihoods depend on prior actions
- Notes
- 8×9 matrix; the decoder classifies which character drew the P300 response (covert attention, no pointing, no cursor), the modern descendant of the 1988 Farwell-Donchin speller. The realized output is English text, so the reference uses character-entropy (~1 bit/char) like every other text entry; the authors' 0.38 bits/s Wolpaw figure assumes a uniform 1-of-72 choice and is kept as a secondary classifier metric. The checkerboard paradigm is a well-cited modern P300 design, useful here as the modern bookend to the 1988 original.
Comparability The strictest bound here is the Shannon entropy of the output text, under one predictor held constant across the whole atlas (≈1 bit per character). That shared predictor makes it directly comparable to every other text entry (keyboards, spellers, silent speech and speech BCIs) regardless of prior or vocabulary size. For most text interfaces it comes out tighter than the raw-selection bounds, but not always. Where a small vocabulary makes Wolpaw tighter, that wins instead. Any Fitts, Wolpaw or log₂(N) figure shown below is another bound on the same channel. Switch the home-page score selector to compare one across entries.
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.
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Bits per selection (Wolpaw formula)
B = log2(N) + P*log2(P) + (1-P)*log2((1-P)/(N-1)) = log2(72) + 0.92*log2(0.92) + 0.08*log2(0.08/71) = 5.276 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.
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Selections per second
T = 13.6 s/selection -> 1 / 13.6 = 0.074 selections/s
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Information transfer rate
ITR = B * selections/s = 5.276 * 0.074 = 0.388 bits/s
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Achieved-bitrate credit per net-correct selection
N = 72 → log2(N − 1) = log2(71) = 6.15 bits per net-correct selection (field-standard achieved bitrate, e.g. Webgrid; Nuyujukian 2015, which introduced the metric, used log2(N)).
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Net-correct selection rate
net-correct = 2P − 1 = 2(0.92) − 1 = 0.84 of selections. At ~4.4 selections/min (13.6 s each) → 0.84 / 13.6 = 0.062 correct/s.
A speller error commits the wrong character rather than timing out, so incorrect = 1 − P. Same N (72), accuracy (92%) and selection time (13.6 s) as the entry's Wolpaw calc. Because a wrong selection commits an error rather than merely timing out, the achieved bitrate nets each mistake against a correct selection (2P − 1); here it lands almost exactly on the authors' 0.38 bits/s Wolpaw figure.
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Achieved bitrate
6.15 bits × 0.062 correct/s = 0.38 bits/s.
Source
- Authors
- Townsend, LaPallo, Boulay et al.
- Publication
- Clinical Neurophysiology 121(7), 2010