Hex-o-Spell Motor-Imagery Speller (Blankertz et al., 2006)
Measured by Blankertz, Dornhege, Krauledat, Schröder, Williamson, Murray-Smith & Müller · 3rd Int. BCI Workshop, Graz (2006)
Inputs
The measured or assumed values behind the calculations, each with its source.
- rate = 7.6 char/min
- Best demonstrated spelling speed (two subjects, CeBIT 2006); across subjects the range was 2.3–7.6 char/min.
- H = 1.0 bits/char
- English-text entropy (Shannon); the same ~1 bit/char standard applied to QWERTY and every other text entry.
- commands = 2
- The Berlin BCI controlled Hex-o-Spell with just two motor-imagery commands (e.g. right-hand vs foot imagery): one rotates a pointer among six hexagons, the other extends it to select. Two two-step selections spell one letter.
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
≈ 7.6 char/min (best demonstrated; across-subject range 2.3–7.6)
Each letter is two motor-imagery selections in the hexagon menu; the rate is gated by the 2-command channel, not by spatial pointing.
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Bits per character
H(English) ≈ 1.0 bit/char (Shannon)
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Information transfer rate
7.6 char/min × 1.0 bit/char ÷ 60 s/min = 0.127 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
- 30 distinguishable actions
- Prior
- Context-conditioned: likelihoods depend on prior actions
- Notes
- Motor imagery used for TEXT, not cursor pointing: two mental commands drive a hexagonal menu (rotate / select) in which each letter is reached by a two-step selection. Because the output is English text, the reference uses character-entropy (~1 bit/char) like every other text entry; the right comparison is to the other spellers and keyboards, not to a Fitts pointing channel. This is the canonical motor-imagery speller; its low rate reflects the narrow 2-command channel, the same reason its bits/s sit far below the visual-evoked spellers.
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 letter at perfect accuracy
log2(30) ≈ 4.91 bits/letter (each letter reached by a two-step hexagon selection)
The paper gives the net letter rate but not a per-command accuracy, so this is shown at perfect accuracy as a uniform-prior comparison rather than a Wolpaw recomputation.
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Information transfer rate
7.6 letter/min × 4.91 bits/letter ÷ 60 s/min = 0.62 bits/s
Uses log2(N) per letter, while the atlas-ranked text figure uses 1 bit/char for consistency with the other English text entries.
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Achieved-bitrate credit per net-correct letter
N = 30 → log2(N − 1) = log2(29) = 4.86 bits per net-correct letter (field-standard achieved bitrate, e.g. Webgrid; Nuyujukian 2015, which introduced the metric, used log2(N)).
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Net-correct letter rate
The paper reports the net letter rate but no per-command accuracy, so this is a perfect-copy ceiling: net-correct = the full 7.6 letters/min = 0.127 correct/s.
Same N and letter rate as the entry's Wolpaw comparison. With no error data the achieved and Wolpaw ceilings differ only by log2(N − 1) vs log2(N), so both land at 0.62 bits/s. Each letter is a two-step hexagon selection driven by the narrow 2-command channel.
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Achieved bitrate
4.86 bits × 0.127 correct/s = 0.62 bits/s.
Source
- Authors
- Blankertz, Dornhege, Krauledat, Schröder, Williamson, Murray-Smith & Müller
- Publication
- 3rd Int. BCI Workshop, Graz, 2006