ITR Atlas
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Tap Strap Wearable Keyboard (Tap Systems, 2018)

Measured by Tu, Jeyachandra, Nagesh, Prabhu & Starner · ISWC '21 Adjunct (2021)

Touch Chord keyboard 2018

Inputs

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

rate = 22.11 wpm
Average final typing rate measured by Tu et al. 2021 in a controlled Tap Strap text-entry study using standard MacKenzie-Soukoreff phrases.
P = 0.9102
Final letter accuracy reported by Tu et al. 2021: 91.02%.
H = 1.0 bits/char
English-text entropy (Shannon).
N = 30
Output alphabet size for the raw-character Wolpaw ceiling (uniform prior). Characters are tap chords, but the produced set is the same ~30-symbol alphabet.
T_char = 0.5428 s/char
Gross character interval for the Wolpaw ceiling: 60 / (22.11 wpm × 5) = 0.5428 s.

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 Shannon (text) Recomputed
Character-entropy throughput
Net of English redundancy and measured letter accuracy
1.68 bits/s

  1. Characters per minute

    22.11 wpm × 5 chars/word = 110.55 char/min

    Tu et al. report the final average Tap Strap typing rate after practice.

  2. Discount by measured letter accuracy

    110.55 × 0.9102 ≈ 100.6 correct char/min

    Tu et al. report final letter accuracy of 91.02%; applying it separately gives a stricter realized-output estimate.

  3. Bits per character

    H(English) ≈ 1.0 bit/char (Shannon)

  4. Information transfer rate

    100.6 char/min × 1.0 bit/char ÷ 60 s/min = 1.68 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
A finger-worn band that detects taps of each finger against any surface; characters are tap combinations (chords), like a Twiddler without a physical keypad. Same ~30-symbol English alphabet, counted at Shannon entropy. The reference now uses the measured Tu et al. text-entry rate rather than Tap's vendor training claim.

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 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.

Wolpaw Recomputed
Wolpaw bitrate over the raw character set
Uniform-prior ceiling on the character channel, before English redundancy
7.43 bits/s

  1. Bits per selection (Wolpaw formula)

    B = log2(N) + P*log2(P) + (1-P)*log2((1-P)/(N-1))
  = log2(30) + 0.9102*log2(0.9102) + 0.0898*log2(0.0898/29)
  = 4.035 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 = 0.5428 s/selection  ->  1 / 0.5428 = 1.842 selections/s

  3. Information transfer rate

    ITR = B * selections/s = 4.035 * 1.842 = 7.433 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 the raw character set
Achieved-bitrate view of the character channel, shown for comparison
7.34 bits/s

  1. Achieved-bitrate credit per net-correct character

    N = 30 → log2(N − 1) = log2(29) = 4.86 bits per net-correct selection (field-standard achieved bitrate, e.g. Webgrid; Nuyujukian 2015, which introduced the metric, used log2(N)).

  2. Net-correct character rate

    net-correct = 2P − 1 = 2(0.9102) − 1 = 0.820 of characters. At 0.5428 s/char → 0.820 / 0.5428 = 1.51 correct/s.

    A chord error commits the wrong character rather than timing out, so incorrect = 1 − P. Same N (30), measured letter accuracy (91.02%) and character interval (0.5428 s) as the entry's raw-character Wolpaw ceiling; netting each wrong chord against a correct one (2P − 1) lands just under the ~7.4 bits/s Wolpaw figure. Both are the uniform-prior character channel, above the 1.68 bits/s Shannon headline.

  3. Achieved bitrate

    4.86 bits × 1.51 correct/s = 7.34 bits/s.

Source

Authors
Tu, Jeyachandra, Nagesh, Prabhu & Starner
Publication
ISWC '21 Adjunct, 2021
Paper
10.1145/3460421.3480428
Reference
System date: Tap press kit listing shipping since February 2018
Reference
Mrazek et al. 2021/2022: independent Tap Strap 2 usability and accuracy evaluation (not the speed source)