ITR Atlas
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Morse Telegraphy (Morse, 1844)

Measured by Historical records; world record by T. R. McElroy (1939), documented by ARRL · ARRL / amateur-radio historical record (1939)

Manual Telegraph 1844

Inputs

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

rate = 25 wpm
Representative skilled professional copy speed; 30 wpm is not uncommon and experts exceed 40 wpm. The all-time world record is 75.2 wpm (McElroy, 1939). The system date is the first official Morse telegraph message in 1844; the speed benchmark is later operator performance.
H = 1.0 bits/char
English-text entropy (Shannon); Morse encodes ordinary English letters.
N = 36
26 letters + 10 numerals, for the raw-symbol Wolpaw ceiling (uniform prior). The dot/dash code is itself frequency-optimized, so real symbols are not uniform; this is a loose upper bound.
T_char = 0.48 s/char
Gross character interval for the Wolpaw ceiling: 60 / (25 wpm × 5) = 0.48 s. Skilled-operator copy error is not reported, so accuracy is taken as perfect (P=1). This is a strict upper bound.

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
2.08 bits/s

  1. Characters per minute

    25 wpm × 5 chars/word = 125 chars/min

    The skilled-operator copy error rate is not reported in the ARRL/record source; the 25 wpm sustained rate assumes accurate copy.

  2. Bits per character

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

  3. Information transfer rate

    125 char/min × 1.0 bit/char ÷ 60 s/min = 2.08 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
36 distinguishable actions
Prior
Context-conditioned: likelihoods depend on prior actions
Notes
26 letters + 10 numerals (plus punctuation/prosigns), keyed serially as English text. The dot/dash code length is itself frequency-optimized for English, so the prior is context-conditioned, not uniform.

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 symbol set
Uniform-prior, perfect-copy ceiling on the 36-symbol channel
11 bits/s

  1. Bits per selection (Wolpaw formula)

    B = log2(N) + P*log2(P) + (1-P)*log2((1-P)/(N-1))
  = log2(36) + 1*log2(1) + 0*log2(0/35)
  = 5.17 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 = 0.48 s/selection  ->  1 / 0.48 = 2.083 selections/s

  3. Information transfer rate

    ITR = B * selections/s = 5.17 * 2.083 = 10.771 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 symbol set
Achieved-bitrate view of the symbol channel, shown for comparison
11 bits/s

  1. Achieved-bitrate credit per net-correct symbol

    N = 36 symbols → log2(N − 1) = log2(35) = 5.13 bits per net-correct selection (field-standard achieved bitrate, e.g. Webgrid; Nuyujukian 2015, which introduced the metric, used log2(N)).

  2. Net-correct symbol rate

    Skilled-operator copy error is not reported, so this is a perfect-copy ceiling: net-correct = 25 wpm × 5 = 125 char/min = 2.08 correct/s (0.48 s/char).

    Same N (36) and symbol interval (0.48 s) as the entry's perfect-copy Wolpaw ceiling. With no error term the achieved and Wolpaw ceilings differ only by log2(N − 1) vs log2(N), so both land near 10.7 bits/s: the uniform-prior symbol channel, above the 2.08 bits/s Shannon headline.

  3. Achieved bitrate

    5.13 bits × 2.08 correct/s = 10.7 bits/s.

Source

Authors
Historical records; world record by T. R. McElroy (1939), documented by ARRL
Publication
ARRL / amateur-radio historical record, 1939
Paper
http://www.arrl.org/Events/view/15729
Reference
System date: Library of Congress record of Morse's first official telegraph message