Last Updated on June 6, 2026 by John Berry
Whilst I’m inclined only to include here useful theory, such that this site stays practical, Claude Shannon’s formula and its implications are important to aid understanding. There’s no need to follow the maths here. I’ve given conclusions at each point and, more importantly, I’ve added a summary table of data rates and Eb/N0 values. The following about data modes and the Shannon limit is developed from the book, Reference Data for Engineers, Section 25: information and coding. A full citation is given in the bibliography.
Shannon’s formula
The capacity of a communications channel in the presence of additive Gaussian noise (like that in a rig) can be calculated.
C=W log2 (1+S/N).
C is the capacity in bits per second. W (sometimes noted as B) is the channel bandwidth in Hz. And S/N is the signal to noise ratio offered by the channel in decoding.
So this formula relates the ability to get data through a channel to the bandwidth of the channel and the signal to noise ratio available. The wider the channel bandwidth the better, and the more signal power at the decoder for constant noise, the better. That’s logical. We see this in action daily with FT8 and other digital modes.
The theory behind Shannon’s equation can be advanced to relate bit error and Eb/N0 to realise the useful graph below to conclude understanding.
Bit energy and bit error rate
Engineers would measure the performance of a digital communications system by the probability of bit error, or bit error rate (abbreviated to BER). The BER can always be improved by raising the transmitted power. The bit energy Eb is calculated from the message energy and the number of information bits at the input to the encoder/modulator. There may be a large number of extra bits transmitted for error correction or frame synchronisation. Only information bits are used in calculating Eb.
The information bits/second Eb is defined by Eb=S/R where S is the message average (received) power and R is the signalling rate. So the higher order or rate the message is, the lower the Eb; and the more power, the higher the Eb.
In addition to Eb, the receiver also sees the white noise signal. Only the ratio Eb/N0 affects the bit error rate. More signal or less noise improve the BER – it’s the ratio that matters.
Signalling schemes can be compared by comparing their respective graphs of BER versus required Eb/N0.
Fundamental limits
Also important in comparing systems is the spectral bit rate, r, in bits per second per Hertz. r = R/W where R is the signalling rate and W is the channel bandwidth.
As the authors of the book, Reference Data for Engineers note, “The spectral bit rate r and the Eb/N0 are the two most important figures of merit for digital communications systems”.
The fundamental limit for a system is where bandwidth is infinite. This gives the notion that Eb/N0 ≥ loge 2 = 0.69. So, fundamentally Eb/N0 can never be less than -1.6dB. No matter how good the signalling system, things always get worse in a real bandwidth.
The energy can never be less than 1.6dB below the noise (Eb/No = 10log10 (0.69) = -1.6) . Below this and the system fails to decode.
If the bandwidth is larger than the data rate, then one can signal close to the channel capacity using a so-called M-ary signalling alphabet (as in the above graph). Such alphabets allow operation at a very low Eb/N0. The graph above relates BER in the y-axis to the Eb/N0. For a large value M and a low BER, the required Eb/N0 is on the theoretical limit. For an arbitrarily reasonable BER (around 10-3), the necessary Eb/N0 reaches roughly 8dB—about 10dB above the limit.
Practical performance of data modes
On the one hand error rates and Eb/N0 are not of great interest to the radio amateur. So long as there’s enough signal power for the chosen transmission system, all is well. Until, on the other hand, you find FT8 giving partial decodes and Q65 not decoding at all because the signal is below the receiver threshold. Then it’s worth understanding if there is anything that you can do to better make the QSOs.
The answer to that is two-fold:
- Change the signalling system to adopt something less complicated, making it easier for the decoder to do its job.
- Improve the noise performance of the system. A typical example is increasing the signal without unduly increasing the noise by using a low noise pre-amplifier.
The latter approach links directly to other pages here.
To put this all in context, a reference I cite in my presentation on data modes notes that JT65 has a receiver threshold of around -24dB below the 2.4kHz bandwidth threshold. This corresponds to a data rate of 1.54b/s requiring a +5dB Eb/N0 – almost 7dB above (worse than) the theoretic limit.
Summary table
Here’s a table of popular data modes and their corresponding data rate and necessary Eb/N0.
| Mode | Typical Use Case | High Sensitivity | Data Rate (R) [bits/sec] | Eb/N0 [dB] | Enhancement | Primary Bands |
|---|---|---|---|---|---|---|
| CW (12 wpm) | General communication / DX | Moderate (-12 dB S/N) | 4.80 | 13.0 | Operator-dependent DSP | 1.8 MHz – 1300 MHz |
| RTTY (45 baud) | Contesting | Low (-5 dB S/N) | 32.50 | 14.0 | Twin-peak filtering | HF (1.8 – 30 MHz) |
| PSK31 | Keyboard-to-keyboard | Moderate (-10 dB S/N) | 31.25 | 9.0 | Varicode efficiency | HF (1.8 – 30 MHz) |
| FT8 | Weak signal / DXing | High (-21 dB S/N) | 5.95 | 5.2 | LDPC (Forward Error Correction) | 1.8 MHz – 144 MHz |
| FT4 | Weak signal contesting | High (-17.5 dB S/N) | 16.74 | 4.3 | Optimized for rapid exchange | HF / 6m |
| JT65 | EME / Extreme weak signal | Very High (-24 dB S/N) | 1.54 | 5.0 | Deep-search decoding | HF / VHF / UHF |
| Q65 (Submode B) | Ionospheric scatter / EME | Extreme (-26 dB S/N) | 1.10 | 4.4 | Robust against fast fading | 50 MHz – 1300 MHz |
| WSPR | Propagation studies | Extreme (-29 dB S/N) | 0.45 | 5.4 | Narrow-band drift correction | 1.8 MHz – 1300 MHz |
| MSK144 | Meteor Scatter | Low (Burst-dependent) | 250.00 | 12.0 | Short packet redundancy | 28 MHz – 432 MHz |
| FST4 | LF / MF Weak signal | Extreme (-30 dB S/N) | 0.30 | 5.1 | Low-frequency drift tolerance | < 1.8 MHz (630m / 2200m) |
I built this table by commanding Google Gemini AI to do a search of the Web to find the most cited values.
Concluding thoughts
FT4 and Q65 sub-mode B come closest to the theoretical limit and might be considered the ‘best’ data modes overall. See my earlier page on Receiver Threshold for discussion about system signal to noise (S/N) ratios. As is convention, the S/N above is referenced to the 2.4kHz SSB channel bandwidth. But what really matters is for radio amateurs to match data modes with the environment in which they are to be used. For example, despite its low Eb/N0, MSK144 is perfectly suited to the short bursts of meteor scatter. And FT8 performs poorly in anything but steady state channels.
Those proposing new data modes like FT2 should always consider the full characteristics and performance of the mode.