Why can so little digital information be stored on a cassette tape?

Question

I had heard that tape is still the best medium for storing large amounts of data. So I figured I can store a relatively large amount of data on a cassette tape. I was thinking of a little project to read/write digital data on a cassette tape from my computer sound card just for the retro feeling. (And perhaps read/write that tape with an Arduino too).

But after reading up about it for a bit it turns out that they can store very small amounts of data. With baud rates varying between 300 to 2400 something between ~200KB to ~1.5MB can be stored on a 90 minute (2x45min) standard cassette tape.

Now I have a lot of problems with understanding why that is.

1- These guys can store 90 minutes of audio. Even if we assume the analog audio quality on them was equivalent of 32Kbps that's about 21MB of data. I have a hard time believing what I listened to was 300bps quality audio.

2- I read about the Kansas City standard and I can't understand why the maximum frequency they're using is 4800Hz yielding a 2400 baud. Tape (according to my internet search) can go up to 15KHz. Why not use 10KHz frequency and achieve higher bauds?

3- Why do all FSK modulations assign a frequency spacing equal to baud rate? In the Kansas example they are using 4800Hz and 2400Hz signals for '1' and '0' bits. In MFSK-16 spacing is equal to baud rate as well.

Why don't they use a MFSK system with a 256-element alphabet? With 20Hz space between each frequency the required bandwidth would be ~5KHZ. We have 10KHz in cassette tape so that should be plenty. Now even if all our symbols were the slowest one (5KHz) we would have 5*8 = 40000 baud. That's 27MB of data. Not too far from the 21MB estimation above.

4- If tape is so bad then how do they store Terabaytes on it?

Answer 1

I had heard that tape is still the best medium for storing large amounts of data.

well, "best" is always a reduction to a single set of optimization parameters (e.g. cost per bit, durability, ...) and isn't ever "universally true".

I can see, for example, that "large" is already a relative term, and for a small office, the optimum solution for backing up "large" amounts of data is a simple hard drive, or a hard drive array.

For a company, backup tapes might be better, depending on how often they need their data back. (Tapes are inherently pretty slow and can't be accessed at "random" points)

So I figured I can store a relatively large amount of data on a cassette tape.

Uh, you might be thinking of a Music Casette, right? Although that's magnetic tape, too, it's definitely not the same tape your first sentence referred to: It's meant to store an analog audio signal with low audible distortion for playback in a least-cost cassette player, not for digital data with low probability of bit error in a computer system.

Also, Music Cassettes are a technology from 1963 (small updates afterwards). Trying to use them for the amounts of data modern computers (even arduinos) deal with sounds like you're complaining your ox cart doesn't do 100 km/h on the autobahn.

But after reading up about it for a bit it turns out that they can store very small amounts of data. With baud rates varying between 300 to 2400 something between ~200KB to ~1.5MB can be stored on a 90 minute (2x45min) standard cassette tape.

Well, so that's a lot of data for when music-cassette-style things were last used with computers (the 1980s).

Also, where do these data rates drop from? That sounds like you're basing your analysis on 1980's technology.

These guys can store 90 minutes of audio. Even if we assume the analog audio quality on them was equivalent of 32Kbps that's about 21MB of data.

32 kb/s of what, exactly? If I play an Opus Voice, Opus Music or MPEG 4 AAC-HE file with a target bitrate of 32 kb/s next to the average audio cassette, I'm not sure the cassette will stand much of a chance, unless you want the "warm audio distortion" that casettes bring – but that's not anything you want to transport digital data.

You must be very careful here, because audio cassette formulations are optimized for specific audio properties. That means your "perceptive" quality has little to do with the "digital data capacity".

I have a hard time believing what I listened to was 300bps quality audio.

again, you're comparing apples to oranges. Just because someone 40 to 50 years ago wrote a 300 bits per second modem that could reconstruct binary data from audio cassette-stored analog signals, doesn't mean 300 bps is the capacity of the music cassette channel.

That's like saying "my Yorkshire Terrier can run 12 km/h on this racetrack, therefore I can't believe you can't have Formula 1 cars doing 350 km/h on it".

I read about the Kansas City standard and I can't understand why the maximum frequency they're using is 4800Hz yielding a 2400 baud. Tape (according to my internet search) can go up to 15KHz. Why not use 10KHz frequency and achieve higher bauds?

Complexity, and low quality of implementation and tapes. I mean, you're literally trying to argue that what was possible in 1975 is representative for what is possible today. That's 45 years in the past, they didn't come anywhere near theoretical limits.

Why do all FSK modulations assign a frequency spacing equal to baud rate?

They don't. Some do. Most modern FSK modulations don't (they're minimum shift keying standards, instead, where you choose the spacing to be half the symbol rate).

In the Kansas example they are using 4800Hz and 2400Hz signals for '1' and '0' bits. In MFSK-16 spacing is equal to baud rate as well.

Again, 1975 != all things possible today.

Why don't they use a MFSK system with a 256-element alphabet? With 20Hz space between each frequency the required bandwidth would be ~5KHZ. We have 10KHz in cassette tape so that should be plenty. Now even if all our symbols were the slowest one (5KHz) we would have 5*8 = 40000 baud. That's 27MB of data. Not too far from the 21MB estimation above.

Well, it's not that simple, because your system isn't free from noise and distortion, but as before:

1975. Low cost.

They simply didn't.

If tape is so bad then how do they store Terabaytes on it?

You're comparing completely different types of tapes, and tape drives:

This 100€ LTO-8 data backup tape

vs this cassette tape type, of which child me remembers buying 5-packs at the supermarket for 9.99 DM, which, given retail overhead, probably means the individual cassette was in the < 1 DM range for business customers:

and this 2500€ tape drive stuffed with bleeding edge technology and a metric farkton of error-correction code and other fancy digital technology

vs this 9€ casette thing that is a 1990's least-cost design using components available since the 1970s, which is actually currently being cleared from Conrad's stock because it's so obsolete:

At the end of the 1980s, digital audio became the "obvious next thing", and that was the time the DAT cassette was born, optimized for digital audio storage:

These things, with pretty "old-schooley" technology (by 2020 standards) do 1.3 Gb/s when used as data cassettes (that technology was called DDS but soon parted from the audio recording standards). Anyway, that already totally breaks with the operating principles of the analog audio cassette as you're working with:

• in the audio cassette, the read head is fixed, and thus, the bandwidth of the signal is naturally limited by the product of spatial resolution of the magnetic material and the head and the tape speed. There's electronic limits to the first factor, and very mechanical ones to the second (can't shoot a delicate tape at supersonic speeds through a machine standing in your living room that's still affordable, can you).
• in DAT, the reading head is mounted on a rotating drum, mounted at a slant to the tape – that way, the speed of the head relative to the tape can be greatly increased, and thus, you get more data onto the same length of tape, at very moderate tape speeds (audio cassete: ~47 mm/s, DAT: ~9 mm/s)
• DAT is a digital format by design. This means zero focus was put into making the amplitude response "sound nice despite all imperfections"; instead, extensive error correction was applied (if one is to believe this source, concatenated Reed-Solomon codes of an overall rate of 0.71) and 8b-10b line coding (incorporating further overhead, that should put us at an effective rate of 0.5).

Note how they do line coding on the medium: This is bits-to-tape, directly. Clearly, this leaves room for capacity increases, if one was to use the tape as the analog medium it actually is, and combined that ability with the density-enabling diagonal recording, to use the tape more like an analog noisy channel (and a slightly nonlinear at that) than a perfect 0/1 storage.

Then, you'd not need the 8b-10b line coding. Also, while re-designing the storage, you'd drop the concatenated RS channel code (that's an interesting choice, sadly I couldn't find anything on why they chose to concatenate two RS codes) and directly go for much larger codes – since a tape isn't random access, an LDPC code (a typically 10000s of bits large code) would probably be the modern choice. You'd incorporate neighbor-interference cancellation and pilots to track system changes during playback.

In essence, you'd build something that is closer to a modern hard drive on a different substrate than it would be to an audio cassette; and lo and behold, suddenly you have a very complex device that doesn't resemble your old-timey audio cassette player at all, but a the modern backup tape drive like I've linked to above.

Answer 2

High-capacity tape formats use helical scanning. Here I look at why that gives a higher capacity than linear recording with four tracks (one stereo track on each side) like in a compact cassette (C-cassette).

Figure 1. Stereo C-cassette player/recorder linear head (left) and a helical scanning head from a data drive (right), same scale. There is a too-short-to-see gap between two polished surfaces of laminated magnetic cores that concentrate the magnetic fields to the inside of the coils and to a thin line on the coated surface of the tape. In case of linear scanning, the head gap is oriented straight across the tape.

Figure 2. A simplified illustration of the tracks on a four-track tape (left) and helical scanning tape (right). In reality there needs to be some space, "guard bands", between the linear scanning tracks to prevent leakage between the channels. In case of helical scanning this need is typically circumvented by having heads that read/write consecutive tracks in different gap angles. This way the magnetizations will be approximately orthogonal and not sensed by the wrong head.

It's not about the speed at which the recording head travels. It is possible to slow things down and record the same spatial wavelengths, only it would take a longer time to do that or to read the recording later. Recording faster does not increase tape capacity. What it does is it gives a higher data rate which is important for practical applications. Also, for analog recording, a high head travel speed may be needed because the analog signal has a high bandwidth. Very small spatial wavelengths are difficult to record because of the magnetic grain size on the tape and because of mechanical design considerations.

For information density, it doesn't matter what the angle of the tracks on the tape is. So for a simplified analysis we can rotate the helical scanning tracks to be horizontal, and we can look at just a 1/4 of the tape and consider that as a single-track tape in case of the C-cassette:

Figure 3. One-track linear recording tape (left) and an n-track linear recording tape (right).

Let's write a spatial version of the Shannon–Hartley theorem that suits our simplified analysis:

$$C = nB \log_2 \left( 1+\frac{S}{nN} \right)\tag{1}$$

Here $C$ is the total capacity (bits/m of tape), $n$ is the number of tracks, $B$ is the spatial bandwidth (1/m) and $S/N$ is the reference signal-to-noise ratio, the ratio between signal power and noise power in the reference case that there is just a single track. If we increase from the reference case the number of tracks by a factor $n$, then the track width decreases to $1/n$ times that in the reference case, giving an effective signal-to-noise ratio of $\frac{S}{nN}$ for each track. This comes from that the signal power gets divided by a factor $n^2$ and the noise power gets divided by a factor $n$. This is because each of the $n$ individual channels has the same signal power as would each of $n$ identical-signal channels that sum to the single full-width track, and because the noise is independent between the $n$ tracks so the power of the noise in the full-width track equals the sum of the powers of the noises in the $n$ tracks. So the signal-to-noise ratio goes down as the number of tracks is increased. But at the same time, the total capacity will be the sum of the individual track capacities, hence the factor $n$ in front of the formula.

If we plot the capacity calculated by Eq. 1 as function of the number of channels, it would appear that we can increase the capacity indefinitely by just increasing the number of tracks:

Figure 4. Proportional total capacity as function of the number of tracks, for an out-of-the-hat signal-to-noise ratio of 50 dB in case of a single track. Calculated using Eq. 1.

The main thing that is wrong with this analysis is that the size of the magnetic grains is not truthfully infinitesimally small, so there will be all kinds of unaccounted for trouble (correlated noise between tracks, leakage, and noise being far from Gaussian assumed by Eq. 1) if the tracks become too narrow and densely spaced. But the result still holds up to some limit, that more and narrower tracks can store more information even when each has a lower signal-to-noise ratio than would a single, or four, tracks. So it is not just that we wouldn't have come up with the right modulation scheme for C-cassettes. The design of data tape formats with helical scanning really is superior in terms of information capacity expressed per tape length, for the same width of tape.

John C. Mallinson, The Foundations of Magnetic Recording, 2nd edition 1993, Academic Press, USA, p. 129, gives a result identical to Eq. 1, and also postulates a limit:

9.8 Ultimate Information Areal Capacity

Consider a tape of unit width, divided, without guardbands between the tracks, into $M$ parallel tracks as shown in Figure 9.9. Clearly, the combined Shannon areal capacity is

$$C(M) = MB\log_2\left(1 + \frac{(\text{SNR})_w}{M}\right),\tag{9.13}$$

where $(\text{SNR})_w$ is the wide-band signal-to-noise ratio when the full tape width is used for a single track ($M = 1$). For unit head–tape relative speed, the bandwidth $B$ is the reciprocal of the minimum wavelength, $\lambda_\text{min}$. It is obvious from this expression that the areal capacity increases as $M$ increases. The ultimate storage capacity, in bits per unit area, occurs when the number of tracks becomes very large, and it is

$$\text{ultimate areal capacity} = \frac{nf^2\lambda_\text{min}}{2\pi\log_2e}.\tag{9.14}$$

For the instrumentation recorders considered in this chapter ($n=10^{15}$ particles per cubic centimeter, $f = 0.2$, and $\lambda_\text{min} = 60 \mu\text{in.}$), the ultimate capacity is, amazingly enough, $10^9$ bits per square centimeter or 6000 megabits per square inch. This is an extremely high areal density in comparison with present achievements in digital recording, where figures in the range of 50–150 megabits per square inch are the norm.

Answer 3

You have already selected your answer, but I would like to put a few more lines.

First of all, objecting to Marcus, I think that your first assumption is correct! We can store one hour of almost CD quality (14-16-bits, 44100Hz, stereo) analog audio into these commercial music casettes; i.e magnetic reels. So on a very rough basis you have almost a 600 MB (Mega Bytes) of data capacity there??

Of course, magnetic mediums have different uses, types and qualities. And I think, one thing to mention at the beginning is that, the commercial casette have a tendency of losing its quality. This is especially true with music recording, where high-fidelity is lost after a few playbacks. Such an untrustable characteristic makes them a bad choice for reliable data storage at high rates. Hence possibly lowering their available capacity, in exchange of increased reliability and durability.

But the oppsite is also true: for example, IBM has developed the hard disc drive technology (very high density digital storage) based on magnetic recording too. Their circular shaped magnetic plates make it possible for random access with the help of a moving read-write head mechanism. Packing together a dozen of such magnetic disks and very sensitively controlling the head mechanism in between the plates, provided one of the most important and successful inventions of the computer industry. Even today HDD dominates, and SSD is still expensive, or Cloud is very unconvenient.

You have to be careful about the medium's physical characteristics, and which way you want to store data. The commercial audio cassette system (magnetic tape, and read-write circuitry together) had a bandwidth $B$ of about less than 20 kHz. And I guess its SNR is about less than 60 dB. This can be an under or over estimation, but if you consider what I've said at the beginning; CD-quality audio, now to be honest, commercial audio cassettes do not provide CD-quality audio, (low-noise metal cassettes with Dolby Type-S noise reduction is said to have achieved a CD quality though), as there is some characteristic high frequency hiss noise in those commercial cassettes, especially on the lower quality tapes. Therefore I will take 60 dB as an average estimate. Also note that this SNR depends on the frequency, as the noise increase by frequency, but I will ignore it too.

The (Shannon) capacity $C$ (in bits per second) of the medium is therefore: $$ 60 = SNR_{dB} = 10 \text{log}_{10}( snr ) \implies snr = 10^6 $$ $$ C = B \times \text{log}_2( snr +1) = 20 k \times 19.9 \approx 400 ~ kbps $$

And assuming a two channel stereo recording this yields about $800 ~kbps$ channel capacity. Indeed, considering that CD had a much better SNR about 96dB, it has a channel capcity of $1.411$ Mbps. Then the commercial audio casette had an equivalent data rate about half of the CD medium. In one hour this makes about $360$ MB (Mega Bytes) of data , as an optimistic upperbound, as the comments indicated.

The capacity is there, but can you utilize it?

The audio CD, for example, uses a very small tiny pattern on the circular track lines. The bits are placed as very short and very thin reflective vs non-reflective sections along the track lines that spiral from the innermost circle to the outermost, just like in Vinyl. There is no noise, but distortion due to optical reflection, diffraction, refraction, and mechanical disturbances, which limit the resolution at which you can write or read those tiny dots on the circular tracks.

But magnetic medium is totally different. You store an electric signal (a magnetic one) into it. And you have noise. But you have an advantage over the CD. The CD medium has only one amplitude level indicated by a reflection or no reflection. This is due to the specific mechanism used to write and read the bits. But the magnetic medium can provide multiple bits per symbol to be written, as multiple amplitude levels can (in principle) be supported.

This kind of M-ary encoding is very well utilized in Satellite communication, where 256-QAM is used to take advantage of (relativlely) low noise transmission channel.

Coming to that Kansas City Standards, it's not about the magnetic medium capacity, but about the commercial phone line allowed channel capacity which was quite limited to about $3-4$ kHz back then...

So the conclusion is; if you can afford a suitable encoding technique, in principle, you can store about less than 360 MB of data into a standard commercial auido cassette. There are low noise (high SNR) casette types (such as Cr or Metal) available which would increase the capacity. Or at least you can roll a longer reel to increase it. Whether you can accomplish this or not is another practical concern though...

Answer 4

Typical cheap cassette tape recorders and players in the 1970's used audio circuitry that did not have a completely flat frequency response and added a lot of phase distortion (mostly inaudible to most consumers). In addition, the computers did not use high sample rate low quantization DACS and ADCs (which cost a fortune back then), sometimes only a simple 1-bit digital output and comparator input between the PC and tape drive, or similar low complexity analog circuitry. DSP processing power was limited to in the neighborhood of 1 to 5 kiloflops.

Thus the older hobbiest/consumer computer tape modulation formats were designed to be reasonably robust for users of the poor signal channels designed into those cheap cassette tape recorders, and for slow DSP engines. Even so, I had a few cheap tape recorders that distorted the audio signal too much to reliably record and reproduce data at 1200 baud into a 2 MHz Z80 system.

The signal channels in those cabinet sized IBM 2400 series 9 track vacuum reel-to-reel tape drives were designed from the ground up for the bandwidths required. Not just for consumer audio.

Answer 5

Despite the title of the question, a 2018 IEEE Spectrum article explains: Why the Future of Data Storage is (Still) Magnetic Tape Disk drives are reaching their limits, but magnetic tape just gets better and better. Indeed, capacity records are regularly broken, one of the latest being published in 201 Gb/in2 Recording Areal Density on Sputtered Magnetic Tape. From the initial 2 megabytes stored on tapes (IBM first commercial tape product: 726 Magnetic Tape Unit, announced more than 60 years ago), the recent announcements (IBM and Sony stuff 330 TB on a tiny tape) over 10+ years are summarized below:

• 2006: size 8 TB; density 6.67 billion bytes per square inch
• 2010: size 35 TB; density 29.5 billion bytes per square inch
• 2014: size 154 TB; density 85.9 billion bytes per square inch
• 2015: size 220 TB; density 123 billion bytes per square inch
• 2017: size 330 TB; density 201 billion bytes per square inch

Those are still research, non commercial, with different media technologies: sputtered tape versus Barium ferrite (BaFe) for commercial tapes up to 15 terabytes. In August 2020, Fujifilm point[ed] to 400TB tape cartridge on the horizon, with a density of 224Gbit/in² using Strontium Ferrite (SrFe). Such performance can be improved further by deduplication and lossless compression (the latter being often disappointing in practice, with less than 2:1 ratios). Far future competitors may be DNA storage or cristal etching (see Will Magnetic Storage Ever Become Completely Obsolete?).

In my workplace, with huge datasets, tapes are still in use for long term backup. Namely, one often uses Data8, a 8 mm Backup Format pionnered by Exabyte corporation.

Some more history on tape formats: Much Ado About Exabyte/8mm Tape Drives.

Answer 6

Because the appliances like Betamax Spool at synchronized time frames.