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Shannon, Beethoven, and the Compact Disc

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Abstract

An audio compact disc (CD) holds up to 74 minutes, 33 seconds of sound, just enough for a complete mono recording of Ludwig von Beethoven's Ninth Symphony ('Alle Menschen werden Brüder') at probably the slowest pace it has ever been played, during the Bayreuther Festspiele in 1951 and conducted by Wilhelm Furtwängler. Each second of music requires about 1.5 million bits, which are represented as tiny pits and lands ranging from 0.9 to 3.3 micrometers in length. More than 19 billion channel bits are recorded as a spiral track of alternating pits and lands over a distance of 5.38 kilometers (3.34 miles), which are scanned at walking speed, 4.27 km per hour. This year it is 25 years ago that Philips and Sony introduced the CD. In this jubilee article I will discuss the various crucial technical decisions made that would determine the technical success or failure of the new medium.
About the author:
Dr. Kees A. Schouhamer Immink worked from 1968 till 1998 at
Philips Research Labs, Eindhoven. In 1998, he founded Turing
Machines Inc, where he currently serves as its CEO and president.
Since 1994, he has been an adjunct professor at the Institute for
Experimental Mathematics, Essen-Duisburg University, Germany,
and a visiting professor at the Data Storage Institute in Singapore.
The photo shows the author (left) with Claude Shannon during
the awards dinner at the Convention of the Audio Engineering
Society (AES) in New York, October 1985, where Shannon
received the AES Gold Medal ‘For contributions that made digital
audio possible’.
Abstract An audio compact disc (CD) holds up to 74 minutes, 33 sec-
onds of sound, just enough for a complete mono recording of Ludwig von
Beethoven's Ninth Symphony (‘Alle Menschen werden Brüder’) at
probably the slowest pace it has ever been played, during the Bayreuther
Festspiele in 1951 and conducted by Wilhelm Furtwängler. Each second
of music requires about 1.5 million
bits, which are represented as tiny
pits and lands ranging from 0.9 to
3.3 micrometers in length. More
than 19 billion channel bits are
recorded as a spiral track of alternating pits and lands over a distance of
5.38 kilometers (3.34 miles), which are scanned at walking speed, 4.27
km per hour.
This year it is 25 years ago that Philips and Sony introduced the CD. In
this jubilee article I will discuss the various crucial technical decisions
made that would determine the technical success or failure of the new
medium.
Shaking the tree
In 1973, I started my work on servo systems and electronics for
the videodisc in the Optics group of Philips Research in
42
recovery of a file possible from reception of data from uncoordinat-
ed senders. Each sender has access to the same piece of data, and
creates an independent fountain for this piece. The receivers then
combine data received from each of the senders. Because the output
symbols have been generated independently at each of the senders,
from the point of view of the receiver the data received may as well
have been generated by one fountain, at the cumulative rate of all
the fountains. Since this way of receiving data is robust against par-
tial or total failure of the senders, this is the method of choice in
applications where there is expectation of such failures.
In other applications, such as IPTV and more generally video trans-
mission over networks, systematic Raptor Codes are used as “tun-
able fixed rate codes.” This means that only a fixed amount of redun-
dancy (or repair data) is generated in a fixed application, this amount
may vary depending on the particular network conditions encoun-
tered. Each instantiation would correspond to a code of a different
rate, but all these codes are generated the same way using the same
Raptor code. This flexibility is a key feature for providing video of
very good quality on networks with widely varying characteristics.
REFERENCES
[1] P. Elias, “Coding for two noisy channels,” in Information
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[4] A. Shokrollahi, S. Lassen, and M. Luby, “Multi-stage code gen-
erator and decoder for communication systems,” June 27, 2006,
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[5] A. Shokrollahi, “Raptor Codes,” IEEE Transactions on
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[6] J. Byers, M. Luby, M. Mitzenmacher, and A. Rege, “A digital
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Decoding of Chain Reaction Codes,” U.S. Patent 6 909 383, June
21, 2005.
IEEE Information Theory Society Newsletter December 2007
Shannon, Beethoven, and the Compact
Disc
Kees A. Schouhamer Immink
Kees A. Schouhamer Immink
with Claude Shannon.
itNL1207.qxd 11/15/07 9:48 AM Page 42
Eindhoven. The videodisc is a 30 cm diameter optical disc that
can store up to 60 minutes of analog FM-modulated video and
sound. It is like a DVD, but much larger, heavier, and less reli-
able. The launch of the videodisc in 1975 was a technical success,
but a monumental marketing failure since the consumers
showed absolutely no interest at all. After two years, Philips
decided to throw in the towel, and they withdrew the product
from the market.
While my colleagues and I were working on the videodisc, two
Philips engineers were asked to develop an audio-only disc
based on optical videodisc technology. The two engineers were
recruited from the audio department, since my research direc-
tor believed a sound-only disc was a trivial matter given a
video and sound videodisc, and he refused to waste costly
researcher’s time. In retrospect, given the long forgotten
videodisc and the CD’s great success, this seems a remarkable
decision.
The audio engineers started by experimenting with an analog
approach using wide-band frequency modulation as in FM radio.
Their experiments revealed that the analog solution was scarcely
more immune to dirt and scratches than a conventional analog LP.
Three years later they decided to look for a digital solution. In
1976, Philips demonstrated the first prototypes of a digital disc
using laser videodisc technology. A year later, Sony completed a
prototype with a 30 cm diameter disc, the same as the videodisc,
and 60 minutes playing time [2].
The Sony/Philips alliance
In October 1979, a crucial high-level decision was made to join
forces in the development of a world audio disc standard.
Philips and Sony, although competitors in many areas, shared
a long history of cooperation, for instance in the joint estab-
lishment of the compact cassette standard in the 1960's. In mar-
keting the final products, however, both firms would compete
against each other again. Philips brought its expertise and the
huge videodisc patent portfolio to the alliance, and Sony con-
tributed its expertise in digital audio technology. In addition,
both firms had a significant presence in the music industry via
CBS/Sony, a joint venture between CBS Inc. and Sony Japan
Records Inc. dating from the late 1960s, and Polygram, a 50%
subsidiary of Philips [4]. Within a few weeks, a joint task force
of experts was formed. As the only electronics engineer within
the ‘Optics’ research group, I participated and dealt with ser-
vos, coding, and electronics at large. In 1979 and 1980, a num-
ber of meetings, alternating between Tokyo and Eindhoven,
were held. The first meeting, in August 1979 in Eindhoven, and
the second meeting, in October 1979 in Tokyo, provided an
opportunity for the engineers to get to know each other and to
learn each other’s main strengths. Both companies had shown
prototypes and it was decided to take the best of both worlds.
During the third technical meeting on December 20, 1979, both
partners wrote down their list of preferred main specifications
for the audio disc. Although there are many other specifica-
tions, such as the dimensions of the pits, disc thickness, diam-
eter of the inner hole, etcetera, these are too technical to be dis-
cussed here.
Item Philips Sony
Sampling rate (kHz) 44.0 - 44.5 44.1
Quantization 14 bit 16 bit
Playing time (min) 60 60
Diameter (mm) 115 100
EC Code t.b.d. t.b.d.
Channel Code M3 t.b.d.
t.b.d. = to be discussed
As can be seen from the list, a lot of work had to be done as the
partners agreed only on one item, namely the one-hour playing
time. The other target parameters, sampling rate, quantization,
and notably disc diameter look very similar, but were worlds
apart.
Shannon-Nyquist sampling theorem
The Shannon-Nyquist sampling theorem dictates that in order to
achieve lossless sampling, the signal should be sampled with a
frequency at least twice the signal’s bandwidth. So for a band-
width of 20 kHz a sampling frequency of at least 40 kHz is
required. A large number of people, especially young people, are
perfectly capable of hearing sounds at frequencies well above 20
kHz. That is, in theory, all we can say. In 1978, each and every
piece of digital audio equipment used its own ‘well-chosen’ sam-
pling frequency ranging from 32 to 50 kHz. Modern digital audio
equipment accepts many different sampling rates, but the CD
task force opted for only one frequency, namely 44.1 kHz. This
sampling frequency was chosen mainly for logistics reasons as
will be discussed later, once we have explained the state-of-the-art
of digital audio recording in 1979.
Towards the end of the 1970s, ‘PCM adapters’ were developed in
Japan, which used ordinary analog video tape recorders as a
means of storing digital audio data, since these were the only
widely available recording devices with sufficient bandwidth.
The best commonly-available video recording format at the time
was the 3/4" U-Matic.
The presence of the PCM video-based adaptors explains the
choice of sampling frequency for the CD, as the number of video
lines, frame rate, and bits per line end up dictating the sampling
frequency one can achieve for storing stereo audio. The sampling
frequencies of 44.1 and 44.056 kHz were the direct result of a need
for compatibility with the NTSC and PAL video formats.
Essentially, since there were no other reliable recording products
available at that time that offered other options in sampling rates,
the Sony/Philips task force could only choose between 44.1 or
44.056 KHz and 16 bits resolution (or less).
During the fourth meeting held in Tokyo from March 18-19, 1980,
Philips accepted (and thus followed Sony’s original proposal) the
16-bit resolution and the 44.1 kHz sampling rate. 44.1 kHz as
opposed to 44.056 kHz was chosen for the simple reason that it
was easier to remember. Philips dropped their wish to use 14 bits
resolution: they had no technical rationale as the wish for the 14
bits was in fact only based on the availability of their 14-bit digi-
tal-analog converter. In summary, Compact Disc sound quality
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44
followed the sound quality of Sony’s PCM-1600 adaptor since
logistically speaking there was no other choice.
Thus, quite remarkably, in recording practice, an audio CD starts
life as a PCM master tape, recorded on a U-Matic videotape cas-
sette, where the audio data is converted to digital information
superimposed within a standard television signal. The industry
standard hardware to do this was the Sony PCM-1600, the first
commercial video-based 16-bit recorder, followed by the PCM-
1610 and PCM-1630 adaptors. Until the 1990s, only video cas-
settes could be used as a means for exchanging digital sound from
the studios to the CD mastering houses. Later, Exabyte computer
tapes, CD-Rs and memory sticks have been used as a transport
vehicle.
Coding systems
Coding techniques form the basis of modern digital transmission
and storage systems. There had been previous practical applica-
tions of coding, especially in space communications, but the
Compact Disc was the first mass-market electronics product
equipped with fully-fledged error correction and channel coding
systems. To gain an idea of the types of errors, random versus
burst errors, burst length distribution and so on, we made discs
that contained known coded sequences. Burst error length distri-
butions were measured for virgin, scratched, or dusty discs. The
error measurement was relatively simple, but scratching or fin-
gerprinting a disc in such a way that it can still be played is far
from easy. How do you get a disc with the right kind of sticky
dust? During playing, most of the dust fell off the disc into the
player, and the optics engineers responsible for the player were
obviously far from happy with our dust experiments. The exper-
imental discs we used were handmade, and not pressed as com-
mercial mass-produced polycarbonate discs. In retrospect, I think
that the channel characterization was a far from adequate instru-
ment for the design of the error correction control (ECC).
There were two competing ECC proposals to be studied.
Experiments in Tokyo and Eindhoven -Japanese dust was not the
same as Dutch dust- were conducted to verify the performance of
the two proposed ECCs. Sony proposed a byte-oriented, rate 3/4,
Cross lnterleaved Reed-Solomon code (CIRC) [6]. Vries of Philips
designed an interleaved convolutional, rate 2/3, code having a
basic unit of information of 3-bit characters [9]. CIRC uses two
short RS codes, namely (32, 28, 5) and (28, 24, 5) RS codes using a
Ramsey-type of interleaver. If a major burst error occurs and the
ECC is overloaded, it is possible to obtain an approximation of an
audio sample by interpolating the neighboring audio samples, so
concealing uncorrectable samples in the audio signal. CIRC has
various nice features to make error concealment possible, so
extending the player's operation range [10].
CIRC showed a much higher performance and code rate (and
thus playing time), although extremely complicated to cast into
silicon at the time. Sony used a 16 kByte RAM for data interleav-
ing, which, then, cost around $50, and added significantly to the
sales price of the player. During the fifth meeting in Eindhoven,
May 1980, the partners agreed on the CIRC error correction code
since our experiments had shown its great resilience against mix-
tures of random and burst errors. The fully correctable burst
length is about 4.000 bits (around 1.5 mm missing data on the
disc). The length of errors that can be concealed is about 12.000
bits (around 7.5 mm). The largest error burst we ever measured
during the many long days of disc channel characterization was
0.1 mm.
We also had to decide on the channel code. This is a vital compo-
nent as it has a great impact on both the playing time and the
quality of ‘disc handling’ or 'playability'. Servo systems follow the
track of alternating pits and lands in three dimensions, namely
radial, focal, and rotational speed. Everyday handling damage,
such as dust, fingerprints, and tiny scratches, not only affects
retrieved data, but also disrupts the servo functions. In worst
cases, the servos may skip tracks or get stuck, and error correction
systems become utterly worthless. A well-designed channel code
will make it possible to remove the major barriers related to these
playability issues.
Both partners proposed some form of (d, k) runlength-limited
(RLL) codes, where d is the minimum number and k is the maxi-
mum number of zeros between consecutive ones. RLL codes had
been widely used in magnetic disk and tape drives, but their appli-
cation to optical recording was a new and challenging task. The
various proposals differed in code rate, runlength parameters d
and k, and the so-called spectral content. The spectral content has
a direct bearing on the playability, and we had to learn how to
trade playability versus the code rate (and thus playing time). In
their prototype, Philips used the propriety M3 channel code, a rate
1
2, d=1, k=5 code, with a well-suppressed spectral content [1]. M3
is a variation on the M2 code, which was developed in the 1970s
by Ampex Inc. for their digital video tape recorder [5]. Sony start-
ed with a rate 1/3, d=5, RLL code, but since our experiments
showed it did not work well, they changed horses halfway, and
proposed a propriety rate 1
2, d=2, k=7 code, a type of code that was
used in an IBM magnetic disk drive. Both Sony codes did not have
spectral suppression, and the engineers had opposing views on
how the servo issue could be solved. Synchronization of signals
with unknown speed read with constant linear velocity (disc rota-
tional speed varies with the radius) was another issue. Little was
known, and every idea had to be tried on the testbed, and this took
time. So that, at the May 1980 meeting, the choice of the channel
code remained open, and ‘more study was needed’. Before contin-
uing with the coding cliffhanger, we take a musical break.
Playing time and Beethoven’s Ninth by
Wilhelm Furtwängler
Playing time and disc diameter are probably the parameters most
visible for consumers. Clearly, these two are related: a 5% increase
in disc diameter yields 10% more disc area, and thus an increase
in playing time of 10%. The Philips’ top made the proposal
regarding the 115mm disc diameter. They argued 'The Compact
Audio Cassette was a great success', and, 'we don't think CD
should be much larger'. The cross diameter of the Compact Audio
Cassette, very popular at that time and also developed by Philips,
is 115 mm. The Philips prototype audio disc and player were
based on this idea, and the Philips team of engineers restated this
view in the list of preferred main parameters. Sony, no doubt with
IEEE Information Theory Society Newsletter December 2007
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portable players in mind, initially preferred a 100 mm disc.
During the May 1980 meeting something very remarkable hap-
pened. The minutes of the May 1980 meeting in Eindhoven liter-
ally reads:
disc diameter: 120 mm,
playing time: 75 minutes,
track pitch: 1.45 µm,
can be achieved with the Philips M3 channel code. However, the
negative points are: large numerical aperture needed which
entails smaller (production) margins, and the Philips’ M3 code
might infringe on Ampex M2.
Both disc diameter and playing time differ significantly from the
preferred values listed during the Tokyo meeting in December
1979. So what happened during the six months? The minutes of
the meetings do not give any clue as to why the changes to play-
ing time and disc diameter were made. According to the Philips’
website with the ‘official’ history: "The playing time was deter-
mined posthumously by Beethoven". The wife of Sony's vice-
president, Norio Ohga, decided that she wanted the composer's
Ninth Symphony to fit on a CD. It was, Sony’s website explains,
Mrs. Ohga's favorite piece of music. The Philips’ website pro-
ceeds:
“The performance by the Berlin Philharmonic, conducted by Herbert
von Karajan, lasted for 66 minutes. Just to be quite sure, a check was
made with Philips’ subsidiary, Polygram, to ascertain what other record-
ings there were. The longest known performance lasted 74 minutes. This
was a mono recording made during the Bayreuther Festspiele in 1951
and conducted by Wilhelm Furtwängler. This therefore became the max-
imum playing time of a CD. A diameter of 120 mm was required for this
playing time”.
Everyday practice is less romantic than the pen of a public rela-
tions guru. At that time, Philips’ subsidiary Polygram –one of the
world's largest distributors of music– had set up a CD disc plant
in Hanover, Germany. This could produce large quantities CDs
with, of course, a diameter of 115mm. Sony did not have such a
facility yet. If Sony had agreed on the 115mm disc, Philips would
have had a significant competitive edge in the music market.
Sony was aware of that, did not like it, and something had to be
done. The result is known.
Channel code continued, EFM
Popular literature, as exemplified in Philips’ website mentioned
above, states that the disc diameter is a direct result of the request-
ed playing time. And that the extra playing time for
Furtwängler’s Ninth subsequently required the change from
115mm to a 120 mm disc (no one mentions Sony’s 100 mm disc
diameter). It suggests that there are no other factors affecting
playing time. Note that in May 1980, when disc diameter and
playing time were agreed, the channel code, a major factor affect-
ing playing time, was not yet settled. In the minutes of the May
1980 meeting, it was remarked that the above (diameter, playing
time, and track pitch) could be achieved with Philips' M3 channel
code. In the mean time, but not mentioned in the minutes of the
May meeting, the author was experimenting with a new channel
code, later coined EFM [3]. EFM, a rate 8/17, d=2, code made it
possible to achieve a 30 percent higher information density than
the Philips' M3. EFM also showed a good resilience against disc
handling damage such as fingerprints, dust, and scratches. Note
that 30 percent efficiency improvement is highly attractive, since,
for example, the increase from 115 to 120 mm only offers a mere10
percent increase in playing time.
A month later, in June 1980, we could not choose the channel
code, and again more study and experiments were needed.
Although experiments had shown the greater information densi-
ty that could be obtained with EFM, it was at first merely rejected
by Sony. At the end of the discussion, which at times was heated,
the Sony people were specifically opposing the complexity of the
EFM decoder, which then required 256 gates. My remark that the
CIRC decoder needed at least half a million gates and that the
extra 256 gates for EFM were irrelevant was jeered at. Then sud-
denly, during the meeting, we received a phone call from the pres-
idents of Sony and Philips, who were meeting in Tokyo. We were
running out of time, they said, and one week for an extra, final,
meeting in Tokyo was all the lads could get. On June 19, 1980 in
Tokyo, Sony agreed to EFM. The 30 percent extra information
density offered by EFM could have been used to reduce the diam-
eter to 115mm or even Sony’s original target diameter100mm,
with, of course, the demanded 74 minutes and 33 seconds for
playing Mrs. Ohga’s favorite Ninth. However such a change was
not considered to be politically feasible, as the powers to be had
decided 120mm. The option to increase the playing time to 97
minutes was not even considered. We decided to improve the pro-
duction margins of player and disc by lowering the information
density by 30 percent: the disc diameter remained 120mm, the
track pitch was increased from 1.45 to 1.6µm, and the user bit
length was increased from 0.5 to 0.6µm. By increasing the bit size
in two dimensions, in a similar vein to large letters being easier to
read, the disc was easier to read, and could be introduced without
too many technical complications.
The maximum playing time of the CD was 74 minutes and 33 sec-
onds, but in practice, however, the maximum playing time was
determined by the playing time of the U-Matic video recorder,
which was 72 minutes. Therefore, rather sadly, Mrs. Ohga’s
favorite Ninth by Furtwängler could not be recorded in full on a
single CD till 1988 (EMI 7698012), when alternative digital trans-
port media became available. On a slightly different note, Jimi
Hendrix's Electric Ladyland featuring a playing time of 75 min-
utes was originally released as a 2 CD set in the early 1980s, but
has been on a single CD since 1997.
The inventor of the CD
The Sony/Philips task force stood on the shoulders of the Philips’
engineers who created the laser videodisc technology in the
1970s. Given the videodisc technology, the task force made choic-
es regarding various mechanical parameters such as disc diame-
ter, pit dimensions, and audio parameters such as sampling rate
and resolution. In addition, two basic patents were filed related to
error correction, CIRC, and channel code, EFM. CIRC, the Reed-
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Solomon ECC format, was completely engineered and developed
by Sony engineers, and EFM was completely created and devel-
oped by the author.
Let us take a look at numbers. The size of the taskforce varied per
meeting, and the average number of attendees listed on the offi-
cial minutes of the joint meetings is twelve. If the persons carry-
ing hierarchical responsibility of the CD project are excluded
(many chiefs, hardly any Indians) then we find a very small group
of engineers who carried the technical responsibility of the
Compact Disc ‘Red Book’ standard.
Philips' corporate public relations department, see The Inventor
of the CD on Philips' website [7], states that the CD was "too com-
plex to be invented by a single individual", and the "Compact
Disc was invented collectively by a large group of people work-
ing as a team". It persuades us to believe that progress is the prod-
uct of institutions, not individuals. Evidently, there were battal-
ions of very capable engineers, who further developed and mar-
keted the CD, and success in the market depended on many other
innovations. For example, the solid-state physicists, who devel-
oped an inexpensive and reliable laser diode, a primary enabling
technology, made CD possible in practice. Credit should also be
given to the persons who designed the transparent Compact Disc
storage case, the ' jewel box', made a clever contribution to the
visual appeal of the CD.
Philips and Sony agreed in a memorandum dated June 1980, that
their contributions to channel and error correction codes are
equal. Sony’s website, however, with their 'official' history is enti-
tled 'Our contributions are equal' [8]. The website proceeds, “We
avoid such comments as, ‘We developed this part and that part’
and to emphasize that the disc's development was a joint effort by
saying, ‘Our contributions are equal’. The leaders of the task force
convinced the engineers to put their companies before individual
achievements.” The myth building even went so far that the
patent applications for both CIRC and EFM were filed with joint
Sony/Philips inventors. Philips receives the lion’s share of the
patent royalty income, which is far from equally shared between
the two partners.
Everything else is gaslight
A favorite expression of audiophiles –particularly during the
early period, when they were comparing both vinyl LP and CD
versions of the same recordings– was: "It is as though a veil has
been lifted from the music". Or, in the words of the famous
Austrian conductor Herbert von Karajan, when he first heard CD
audio: "Everything else is gaslight". Von Karajan was fond of the
gaslight metaphor: he first conducted Der Rosenkavalier in 1956
with the soprano Elisabeth Schwarzkopf. Later, when he revived
the opera in 1983 with Anna Tomowa, he referred to his 1956 cast
as "gaslight", which rather upset Schwarzkopf.
Philips and Sony settled the introduction of the new product to be
on November 1, 1982. The moment the ink of the “Red Book”,
detailing the CD specifications, was dry, the race started, and
hundreds of developers in Japan and the Netherlands were on
their way. Early January 1982 it became clear that Philips was run-
ning behind, the electronics was seriously delayed, and they
asked Sony to postpone the introduction. Sony rejected the delay,
but agreed upon a two-step launch. Sony would first market their
CD players and discs in Japan, where Philips had no market
share, and half a year later, March 1983, the worldwide introduc-
tion would take place by Philips and Sony. Philips Polygram
could supply discs for the Japanese market. This gave Philips
some breathing space for the players, but not enough, as in order
to make the new deadline, the first generation of Philips CD play-
ers was equipped with Sony electronics.
The first CD players cost over $2000, but just two years later it was
possible to buy them for under $350. Five years after the introduc-
tion, sales of CD were higher than vinyl LPs. Yet this was no great
achievement, as in 1980 sales of vinyl records had been declining
for many years although the music industry was all but dead. A
few years later, the Compact Disc had completely replaced the
vinyl LP and cassette tape. Compact Disc technology was ideal for
use as a low-cost, mass-data storage medium, and the CD-ROM
and record-once and re-writable media, CD-R and CD-RW, respec-
tively, were developed. Hundreds of millions of players and more
than two hundred billion CD audio discs were sold.
Further reading
[1] M.G. Carasso, W.J. Kleuters, and J.J Mons, Method of coding
data bits on a recording medium (M3 Code), US Patent 4,410,877,
1983.
[2] T. Doi, T. Itoh, and H. Ogawa, ALong-Play Digital Audio Disk
System, AES Preprint 1442, Brussels, Belgium, March 1979.
[3] K.A.S. Immink and H. Ogawa, Method for Encoding Binary
Data (EFM), US Patent 4,501,000, 1985.
[4] T. Kretschmer and K. Muehlfeld, Co-opetition in Standard-
Setting: The Case of the Compact Disc,
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=618484
[5] J.W. Miller, DC Free encoding for data transmission (M2
Code), US Patent 4,234,897, 1980.
[6] K. Odaka, Y. Sako, I. Iwamoto, T. Doi, and L. Vries, Error cor-
rectable data transmission method (CIRC), US Patent 4,413,340,
1983.
[7] The inventor of the CD, Philips’ historical website:
http://www.research.philips.com/newscenter/dossier/optrec/i
ndex.html
[8] Our contributions are equal, Sony’s historical website:
www.sony.net/Fun/SH/1-20/h2.html
[9] L.B. Vries, The Error Control System of Philips Compact Disc,
AES Preprint 1548, New York, Nov. 1979.
[10] K.A.S. Immink, ''Reed-Solomon Codes and the Compact
Disc'' in S.B. Wicker and V.K. Bhargava, Eds., Reed-Solomon
Codes and Their Applications, IEEE Press, 1994.
IEEE Information Theory Society Newsletter December 2007
itNL1207.qxd 11/15/07 9:48 AM Page 46
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Przeciętnemu użytkownikowi Internet jawi się jako źródło nieprzebranych informacji, licznych udogodnień i aplikacji oraz ogromnych zasobów treści rozrywkowych. Co dzień miliardy ludzi korzysta z dobrodziejstw Internetu, nie zastanawiając się nad tym, że większość z jego zasobów, dostarczanych jako produkty wirtualne, jest nieodpłatna. Wartościowe produkty wirtualne są dostarczane przy cenach zerowych, co stoi w sprzeczności z zasadą gospodarowania. Z ekonomicznego punktu widzenia jest to paradoks. Niniejsza książka jest próbą jego wyjaśnienia na kanwie trzech programów badawczych: ekonomii neoklasycznej, ekonomii kosztów transakcyjnych i teorii wymiany społecznej. Prowadzone tu rozważania mają zarówno charakter praktyczny, ukazując strategie biznesowe przedsiębiorców udostępniających nieodpłatnie produkty wirtualne, jak i teoretyczny, dotyczący możliwości eksplanacyjnych poszczególnych programów badawczych.
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