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Binary Erasure Channel
A binary erasure channel (or BEC) is a common communications channel model used
in coding theory and information theory. In this model, a transmitter sends a bit (a zero or
a one), and the receiver either receives the bit or it receives a message that the bit was not
received ("erased"). This channel is used frequently in information theory because it isone of the simplest channels to analyze. The BEC was introduced by Peter Elias of MIT
in 1954 as a toy example.
Closely related to the binary erasure channel is the packet erasure channel which shares
many similar theoretical results with the binary erasure channel
Description
The BEC is a binary channel ; that is, it can transmit only one of two symbols (usually
called 0 and 1). (A non-binary channel would be capable of transmitting more than twosymbols, possibly even an infinite number of choices.) The channel is not perfect and
sometimes the bit gets "erased"; that is, the bit gets scrambled so the receiver has no idea
what the bit was.
The BEC is, in a sense, error-free. Unlike the binary symmetric channel, when the
receiver gets a bit, it is 100% certain that the bit is correct. The only confusion arises
when the bit is erased.
This channel is often used by theorists because it is one of the simplest noisy channels to
analyze. Many problems in communication theory can be reduced to a BEC.
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Dolby AC3
Dolby Digital is the name for audio compression technologies developed by Dolby
Laboratories. It was originally called Dolby Stereo Digital until 1994. Except for Dolby
TrueHD, the audio compression is lossy. The first use of Dolby Digital was to provide
digital sound in cinemas from 35mm film prints. It is now also used for other applications
such as HDTV broadcast, DVDs, Blu-ray discs and game consoles.
Batman Returns was the first film to use Dolby Digital technology when it premiered in
theaters in Summer 1992. Dolby Digital cinema soundtracks are optically recorded on a
35 mm release print using sequential data blocks placed between every perforation hole
on the sound track side of the film. A constant bit rate of 320kbit/s is used. A CCD
scanner in the projector picks up a scanned video image of this area, and a processor
correlates the image area and extracts the digital data as an AC-3 bitstream. This data is
finally decoded into a 5.1 channel audio source. All film prints with Dolby Digital data
also have Dolby Stereo analogue soundtracks using Dolby SR noise reduction and such
prints are known as Dolby SR-D prints. The analogue soundtrack provides a fall-back
option in case of damage to the digital data or failure of the digital decoding, it also
provides compatibility with projectors not equipped with digital soundheads. Almost all
current release cinema prints are of this type and will probably also include SDDS data
and a time code track to synchronize CD-ROMs carrying DTS soundtracks.
A Dolby Digital 'Penthouse' Soundhead mounted on a mid-'50s vintage Kalee model 20
projector
A photo of a 35 mm film print featuring all four audio formats (or "quad track")- from
left to right: SDDS (blue area to the left of the sprocket holes), Dolby Digital (grey area
between the sprocket holes labelled with the Dolby "Double-D" logo in the middle),
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analog optical sound (the two white lines to the right of the sprocket holes), and the DTS
time code (the dashed line to the far right.)
The simplest way of converting existing projectors is to add a so-called "penthouse"
digital sound head above the projector head. However for new projectors it made sense to
use dual analogue/digital sound heads in the normal optical sound head position under the
projector head. To allow for the dual-sound head arrangement the digital data is recorded
26 frames ahead of the picture. If a penthouse sound head is used then the data must be
delayed in the processor for the required amount of time, around 2 seconds. This delay
can be adjusted in steps of the time between perforations, (approximately 10.4msec)
Dolby Digital
Dolby Digital is the common version containing up to six discrete channels of sound. The
most elaborate mode in common usage involves five channels for normal-range speakers
(20 Hz – 20,000 Hz) (right front, center, left front, rear right, rear left) and one channel
(20 Hz – 120 Hz allotted audio) for the subwoofer driven low-frequency effects. Mono
and stereo modes are also supported. AC-3 supports audio sample-rates up to 48 kHz.
The Laserdisc version of Clear and Present Danger featured the first Home theater
Dolby Digital mix in 1995.
This format has different names:
Dolby Digital DD (an abbreviation for Dolby Digital, often combined with channel count; for
instance, DD 2.0, DD 5.1)
AC-3 (Audio Codec 3, Advanced Codec 3, Acoustic Coder 3. These are
backronyms. However, Adaptive Transform Acoustic Coding 3, or ATRAC3, is a
separate format developed by Sony)[10]
ATSC A/52 (name of the standard)
Applications
Dolby Digital audio is used on DVD-Video and other purely digital media, like
home cinema. In this format, the AC-3 bitstream is interleaved with the video and
control bitstreams.
The system is used in bandwidth-limited applications other than DVD-Video, such
as digital TV. The AC-3 standard allows a maximum coded bit rate of 640 kbit/s.
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Thirty-five millimeter film prints use a fixed rate of 320 kbit/s, which is the same
as the maximum bit rate for 2-channel MP3. DVD-Video discs are limited to
448 kbit/s, although many players can successfully play higher-rate bitstreams
(which are non-compliant with the DVD specification). HD DVD limits AC-3 to
448 kbit/s. ATSC and digital cable standards limit AC-3 to 448 kbit/s. Blu-rayDisc, the PlayStation 3 and the Xbox game console can output an AC-3 signal at a
full 640 kbit/s. Some Sony PlayStation 2 console games are able to output AC-3
standard audio as well, mostly during pre-rendered cutscenes though.
Dolby is part of a group of organizations involved in the development of AAC
(Advanced Audio Coding), part of MPEG specifications, and considered the
successor to MP3. AAC outperforms MP3 at any bitrate, but is more complex.
MASKING
Simultaneous masking
Simultaneous masking is when a sound is made inaudible by a "masker", a noise or
unwanted sound of the same duration as the original sound.
Critical bandwidth
If two sounds of two different frequencies (pitches) are played at the same time, two
separate sounds can often be heard rather than a combination tone. This is otherwise
known as frequency resolution or frequency selectivity. This is thought to occur due to
filtering within the cochlea, also known as critical bandwidths, in the hearing organ in the
inner ear. A complex sound is split into different frequency components and these
components cause a peak in the pattern of vibration at a specific place on the cilia inside
the basilar membrane within the cochlea. These components are then coded
independently on the auditory nerve which transmits sound information to the brain. This
individual coding only occurs if the frequency components are different enough in
frequency, otherwise they are coded at the same place and are perceived as one sound
instead of two.
The filters that distinguish one sound from another are called auditory filters or listening
channels, or also critical bandwidths. It is thought that they line up along the basilar
membrane and when a sound wave excites the cilia it detects the perceived frequency and
filters it into the appropriate critical band depending on whether it is a high low or mid
frequency. Frequency resolution occurs on the basilar membrane due to the listener
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choosing a filter which is centered over the frequency they expect to hear, the signal
frequency. A sharply tuned filter has good frequency resolution as it allows the centre
frequencies through but not other frequencies (Pickles 1982). Damage to the cochlea and
the outer hair cells in the cochlea can impair the ability to tell sounds apart (Moore 1986).
This explains why someone with a hearing loss due to cochlea damage would have moredifficulty than a normal hearing person in distinguishing between different consonants in
speech.
Masking illustrates the limits of frequency selectivity. If a signal is masked by a masker
with a different frequency to the signal then the auditory system was unable to distinguish
between the two frequencies. By experimenting with conditions where one sound can
mask a previously heard signal, the frequency selectivity of the auditory system can be
tested
Effect of frequency on masking patterns
Similar frequencies
How effective the masker is at raising the threshold of the signal depends on the
frequency of the signal and the frequency of the masker. The graphs in figure B are a
series of masking patterns, also known as masking audiograms. Each graph shows the
amount of masking produced at each masker frequency shown at the top corner, 250,
500, 1000 and 2000 Hz. For example, in the first graph the masker is presented at a
frequency of 250 Hz at the same time as the signal. The amount the masker increases the
threshold of the signal is plotted and this is repeated for different signal frequencies,
shown on the X axis. The frequency of the masker is kept constant. The masking effect is
shown in each graph at various masker sound levels.
figure B - Adapted from Ehmer
Figure B shows along the Y axis the amount of masking. The greatest masking is when
the masker and the signal are the same frequency and this decreases as the signal
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frequency moves further away from the masker frequency. This phenomenon is called
on-frequency masking and occurs because the masker and signal are within the same
auditory filter (figure C). This means that the listener cannot distinguish between them
and they are perceived as one sound with the quieter sound masked by the louder one
(figure D).
figure C - Adapted from Gelfand 2004
figure D- Adapted from Gelfand 2004
The amount the masker raises the threshold of the signal is much less in off frequency
masking, but it does have some masking effect because some of the masker overlaps into
the auditory filter of the signal (figure E)
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figure E - adapted from Moore 1998
Off frequency masking requires the level of the masker to be greater in order to have a
masking effect; this is shown in figure F.
figure F - adapted from Moore 1998
This is because only a certain amount of the masker overlaps into the auditory filter of the
signal and more masker is needed to cover the signal.
Lower frequencies
The masking pattern changes depending on the frequency of the masker and the intensity
(figure B). For low levels on the 1000 Hz graph, such as the 20-40 dB range, the curve is
relatively parallel. As the masker intensity increases the curves separate, especially for
signals at a frequency higher than the masker. This shows that there is a spread of the
masking effect upward in frequency as the intensity of the masker is increased. The curve
is much shallower in the high frequencies than in the low frequencies. This flattening is
called upward spread of masking and is why an interfering sound masks high frequency
signals much better than low frequency signals.
Figure B also shows that as the masker frequency increases, the masking patterns become
increasingly compressed. This demonstrates that high frequency maskers are only
effective over a narrow range of frequencies, close to the masker frequency. Low
frequency maskers on the other hand are effective over a wide frequency range.
Fletcher carried out an experiment to discover how much of a band of noise contributes
to the masking of a tone. In the experiment, a fixed tone signal had various bandwidths of
noise centred on it. The masked threshold was recorded for each bandwidth. His research
showed that there is a critical bandwidth of noise which causes the maximum masking
effect and energy outside that band does not affect the masking. This can be explained by
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the auditory system having an auditory filter which is centred over the frequency of the
tone. The bandwidth of the masker that is within this auditory filter effectively masks the
tone but the masker outside of the filter has no ffect (figure G.)
This is used in MP3 files to reduce the size of audio files. Parts of the signals which are
outside the critical bandwidth are cut out leaving only the parts of the signals which are
perceived by the listenerAnother application of auditory masking in everyday situations
is the cocktail party effect.
Effects of intensity
Varying intensity levels can also have an effect on masking. The lower end of the filter
becomes flatter with increasing decibel level, whereas the higher end becomes slightlysteeper (Moore 1998). Changes in slope of the high frequency side of the filter with
intensity are less consistent than they are at low frequencies. At the medium frequencies
(1 – 4 kHz) the slope increases as intensity increases, but at the low frequencies there is no
clear inclination with level and the filters at high centre frequencies show a small
decrease in slope with increasing level. The sharpness of the filter depends on the input
level and not the output level to the filter. The lower side of the auditory filter also
broadens with increasing level. These observations are illustrated in figure H.
figure H - adapted from Moore 1998
Other masking conditions
Ipsilateral masking ("same side") is not the only condition where masking takes place.
Another situation where masking occurs is called contralateral ("other side")
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simultaneous masking. In this case, the instance where the signal might be audible in one
ear but is deliberately taken away by applying a masker to the other ear.
The last situation where masking occurs central masking. This refers to the case where a
masker causes a threshold elevation. This can be in the absence of, or in addition to,
another effect and is due to interactions within the central nervous system between the
separate neural inputs obtained from the masker and the signal.
Effects of different stimulus types
Experiments have been carried out to see the different masking effects when using a
masker which is either in the form of a narrow band noise or a sinusoidal tone.
When a sinusoidal signal and a sinusoidal masker (tone) are presented simultaneously the
envelope of the combined stimulus fluctuates in a regular pattern described as beats. Thedifference between the frequencies of the two sounds equals the rate that the fluctuations
occur. If the frequency difference is small then the sound is perceived as a periodic
change in the loudness of a single tone. If the beats are fast then this can be described as a
sensation of roughness. When there is a large frequency separation, the two components
are heard as separate tones without roughness or beats. Beats can be a cue to the presence
of a signal even when the signal itself is not audible. The influence of beats can be
reduced by using a narrowband noise rather than a sinusoidal tone for either signal or
masker.
Mechanisms of masking
There are many different mechanisms of masking, one being suppression. This is when
there is a reduction of a response to a signal due to the presence of another. This happens
because the original neural activity caused by the first signal is reduced by the neural
activity of the other sound.
Addition is the adding of several maskers to result in an increased final masker threshold
greater than the original maskers (Lincoln 1998).
Combination tones are products of a signal/s and a masker/s. This happens when the two
sounds interact causing new sound, which can be more audible than the original signal.
This is caused by the non linear distortion that happens in the ear
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For example, the combination tone of two maskers can be a better masker than the two
original maskers alone.
The sounds interact in many ways depending on the difference in frequency between the
two sounds. The most important two are cubic difference tones and quadratic difference
tones
Cubic difference tones are calculated by the sum
F1 – F2
(F1 being the first frequency, F2 the second) These are audible most of the time and
especially when the level of the original tone is low. Hence they have a greater effect on
psychoacoustic tuning curves than quadratic difference tones. Quadratic difference tones
are the result of
F2 – F1
This happens at relatively high levels hence have a lesser effect on psychoacoustic tuning
curves.
Combination tones can interact with primary tones resulting in secondary combination
tones due to being like their original primary tones in nature, stimulus like. An example
of this is Secondary combination tones are again similar to the combination tones of the primary tone.
Off frequency listening
Off frequency listening is when a listener chooses a filter just lower than the signal
frequency to improve their auditory performance. This “off frequency” filter reduces the
level of the masker more than the signal at the output level of the filter, which means they
can hear the signal more clearly hence causing an improvement of auditory performance.
Non-simultaneous masking
Temporal masking or non-simultaneous masking is when the signal and masker are not
presented at the same time. This can be split into forward masking and backward
masking. Forward masking is when the masker is presented first and the signal follows it.
Backward masking is when the signal precedes the masker.
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Sound masking Systems
The effect of auditory masking is used in Sound masking systems. These are audio
systems that broadcast White noise for the purpose of hiding an unwanted sound. The
unwanted noise may be intermittent sounds from machinery, people or other sources.
Usually, this sound is filtered to provide the best effect of hiding the unwanted noise.
Spectral masking
Spectral masking is a frequency-domain version of temporal masking, and tends to occur
in sounds with similar frequencies: a powerful spike at 1 kHz will tend to mask out a
lower-level tone at 1.1 kHz. This too, can be exploited by the psychoacoustic model.