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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.