Editing G.711

{{short description|ITU-T recommendation}}
{{Infobox technology standard
| title             = G.711
| long_name         = Pulse code modulation (PCM) of voice frequencies    
| image             = Pcm.svg 
| caption           = 
| status            = In force
| year_started      = 1972
| version           = (02/00)
| version_date      = February 2000
| preview           = 
| preview_date      = 
| organization      = [[ITU-T]]
| committee         = 
| base_standards    = 
| related_standards = [[G.191]], [[G.711.0]], [[G.711.1]], [[G.729]]
| abbreviation      = 
| domain            = [[audio compression (data)|audio compression]]
| license           = 
| website           = https://www.itu.int/rec/T-REC-G.711
}}
{{Floating-point}}

'''G.711''' is a [[narrowband]] [[audio codec]] originally designed for use in [[telephony]] that provides toll-quality audio at 64&nbsp;kbit/s. It is an [[ITU-T]] standard (Recommendation) for audio [[encoding]], titled '''Pulse code modulation (PCM) of voice frequencies''' released for use in 1972. 

G.711 passes audio signals in the [[frequency band]] of 300–3400&nbsp;Hz and [[Sampling rate|samples them at the rate of]] 8000&nbsp;Hz, with the tolerance on that rate of 50 [[parts per million]] (ppm).

It uses one of two different logarithmic [[companding]] algorithms: [[μ-law]], which is used primarily in North America and Japan, and [[A-law]], which is in use in most other countries outside North America. Each companded sample is quantized as 8 bits, resulting in a 64&nbsp;kbit/s [[bit rate]]. 

G.711 is a required standard in many technologies, such as in the [[H.320]] and [[H.323]] standards.<ref name=":0">{{Cite web|url=https://www.itu.int/rec/T-REC-G.711|title=G.711 : Pulse code modulation (PCM) of voice frequencies|website=www.itu.int|url-status=live|archive-url=https://web.archive.org/web/20190617130328/https://www.itu.int/rec/T-REC-G.711|archive-date=2019-06-17|access-date=2019-11-11}}</ref> It can also be used for [[fax]] communication over IP networks (as defined in [[T.38]] specification). 

Two enhancements to G.711 have been published: '''G.711.0''' utilizes [[lossless data compression]] to reduce the bandwidth usage and '''G.711.1''' increases audio quality by increasing bandwidth.

==Features==
* 8&nbsp;kHz sampling frequency
* 64&nbsp;kbit/s bitrate (8&nbsp;kHz sampling frequency × 8 bits per sample)
* Typical algorithmic delay is 0.125 ms, with no look-ahead delay
* G.711 is a waveform [[speech coder]]
* G.711 Appendix I defines a [[packet loss concealment]] (PLC) algorithm to help hide transmission losses in a packetized network
* G.711 Appendix II defines a [[discontinuous transmission]] (DTX) algorithm which uses [[voice activity detection]] (VAD) and [[Comfort noise|comfort noise generation]] (CNG) to reduce bandwidth usage during silence periods
* [[PSQM]] testing under ideal conditions yields [[mean opinion score]]s of 4.45 for G.711 μ-law, 4.45 for G.711 A-law{{cn|date=May 2020}}
* PSQM testing under network stress yields [[mean opinion score]]s of 4.13 for G.711 μ-law, 4.11 for G.711 A-law{{cn|date=May 2020}}

==Types==
G.711 defines two main [[companding]] algorithms, the [[μ-law algorithm]] and [[A-law algorithm]]. Both are [[logarithmic scale|logarithmic]], but A-law was specifically designed to be simpler for a computer to process{{Citation Needed|date=October 2023}}. The standard also defines a sequence of repeating code values which defines the power level of 0 [[Decibel|dB]].

The μ-law and A-law algorithms encode 14-bit and 13-bit signed linear PCM samples (respectively) to logarithmic 8-bit samples. Thus, the G.711 [[data compression|encoder]] will create a 64&nbsp;kbit/s bitstream for a signal sampled at 8&nbsp;kHz.<ref name=":0" />

G.711 μ-law tends to give more resolution to higher range signals while G.711 A-law provides more quantization levels at lower signal levels.

The terms ''PCMU'', ''G711u'' and ''G711MU'' are also used for G.711 μ-law, and ''PCMA'' and ''G711A'' for G.711 A-law.<ref>{{cite web |url=http://www.grandstream.com/support/faq/common-questions/video/voice/speech-codecs |title=Video/Voice/Speech Codecs |website=Grandstream=|access-date= 19 July 2020}}</ref>

=== A-law ===
{{Main|A-law algorithm}}
A-law encoding thus takes a 13-bit signed linear audio sample as input and converts it to an 8 bit value as follows:

{| class="wikitable" style="text-align:left"
|-
! Linear input code<br><ref group=note>This value is produced by taking the [[two's complement]] representation of the input value, and inverting all bits after the sign bit if the value is negative.</ref>
! Compressed code<br>XOR 01010101
! Linear output code<br><ref group=note>[[Signed magnitude]] representation</ref>
|-
| <code>s0000000abcdx</code> || <code>{{overline|s}}000abcd</code> || <code>s0000000abcd1</code>
|-
| <code>s0000001abcdx</code> || <code>{{overline|s}}001abcd</code> || <code>s0000001abcd1</code>
|-
| <code>s000001abcdxx</code> || <code>{{overline|s}}010abcd</code> || <code>s000001abcd10</code>
|-
| <code>s00001abcdxxx</code> || <code>{{overline|s}}011abcd</code> || <code>s00001abcd100</code>
|-
| <code>s0001abcdxxxx</code> || <code>{{overline|s}}100abcd</code> || <code>s0001abcd1000</code>
|-
| <code>s001abcdxxxxx</code> || <code>{{overline|s}}101abcd</code> || <code>s001abcd10000</code>
|-
| <code>s01abcdxxxxxx</code> || <code>{{overline|s}}110abcd</code> || <code>s01abcd100000</code>
|-
| <code>s1abcdxxxxxxx</code> || <code>{{overline|s}}111abcd</code> || <code>s1abcd1000000</code>
|}
<references group=note/>

Where {{code|s}} is the sign bit, <code>{{overline|s}}</code> is its inverse (i.e. positive values are encoded with [[most significant bit|MSB]]&nbsp;=&nbsp;{{var|{{overline|s}}}}&nbsp;=&nbsp;1), and bits marked {{code|x}} are discarded. Note that the first column of the table uses different representation of negative values than the third column. So for example, input decimal value −21 is represented in binary after bit inversion as 1000000010100, which maps to 00001010 (according to the first row of the table). When decoding, this maps back to 1000000010101, which is interpreted as output value −21 in decimal. Input value +52 (0000000110100 in binary) maps to 10011010 (according to the second row), which maps back to 0000000110101 (+53 in decimal).

This can be seen as a [[Floating-point arithmetic|floating-point]] number with 4 bits of [[Significand|mantissa]] {{var|m}} (equivalent to a 5-bit precision), 3 bits of [[exponent]] {{var|e}} and 1 sign bit {{var|s}}, formatted as <code>{{overline|s}}eeemmmm</code> with the decoded linear value {{var|y}} given by formula
:<math>y = (-1)^s \cdot (16 \cdot \min \{ e, 1 \} + m + 0.5) \cdot 2^{\max \{ e, 1 \} },</math>
which is a 13-bit signed integer in the range ±1 to ±(2{{sup|12}}&nbsp;−&nbsp;2{{sup|6}}). Note that no compressed code decodes to zero due to the addition of 0.5 (half of a quantization step).

In addition, the standard specifies that all resulting even bits ([[least significant bit|LSB]] is even) are inverted before the octet is transmitted. This is to provide plenty of 0/1 transitions to facilitate the [[clock recovery]] process in the PCM receivers. Thus, a silent A-law encoded PCM channel has the 8 bit samples coded 0xD5 instead of 0x80 in the octets.

When data is sent over E0 ([[G.703]]), MSB (sign) is sent first and LSB is sent last.

ITU-T STL<ref>[http://www.itu.int/rec/T-REC-G.191-201003-I/en G.191 : Software tools for speech and audio coding standardization]. Function {{code|alaw_expand}} in file {{code|Software/stl2009/g711/g711.c}}. Itu.int. Retrieved on 2013-09-18.</ref> defines the algorithm for decoding as follows (it puts the decoded values in the 13 most significant bits of the 16-bit output data type).

<syntaxhighlight lang="c">
void            alaw_expand(lseg, logbuf, linbuf)
  long            lseg;
  short          *linbuf;
  short          *logbuf;
{
  short           ix, mant, iexp;
  long            n;

  for (n = 0; n < lseg; n++)
  {
    ix = logbuf[n] ^ (0x0055);	/* re-toggle toggled bits */

    ix &= (0x007F);		/* remove sign bit */
    iexp = ix >> 4;		/* extract exponent */
    mant = ix & (0x000F);	/* now get mantissa */
    if (iexp > 0)
      mant = mant + 16;		/* add leading '1', if exponent > 0 */

    mant = (mant << 4) + (0x0008);	/* now mantissa left justified and */
    /* 1/2 quantization step added */
    if (iexp > 1)		/* now left shift according exponent */
      mant = mant << (iexp - 1);

    linbuf[n] = logbuf[n] > 127	/* invert, if negative sample */
      ? mant
      : -mant;
  }
}
</syntaxhighlight>

See also "ITU-T Software Tool Library 2009 User's manual" that can be found at.<ref>[http://www.itu.int/rec/T-REC-G.191/recommendation.asp?lang=en&parent=T-REC-G.191-200911-I G.191 : ITU-T Software Tool Library 2009 User's manual]. Itu.int (2010-07-23). Retrieved on 2013-09-18.</ref>

=== μ-law ===
{{Main|μ-law algorithm}}
The μ-law (sometimes referred to as ulaw, G.711Mu, or G.711μ) encoding takes a 14-bit signed linear audio sample in [[two's complement]] representation as input, inverts all bits after the sign bit if the value is negative, adds 33 (binary 100001) and converts it to an 8 bit value as follows:

{| class="wikitable" style="text-align:left"
|-
! Linear input value<br><ref group=note>This value is produced by taking the [[two's complement]] representation of the input value, inverting all bits after the sign bit if the value is negative, and adding 33.</ref>
! Compressed code<br>XOR 11111111
! Linear output value<br><ref group=note>[[Signed magnitude]] representation. Final result is produced by decreasing the magnitude of this value by 33.</ref>
|-
| <code>s00000001abcdx</code> || <code>s000abcd</code> || <code>s00000001abcd1</code>
|-
| <code>s0000001abcdxx</code> || <code>s001abcd</code> || <code>s0000001abcd10</code>
|-
| <code>s000001abcdxxx</code> || <code>s010abcd</code> || <code>s000001abcd100</code>
|-
| <code>s00001abcdxxxx</code> || <code>s011abcd</code> || <code>s00001abcd1000</code>
|-
| <code>s0001abcdxxxxx</code> || <code>s100abcd</code> || <code>s0001abcd10000</code>
|-
| <code>s001abcdxxxxxx</code> || <code>s101abcd</code> || <code>s001abcd100000</code>
|-
| <code>s01abcdxxxxxxx</code> || <code>s110abcd</code> || <code>s01abcd1000000</code>
|-
| <code>s1abcdxxxxxxxx</code> || <code>s111abcd</code> || <code>s1abcd10000000</code>
|}
<references group=note/>

Where {{code|s}} is the sign bit, and bits marked {{code|x}} are discarded.

In addition, the standard specifies that the encoded bits are inverted before the octet is transmitted. Thus, a silent μ-law encoded PCM channel has the 8 bit samples transmitted 0xFF instead of 0x00 in the octets.

Adding 33 is necessary so that all values fall into a compression group and it is subtracted back when decoding. 

Breaking the encoded value formatted as <code>seeemmmm</code> into 4 bits of mantissa {{var|m}}, 3 bits of exponent {{var|e}} and 1 sign bit {{var|s}}, the decoded linear value {{var|y}} is given by formula
:<math>y = (-1)^s \cdot [(33 + 2m) \cdot 2^e - 33],</math>
which is a 14-bit signed integer in the range ±0 to ±8031.

Note that 0 is transmitted as 0xFF, and −1 is transmitted as 0x7F, but when received the result is 0 in both cases.

== G.711.0 ==
G.711.0, also known as G.711 LLC, utilizes [[lossless data compression]] to reduce the bandwidth usage by as much as 50 percent.<ref>{{cite web|url=http://www.itu.int/ITU-T/newslog/Voice+Codec+Gets+New+Lossless+Compression.aspx|title=ITU-T Newslog - Voice codec gets new lossless compression|author=ITU-T|date=2009-07-17|url-status=live|archive-url=https://web.archive.org/web/20160303224212/https://www.itu.int/ITU-T/newslog/Voice+Codec+Gets+New+Lossless+Compression.aspx|archive-date=2016-03-03|access-date=2010-02-28}}</ref> The ''Lossless compression of G.711 pulse code modulation'' standard was approved by ITU-T in September 2009.<ref>{{cite web |url=https://www.itu.int/rec/T-REC-G.711.0-200909-I/en |title=G.711.0 : Lossless compression of G.711 pulse code modulation |author=ITU-T |access-date=2010-02-28}}</ref><ref name="itu-t-devel">{{citation |url=http://www.eurasip.org/Proceedings/Eusipco/Eusipco2008/plenaries/lamblin.pdf |title=Recent Audio/Speech Coding Developments in ITU-T and future trends |date=August 2008 |access-date=2010-02-28}}</ref>

== G.711.1 ==
G.711.1 ''"Wideband embedded extension for G.711 pulse code modulation"'' is a higher-fidelity extension to G.711, ratified in 2008 and further extended in 2012.<ref name="g711-1-2012">{{citation |publisher=ITU-T |date=2012 |url=http://www.itu.int/rec/T-REC-G.711.1/en |title=G.711.1 : Wideband embedded extension for G.711 pulse code modulation |access-date=2022-12-24}}</ref>

G.711.1 allows a series of enhancement layers on top of a raw G.711 core stream (Layer 0): Layer 1 codes 16-bit audio in the same 4kHz narrowband, and Layer 2 allows 8kHz [[wideband]] using [[MDCT]]; each uses a fixed 16&nbsp;kbps in addition to the 64&nbsp;kbps core. They may be used together or singly, and each encodes the differences from the previous layer. Ratified in 2012, Layer 3 extends Layer 2 to 16kHz "superwideband," allowing another 16&nbsp;kbps for the highest frequencies, while retaining layer independence. Peak bitrate becomes 96&nbsp;kbps in original G.711.1, or 112&nbsp;kbps with superwideband. No internal method of identifying or separating the layers is defined, leaving it to the implementation to packetize or signal them.<ref>{{citation |url=http://www.eurasip.org/Proceedings/Eusipco/Eusipco2008/papers/1569105406.pdf |title=Noise shaping in an ITU-T G.711-Interoperable embedded codec |author=Lapierre |date=2008-08-25 |access-date=2024-06-11|display-authors=etal}}</ref><ref>{{citation |url=http://www.eurasip.org/Proceedings/Eusipco/Eusipco2008/papers/1569104469.pdf |title=G. 711.1: a wideband extension to ITU-T G. 711 |author=Hiwasaki |date=2008-08-25 |access-date=2024-06-11|display-authors=etal}}</ref>

A decoder that doesn't understand any set of fidelity layers may ignore or drop non-core packets without affecting it, enabling graceful degradation across any G.711 (or original G.711.1) telephony system with no changes.

Also ratified in 2012 was G.711.0 lossless extended to the new fidelity layers. Like G.711.0, full G.711 backward compatibility is sacrificed for efficiency, though a G.711.0 aware node may still ignore or drop layer packets it doesn't understand.

== Licensing ==
The patents for G.711, released in 1972, have expired, so it may be used without the need for a license.<ref name=":0" />

== See also ==
*[[List of codecs]]
*[[Comparison of audio coding formats]]
*[[RTP audio video profile]]
*[[Au file format]]

== References ==
<references/>

== External links ==
* [https://www.itu.int/rec/T-REC-G.711 ITU-T Recommendation G.711]
* [http://www.itu.int/rec/T-REC-G.191 ITU-T G.191 software tools for speech and audio coding, including G.711 C code]
* [https://web.archive.org/web/20060720180425/http://www.codeproject.com/csharp/g711audio.asp Code Project C# implementation of G.711 with source code]
* [http://tools.ietf.org/html/rfc3551#page-28 RFC 3551 - RTP Profile for Audio and Video Conferences with Minimal Control] - G.711 - PCMA and PCMU definition.
* [http://tools.ietf.org/html/rfc4856#page-21 RFC 4856 - Registration of Media Type audio/PCMA and audio/PCMU]
* {{IETF RFC|5391|link=no}} - RTP Payload Format for ITU-T Recommendation G.711.1 (PCMA-WB and PCMU-WB)

{{Compression formats}}

[[Category:Audio codecs]]
[[Category:Speech codecs]]
[[Category:ITU-T recommendations]]
[[Category:ITU-T G Series Recommendations]]
[[Category:Telecommunications-related introductions in 1972]]