Editing Bit rate (section)

=== Gross bit rate <span class="anchor" id="UNCODED"></span> ===
{{See also|Data signaling rate}}

In digital communication systems, the [[physical layer]] ''gross bitrate'',<ref name="Guimarães">{{cite book |chapter-url= https://books.google.com/books?id=x4jOplMbLx0C&q=gross+bit+rate&pg=PA692 |title=Digital Transmission: A Simulation-Aided Introduction with VisSim/Comm | first =Dayan Adionel | last = Guimarães |publisher=Springer |year=2009 |chapter=section 8.1.1.3 Gross Bit Rate and Information Rate |isbn=9783642013591 |access-date = 10 July 2011}}</ref> ''raw bitrate'',<ref name="Pahlavan">{{cite book |url=https://books.google.com/books?id=WOCrSSfxE-EC&pg=PA133 |title=Networking Fundamentals |author=Kaveh Pahlavan, Prashant Krishnamurthy | publisher= John Wiley & Sons |year=2009 |isbn=9780470779439 |access-date=10 July 2011}}</ref> ''[[data signaling rate]]'',<ref>{{cite book |url= https://books.google.com/books?id=On_Hh23IXDUC&pg=PA135 |title= Network Dictionary |publisher= Javvin Technologies |year = 2007 |isbn= 9781602670006 |access-date=10 July 2011}}</ref> ''gross data transfer rate''<ref name="3G">{{cite book|url=https://books.google.com/books?id=RoJj0zw_pDMC&pg=PA277|title=3G wireless demystified|last1=Harte|first1=Lawrence|last2=Kikta|first2=Roman|last3=Levine|first3=Richard|publisher=[[McGraw-Hill Professional]]|year=2002|isbn=9780071382823|access-date=10 July 2011}}</ref> or ''uncoded transmission rate''<ref name= "Pahlavan" /> (sometimes written as a variable ''R''<sub>b</sub><ref name="Guimarães"/><ref name="Pahlavan"/> or ''f''<sub>b</sub><ref>{{cite book |url=https://books.google.com/books?id=6Hd6WqsgKIMC&pg=PA30 |title=Principles of Digital Communication |author=J.S. Chitode |publisher=Technical Publication |year=2008 |isbn=9788184314519 |access-date=10 July 2011 }}{{Dead link|date=August 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref>) is the total number of physically transferred bits per second over a communication link, including useful data as well as protocol overhead.

In case of [[serial communication]]s, the gross bit rate is related to the bit transmission time <math>T_\text{b}</math>
as:
: <math>R_\text{b} = {1 \over T_\text{b}},</math>

The gross bit rate is related to the [[symbol rate]] or modulation rate, which is expressed in [[baud]]s or symbols per second. However, the gross bit rate and the baud value are equal ''only'' when there are only two levels per symbol, representing 0 and 1, meaning that each symbol of a [[data transmission]] system carries exactly one bit of data; for example, this is not the case for modern modulation systems used in [[modem]]s and LAN equipment.<ref>
Lou Frenzel. 27 April 2012,
[http://electronicdesign.com/communications/what-s-difference-between-bit-rate-and-baud-rate "What's The Difference Between Bit Rate And Baud Rate?"].
Electronic Design. 2012.
</ref>

For most [[line code]]s and [[modulation]] methods:
: <math>\text{symbol rate} \leq \text{gross bit rate}</math>

More specifically, a line code (or [[baseband]] transmission scheme) representing the data using [[pulse-amplitude modulation]] with <math>2^N</math> different voltage levels, can transfer <math>N</math> bits per pulse. A [[digital modulation]] method (or [[passband transmission]] scheme) using <math>2^N</math> different symbols, for example <math>2^N</math> amplitudes, phases or frequencies, can transfer <math>N</math> bits per symbol. This results in:
: <math>\text{gross bit rate}  =  \text{symbol rate} \times N</math>

An exception from the above is some self-synchronizing line codes, for example [[Manchester coding]] and [[return-to-zero]] (RTZ) coding, where each bit is represented by two pulses (signal states), resulting in:
: <math>\text{gross bit rate  =  symbol rate/2}</math>

A theoretical upper bound for the symbol rate in baud, symbols/s or pulses/s for a certain [[bandwidth (signal processing)|spectral bandwidth]] in hertz is given by the [[Nyquist rate|Nyquist law]]:
: <math>\text{symbol rate} \leq \text{Nyquist rate} = 2 \times \text{bandwidth}</math>

In practice this upper bound can only be approached for [[line coding]] schemes and for so-called [[vestigial sideband]] digital modulation. Most other digital carrier-modulated schemes, for example [[amplitude-shift keying|ASK]], [[phase-shift keying|PSK]], [[quadrature amplitude modulation|QAM]] and [[OFDM]], can be characterized as [[double sideband]] modulation, resulting in the following relation:
: <math>\text{symbol rate} \leq \text{bandwidth}</math>

In case of [[parallel port|parallel communication]], the gross bit rate is given by
: <math>\sum_{i = 1}^{n} \frac{\log_2 {M_i} }{T_i}</math>
where ''n'' is the number of parallel channels, ''M<sub>i</sub>'' is the number of symbols or levels of the [[modulation]] in the ''i''th [[channel (communications)|channel]], and ''T<sub>i</sub>'' is the [[symbol duration time]], expressed in seconds, for the ''i''th channel.