Symbol (data)
From Wikipedia, the free encyclopedia
 |
It has been suggested that this article or section be merged into baud. (Discuss) |
 |
It has been suggested that significant condition be merged into this article or section. (Discuss) |
In digital communications, a symbol is a state or significant condition of the communication channel that persists for a fixed period of time. A sending device places symbols on the channel at a fixed and known rate (the symbol rate, measured in baud) and the receiving device has the job of detecting the sequence of symbols in order to reconstruct the transmitted data. There may be a direct correspondence between a symbol and a small unit of data (for example, each symbol may encode some number of binary bits) or the data may be represented by the transitions between symbols or even in the sequence of many symbols. The selection of the set of symbols, or "constellation", is an important part of the design of a data communication system.
Contents |
[edit] Modulation
Many data transmission systems operate by the modulation of a carrier signal. For example, in frequency-shift keying (FSK), the frequency of a tone is varied among a small, fixed set of possible values. In a synchronous data transmission system, the tone can only be changed from one frequency to another at regular and well-defined intervals. The presence of one particular frequency during one of these intervals constitutes a symbol. (The concept of symbols does not apply to asynchronous data transmission systems.) In a modulated system, the term modulation rate may be used synonymously with symbol rate.
[edit] Binary Modulation
If the carrier signal has only two states, then only one bit of data (i.e., a 0 or 1) can be transmitted in each symbol. The bit rate is in this case equal to the symbol rate. For example, a binary FSK system would allow the carrier to have one of two frequencies, one representing a 0 and the other a 1. A more practical scheme is differential binary phase-shift keying, in which the carrier remains at the same frequency, but can be in one of two phases. During each symbol, the phase either remains the same, encoding a 0, or jumps by 180°, encoding a 1. Again, only one bit of data (i.e., a 0 or 1) is transmitted by each symbol. This is an example of data being encoded in the transitions between symbols (the change in phase), rather than the symbols themselves (the actual phase). (The reason for this in phase-shift keying is that it is impractical to know the reference phase of the transmitter.)
[edit] N-ary Modulation, N greater than 2
By increasing the number of states that the carrier signal can take, the number of bits encoded in each symbol can be greater than one. The bit rate can then be greater than the symbol rate. For example, a differential phase-shift keying system might allow four possible jumps in phase between symbols. Then two bits could be encoded at each symbol interval, achieving a data rate of double the symbol rate. In a more complex scheme such as 16-QAM, four bits of data are transmitted in each symbol, resulting in a bit rate of four times the symbol rate.
[edit] Data Rate versus Error Rate
Modulating a carrier increases the bandwidth it occupies. Transmission channels are generally limited in the bandwidth they can carry. The bandwidth depends on the symbol (modulation) rate (not directly on the bit rate). As the data rate is the product of the symbol rate and the number of bits encoded in each symbol, it is clearly advantageous to increase the latter if the former is fixed. However, for each additional bit encoded in a symbol, the constellation of symbols (the number of states of the carrier) doubles in size. This makes the states less distinct from one another which in turn makes it more difficult for the receiver to detect the symbol correctly in the presence of disturbances on the channel.
The history of modems is the attempt at increasing the bit rate over a fixed bandwidth (and therefore a fixed maximum symbol rate), leading to increasing bits per symbol. For example, the V.29 specifies 4 bits per symbol, at a symbol rate of 2,400 baud, giving an effective bit rate of 9,600 bits per second.
The history of spread spectrum goes in the opposite direction, leading to fewer and fewer data bits per symbol in order to spread the bandwidth. In the case of GPS, we have a data rate of 50 bit/s and a symbol rate of 1.023 Mchips/s. If each chip is considered a symbol, each symbol contains far less than one bit ( 50 bit/s / 1023 Ksymbols/s =~= 0.000 05 bits/symbol ).
The complete collection of M possible symbols over a particular channel is called a M-ary modulation scheme. Most modulation schemes transmit some integer number of bits per symbol b, requiring the complete collection to contain M = 2^b different symbols. Most popular modulation schemes can be described by showing each point on a constellation diagram, although a few modulation schemes (such as MFSK, DTMF, pulse-position modulation, spread spectrum modulation) require a different description.
[edit] See also
- Chip rate
- Gross bit rate, also known as data signaling rate or line rate.
