Encoding is the process of transforming information from one format into another. The opposite operation is called decoding. This is often used in many digital devices

There are a number of more specific meanings that apply in certain contexts:

• Encoding (in cognition) is a basic perceptual process of interpreting incoming stimuli; technically speaking, it is a complex, multi-stage process of converting relatively objective sensory input (e.g., light, sound) into subjectively meaningful experience.

Data Encoding

This outlines basics of encoding analog or digital data using analog or digital signals.

Encoding signals

• Basics - Fourrier analysis of periodic signal into harmonic components
• Three parameters to sinusoid function:
• amplitude
• frequency
• phase
• frequency and phase are "angle" parameters
• varying these parameters over time allows encoding of a signal
• Encoding signals -
• analog/analog encoding (modulation)
• rationales :
• 1. necessity (may require high frequencies to transmit over medium)
• 2. ability to use FDM
• AM - Amplitude modulation
• value of amplitude encodes modulating signal
• increased amplitude of modulating signal increases power of output power, but not bandwidth
• DSBTC - double sideband transmitted carrier
• Waveform:
• s(t) = [1+n_a x(t)]cos(2 pi f_c t) where
• s(t) = output signal
• x(t) = input signal (normalized)
• f_c = carrier frequency
• cos(2 pi f_c t) = carrier signal (normalized)
• n_a = modulation index, ratio of amplitude of input signal to carrier (so that the modulating signal, n_a x(t) has amplitude <>
• 1 = dc component to avoid loss of information (otherwise the peak negative amplitudes would cause the output signal to cross the axis)
• multiply carrier signal by modulating signal plus a dc component to obtain output
• output has redundancy in that the output is the sum of the carrier signal plus symmetric components spaced at f_m from the carrier frequency (where f_m is the modulating signal's frequency)
• spectrum of AM signal is f_c +- spectrum of modulating signal: the upper sideband (above f_c) is the mirror image of the lower sideband (spectrum below f_c). Both are 1/2 power replicas of the original spectrum, with the lower sideband frequency-reversed.
• Power transmitted = P_t = P_c(1+n_a^2/2), where P_c is the carrier power. Hence, n_a should be as large as possible, so that most of the signal power carries information, but remaining <>
• Bandwidth needed B_t = 2B_m, where B_m is original bandwidth
• SSB - Single Sideband
• Since the spectrum of the AM signal has redundant information in the two sideband, and no information in the carrier signal, less power and less bandwidth can be used to transmit the same information by sending only one sideband. Half the bandwidth of DSBTC is used, and less power. Synchronization in the carrier signal is lost.
• DSBSC - Double Sideband Supressed Carrier
• Less power is used since carrier is not sent, but the same bandwidth is used and carrier sync lost.
• VSB - Vestigial Sideband
• One sideband is transmitted, and a reduced-power carrier.
• FM - Frequency modulation (a form of angle modulation)
• time derivative of phase angle encodes modulating signal
• Waveform:
• s(t) = A_c cos[2 pi f_c + phi(t)],
• where phi'(t) = n_f m(t) is the derivative of the phase, and
• A_c, f_c = carrier amplitude, frequency
• m(t) = input modulating signal
• Increased amplitude of input signal does not increase output power, but does increase bandwidth required.
• Bandwidth required is, in theory, infinite, since the spectrum will contain components at f_c + K f_m for K=0,1,...
• In practice, Carson's rule for FM says that B_t = 2[(n_f A_m)/(1 pi B_m) + 1]B_m
• PM - Phase modulation (a form of angle modulation)
• value of phase angle encodes modulating signal
• Waveform:
• s(t) = A_c cos[2 pi f_c + n_p m(t)],
• where n_p = the phase modulation index (to normalize
• n_p m(t) to the range 0..2 pi)
• A_c, f_c = carrier amplitude, frequency
• m(t) = input modulating signal
• Bandwidth required is, in theory, infinite, since the spectrum will contain components at f_c + K f_m for K=0,1,...
• In practice, Carson's rule for PM says that B_t = 2(n_p A_m + 1)B_m
• PAM - pulse amplitude modulation
• Thm: analog samples taken at more than twice the highest significant signal frequency will contain all the information of the original signal. The original signal may be reconstructed from the samples by use of a low-pass filter.
• Bell's Dimension PBX products use this - analog samples are taken at twice the frequency of the signal, and only very short pulses reflecting these samples is transmitted.
• analog/digital encoding (pulse code modulation, PCM)
• PCM - pulses of PAM are quantized into discrete levels, then these levels are encoded in log (# levels) bits and sent. Two choices : sampling rate and number of levels
• Noise -
• quantizing noise - the original signal cannot be recovered since the pulses have been quantized.
• SNR = 6n + 1.8 dB, where n = #bits/sample
• Non-linear encoding - reduces quantizing distortion of weak signals by having finer gradations of discrete levels at the lower signal power levels, and coarser at higher power.
• Companding function - same effect as n-l encoding may be had by compressing the analog signal before digitizing and expanding it after decoding. The companding function will giver greater gain to the weaker signals and less gain to strong signals.
• Differential Encoding - only encode difference in signal rather than its absolute value
• Delta Modulation (DM) - binary staircase function used to approximate the signal - on each time interval, either the staircase function goes up a quantum or down a quantum, (encoded as a 1 or a 0).
• note: there is no limit on the amplitude of the signal encoded
• note: similar to chain coding for contours in discrete 2-D.
• Two choices : sampling rate and quantum size
• Noise - two types: quantizing and slope overload
• Large delta increases quantizing noise
• Small delta increases slope overload noise
• Predictive encoding - like DM only use an extrapolated value for point from which the difference is calculated. This is a generalized version of DM, with DM the special case where the predicted value is the same as the previous value, ie, a zero-order (constant) extrapolation function is used. DM has problems with rapid changes in the first derivative; in general, PDM using an nth order predictive encoding will have problems with rapid changes in the (n+1)th derivative.
• digital/analog encoding (shift keying)
• ASK - V amplitude levels can encode lg V bits per signal unit
• FSK - V frequency levels can encode lg V bits per signal unit
• PSK/QPSK - V phases can encode lg V bits per signal unit. QPSK uses four phases offset 90 degrees.
• QAM - Mixed PSK and ASK, use pairs (p,a) to describe signal units, where p is the phase and a is the amplitude. This can keep power requirements lower and discrimination better than either technique alone.
• PPM - pulse position modulation May be used with either analog or digital transmission to encode digital signals Signal is divided into frames, each frame has N slots (plus some synchronization overhead every so often) In each frame, exactly one slot has a pulse in it, A<>0; the other slots have A = 0 (no pulse). This allows lg N bits/frame to be encoded. It is useful when power requirements must be kept low and the transmission medium may be pulsed easily (e.g., lasers in deep-space communication)
• digital/digital encoding
• Needs - synch, no dc component
• Evaluation
• spectrum - max frequency (increased bandwidth requirement)
• dc component (drift, direct coupling required)
• synchronization
• signal-based error-detection
• susceptibility to interference (expressed as bit error rate)
• cost/complexity
• Methods
• Level (L) - use same form to represent same bit value (1's always look the same, 0's always look the same)
• Differential - use a change in signal element form to indicate a 1 (Mark or M), or a 0 (Space or S)
• Examples -
• NRZ-L: 1 = high, 0 = low
• NRZ-M: 1 = transition at start of bit, 0 = no transition
• NRZ-S: 1 = no transition, 0 = transition at start of bit
• RZ: 1 = pulse to high, dropping back to low, 0 = low
• bipolar: like NRZ except marks (1's) alternate polarity +1-1+1 (aka Bipolar AMI - alternate mark inversion) (sometime RZ technique used) (note: this will be shown below using _ for 0, + for a positive pulse, and - for a negative pulse)
• pseudoternary - like bipolar only spaces (0's)
• biphase-L (Manchester): always transition in middle of bit, 1 = high/low, 0 = low/high
• differential Manchester: always transition in middle of bit, 1 = no transition, 0 = transition at start of bit
• biphase-M: always transition at start of bit, 1 = transition in middle of bit, 0 = no transition
• biphase-S: always transition at start of bit, 1 = no transition, 0 = transition in middle of bit
• delay (Miller): 1 = transition in middle of bit, 0 = no transition if followed by a 1, transition at end of bit if followed by a 0
• PPM - (see above under digital/analog encodings)

§      Method      Waveform               Comments

§                     

§      data:    0 1 1 0 1 0 0 0 1

§                     

§      NRZ-L    __----__--______--        dc component

§                     

§      NRZ-M    __--____--------__        dc component

§                     

§      NRZ-S    ------____--__----        dc component

§                     

§      RZ       __-_-___-_______-_        dc component, twice B/W

§                     

§      bipolar  __++--__++______--        three levels, e.d.

§                     

§      Manch.   _--_-__--__-_-_--_        synch, twice BW, e.d.

§                     

§      D.Man.   -__--_-__-_-_-_--_        synch, twice BW, e.d.

§             

§      Bip.-M   --_-_-__-_--__--_-        synch, twice BW, e.d.

§                     

§      Bip.-S   -_--__-_--_-_-_-__        synch, twice BW, e.d.

§                     

§      Miller   ___--____---__---_        synch, 3/2 BW, e.d., complex

§      

§ Scrambling

§ To add synchronization capabilities to bipolar-AMI, which looses synchronization when a long string of 0's is sent, a run of 0's may be encoded by one of two fixed strings of 0's and 1's of the same length. These are distinguished from normal data by having one (or more) code violations (having two pulses of the same polarity in a row) in short succession, so that the receiver may detect these substituted patterns and decode them as a run of 0's.

§ Examples -

§ Bipolar with 8 Zero Substitution (B8ZS) - whenever 8 consecutive 0's are encountered in the data, then the 8 0's are replaced with the pattern 000VB0VB, where {V,B} = {+,-} with V the polarity of the last mark (causing a code violation) and B a pulse of the opposite polarity of the preceeding one. Popular in the USA. Requires only memory of polarity of last pulse and number of consecutive 0's seen, buffering the last 5 bits.

§ EX:

§            data    = 011001000000000000100

§                                   

§                            ^^^^^^^^        - run of 8 0's

§                                   

§            encoded = 0+-00+000+-0-+0000-00

§                                   

§                           ^---^^-^         - code violations

§                                   

§                            ||||||||        - special pattern

§                                  

§ High-density Bipolar - 3 Zeros (HDB3) - Popular in Europe and Japan. Starts with Bipolar-AMI, and substitutes 4 consecutive 0's with one of four patterns, according to both the polarity of the preceding pulse and the number of pulses since the last substitution (so that no dc component is introduced). Requires memory of polarity of last pulse, parity of number of pulses seen since last substitution, and number of consecutive 0's seen. Must buffer 4 bits.

§                              Pulses since last substitution

§                                   

§           Preceding Polarity         Odd         Even

§                                   

§                   -                  000-        +00+

§                                   

§                   +                  000+        -00-

§                                  

§            IN GENERAL                000V        BOOV

§                                  

§ EX:

§            data = 011001000000100000100

§                                   

§                         ^^^^   ^^^^    - runs of 4 zeros each

§                                   

§            HDB3 = 0+-00+-00-00+000+0-00

§                                   

§                         ^--^  ^---^        - code violations

§                                   

§                         ||||   ||||        - special patterns

§                                  

§ Note: since repeating a pulse of the same polarity to cause a code violation will introduce dc bias, this must be remedied - B8ZS does this by balancing the number of positive and negative pulses in its substitution pattern, but the pattern is long, so 7 0's in the data can go through unsubstituted. HDB3 compensates for imbalance its shorter pattern could introduce by a more complex method for choosing the pattern used, so that the net imbalance is never bad. It does this by insuring that the unbalanced substitution patterns are always of alternating polarity.

Manchester Phase Encoding (MPE)

802.3 Ethernet uses Manchester Phase Encoding (MPE). A data bit '1' from the level-encoded signal (i.e. that from the digital circuitry in the host machine sending data) is represented by a full cycle of the inverted signal from the master clock which matches with the '0' to '1' rise of the phase-encoded signal (linked to the phase of the carrier signal which goes out on the wire). i.e. -V in the first half of the signal and +V in the second half.

The data bit '0' from the level-encoded signal is represented by a full normal cycle of the master clock which gives the '1' to '0' fall of the phase-encoded signal. i.e. +V in the first half of the signal and -V in the second half.

The above diagram shows graphically how MPE operates. The example at the bottom of the diagram indicates how the digital bit stream 10110 is encoded.

A transition in the middle of each bit makes it possible to synchronize the sender and receiver. At any instant the ether can be in one of three states: transmitting a 0 bit (-0.85v), transmitting a 1 bit (0.85v) or idle (0 volts). Having a normal clock signal as well as an inverted clock signal leads to regular transitions which means that synchronisation of clocks is easily achieved even if there are a series of '0's or '1's. This results in highly reliable data transmission. The master clock speed for Manchester encoding always matches the data speed and this determines the carrier signal frequency, so for 10Mbps Ethernet the carrier is 10MHz.

Differential Manchester Encoding (DME)

A '1' bit is indicated by making the first half of the signal, equal to the last half of the previous bit's signal i.e. no transition at the start of the bit-time. A '0' bit is indicated by making the first half of the signal opposite to the last half of the previous bit's signal i.e. a zero bit is indicated by a transition at the beginning of the bit-time. In the middle of the bit-time there is always a transition, whether from high to low, or low to high. Each bit transmitted means a voltage change always occurs in the middle of the bit-time to ensure clock synchronisation. Token Ring uses DME and this is why a preamble is not required in Token Ring, compared to Ethernet which uses Manchester encoding.

Non Return to Zero (NRZ)

NRZ encoding uses 0 volts for a data bit of '0' and a +V volts for a data bit of '1'. The problem with this is that it is difficult to distinguish a series of '1's or '0's due to clock synchronisation issues. Also, the average DC voltage is 1/2V so there is high power output. In addition, the bandwidth is large i.e. from 0Hz to half the data rate because for every full signal wave, two bits of data can be transmitted (remember that with MPE the data rate equals the bit rate which is even more inefficient!) i.e. two bits of information are transmitted for every cycle (or hertz).

After 50m of cable attenuation the signal amplitude may have been reduced to 100mV giving an induced noise tolerance of 100mV.

Return to Zero (RZ)

With RZ a '0' bit is represented by 0 volts whereas a '1' data bit is represented by +V volts for half the cycle and 0 volts for the second half of the cycle. This means that the average DC voltage is reduced to 1/4V plus there is the added benefit of there always being a voltage change even if there are a series of '1's. Unfortunately, the efficiency of bandwidth usage decreases if there are a series of '1's since now a '1' uses a whole cycle.

Non Return to Zero Invertive (NRZ-I)

With NRZ-I a '1' bit is represented by 0 volts or +V volts depending on the previous level. If the previous voltage was 0 volts then the '1' bit will be represented by +V volts, however if the previous voltage was +V volts then the '1' bit will be represented by 0 volts. A '0' bit is represented by whatever voltage level was used previously. This means that only a '1' bit can 'invert' the voltage, a '0' bit has no effect on the voltage, it remains the same as the previous bit whatever that voltage was.

This can be demonstrated in the following examples for the binary patterns 10110 and 11111:

Note how that a '1' inverts the voltage whilst a '0' leaves it where it is. This means that the encoding is different for the same binary pattern depending on the voltage starting point.

The bandwidth usage is minimised with NRZ-I, plus there are frequent voltage changes required for clock synchronisation.

With fibre there are no issues with power output so a higher clock frequency is fine whereas with copper NRZ-I would not be acceptable.

4B/5B

4B/5B encoding is sometimes called 'Block coding'. To get around this problem, an intermediate encoding takes place before the MLT-3 encoding. Each 4-bit 'nibble' of received data has an extra 5th bit added. If input data is dealt with in 4-bit nibbles there are 2⁴ = 16 different bit patterns. With 5-bit 'packets' there are 2⁵ = 32 different bit patterns. As a result, the 5-bit patterns can always have two '1's in them even if the data is all '0's a translation occurs to another of the bit patterns. This enables clock synchronisations required for reliable data transfer.

Notice that the clock frequency is 125MHz. The reason for this is due to the 4B/5B encoding. A 100MHz signal would not have been enough to give us 100Mbps, we need a 125MHz clock.

5B/6B

Same idea as 4B/5B but you can have DC balance (3 zero bits and 3 one bits in each group of 6) to prevent polarisation. 5B/6B Encoding is the process of encoding the scrambled 5-bit data patterns into predetermined 6-bit symbols. This creates a balanced data pattern, containing equal numbers of 0's and 1's, to provide guaranteed clock transitions synchronization for receiver circuitry, as well as an even power value on the line.

5B6B encoding also provides an added error-checking capability. Invalid symbols and invalid data patterns, such as more than three 0's or three 1's in a row, are easily detected

For 100VG-AnyLAN for instance, the clock rate on each wire is 30MHz, therefore 30Mbits per second are transmitted on each pair giving a total data rate of 120Mbits/sec. Since each 6-bits of data on the line represents 5 bits of real data due to the 5B/6B encoding, the rate of real data being transmitted is 25Mbits/sec on each pair, giving a total rate of real data of 100Mbits/sec. For 2-pair STP and fiber, the data rate is 120Mbits/sec on the transmitting pair, for a real data transmission rate of 100Mbits/sec.

8B/6T

8B/6T means send 8 data bits as six ternary (one of three voltage levels) signals. 3/4 (6/8) wave transitions transitions per bit i.e. the carrier just needs to be running at 3/4 of the speed of the data rate.

The incoming data stream is split into 8-bit patterns. Each 8-bit data pattern with two voltage levels 0 volts and V volts is examined. This 8-bit pattern is then converted into a 6-bit pattern but using three voltage levels -V, 0 and V volts, so each 8-bit pattern has a unique 6T code. For example the bit pattern 0000 0000 (0x00) uses the code +-00+- and 0000 1110 (0x)E) uses the code -+0-0+. There are 3⁶ = 729 possible patterns (symbols). The rules for the symbols are that there must be at least two voltage transitions (to maintain clock synchronisation) and the average DC voltage must be zero (this is called 'DC balance' that is the overall DC voltage is summed up to 0v, the +V and -V transitions are evenly balanced either side of 0V) which stops any polarisation on the cable.

The maximum frequency that the 6T codes could generate on one carrier is 37.5MHz. FCC rules do not allow anything above 30MHz on cables and Category 3 cable does not allow anything above 16MHz (which is what 100BaseT4 was designed for). The 100BaseT4 standard uses 8B/6T encoding on three pairs in a round robin fashion such that the maximum carrier frequency on any single pair is 37.5/3 = 12.5MHz.

8B/10B

Each octet of data is examined and assigned a 10 bit code group. The data octet is split up into the 3 most significant bits and the 5 least significant bits. This is then represented as two decimal numbers with the least significant bits first e.g. for the octet 101 00110 we get the decimal 6.5. 10 bits are used to create this code group and the naming convention follows the format /D6.5/. There are also 12 special code groups which follow the naming convention /Kx.y/.

The 10 bit code groups must either contain five ones and five zeros, or four ones and six zeros, or six ones and four zeros. This ensures that not too many consecutive ones and zeros occurs between code groups thereby maintaining clock synchronisation. Two 'commas' are used to aid in bit synchronisation, these 'commas' are the 7 bit patterns 0011111 (+comma)and 1100000 (-comma).

In order to maintain a DC balance, a calculation called the Running Disparity calculation is used to try to keep the number of '0's transmitted the same as the number of '1's transmitted.

This uses 10 bits for each 8 bits of data and therefore drops the data rate speed relative to the line speed, for instance in order to gain a data rate of 1Gbps the line peed has to be 10/8 x 1 = 1.25Gbps .

MLT-3

This scheme was specified by ANSI X3T9.5 committee. It is used by FDDI and TP-PMD to obtain 100MB/s out of a 31.25MHz signal.

UTP is low pass in nature, meaning that it hinders high frequency signal (like a low-pass filter). So it is not feasible to merely increase the clock frequency by 10 to 100MHz and use Manchester encoding to give us 100Mbps. In addition, the FCC (Federal Communications Commission) have severely curtailed the power that is allowed to be emitted above 30MHz. We have to use another encoding technique in order to transmit high data rates across UTP.

If you take an averaging spectrum analyser and look at the output signal of the 10Mbps Ethernet phase-encoded signal, you will see a power peak at 10MHz where there is a stream of '1's or '0's, you will see a smaller harmonic at 30MHz and if there is a stream of '1's and '0's, you will see a peak at 5MHz. Now 100BaseT uses a master clock running at 125MHz instead of 10MHz. The equivalent peaks would then be at 125MHz, 375MHz and 62.5MHz. Transmission electronics designed to work within the FCC rules will block the frequencies higher than 30MHz.

To get around this issue we need to concentrate the signal power below 30MHz if possible. To do this the encoding method Multi-Level Transition 3 (MLT-3) is used. This involves using the pattern 1, 0, -1, 0. If the next data signal is a '1' then the output 'transitions' to the next bit in the pattern e.g. if the last output bit was a '-1', and the input bit is a '1', then the next output bit is a '0'. If the next data signal is a '0' then there is no transition which means that the next output bit is the same as last time, in our case a '0'.

The cycle length of the output signal is therefore going to be 1/4 that of the MPE method so that instead of the main signal peak being at 125MHz as measured by the averaging spectrum analyser, it will be at 31.25MHz which is near enough to be OK as far as FCC are concerned. 5 bits are transmitted for every 4 bits of data so that the data bit rate is actually 125Mb/s for 100Mb/s data throughput.

There is an issue with this in that you can end up with a series of '0's or '1's which force the local circuitry to count the bits using its own free running clock rather than have the check of the clock synchronisation from the transmit source.

PAM-5

This employs multi-level amplitude signalling. To encode 8 bits, 2⁸ = 256 codes or symbols, are required since there are 256 possible pattern combinations. A five level signal (e.g. -2v, -1v, 0v, 1v and 2v) called Pulse Amplitude Modulation 5 is used (This works in a similar manner to MLT-3). Bearing in mind that there are 4 separate pairs being used for transmission and reception of data, this gives us a possibility of 5⁴ = 625 codes to choose from when using all four pairs. Actually only four levels are used for data, the fifth level (0v) is used for the 4-dimensional 8-state Trellis Forward Error Correction used to recover the transmitted signal from the high noise.

If you plot time (nanoseconds) against voltage you will see an 'eye pattern' effect showing the different signal levels. Comparing a plot for MLT-3 against PAM-5 will demonstrate how that the separate levels for PAM-5 are less discreet. This is why extra convolution coding is used called Trellis coding, which uses Viterbi decoding for error detection and correction.

2 bits are represented per symbol and the symbol rate is 125Mbps in each direction on a pair because the clock rate is set at 125MHz. This gives 250Mbps data per pair and therefore 1000Mbps for the whole cable.

This type of encoding is used by Gigabit Ethernet. The data signals have distinct and measurable amplitude and phases relative to a 'marker signal'. Using this two way matrix allows more data bits per cycle, in the case of Gigabit Ethernet 1000Mbps is squeezed into 125MHz signals. The electronics are more complex and the technology is more susceptible to noise.

Thnx To Mr. R. E. Newman-Wolfe, University of Florida