Editing Scrambler (section)

== Types of scramblers ==

=== Additive (synchronous) scramblers ===
[[File:Scrambler randomizer additive.png|right|thumb|350px|An additive scrambler (descrambler) used in [[Digital Video Broadcasting|DVB]]]]

''Additive scramblers'' (they are also referred to as ''synchronous'') transform the input data stream by applying a [[Pseudorandom binary sequence|pseudo-random binary sequence]] (PRBS) (by modulo-two addition). Sometimes a pre-calculated PRBS stored in the [[read-only memory]] is used, but more often it is generated by a [[linear-feedback shift register]] (LFSR).

In order to assure a synchronous operation of the transmitting and receiving LFSR (that is, ''scrambler'' and ''descrambler''), a ''[[Syncword|sync-word]]'' must be used.

A sync-word is a pattern that is placed in the data stream through equal intervals (that is, in each [[Frame (networking)|frame]]). A receiver searches for a few sync-words in adjacent frames and hence determines the place when its LFSR must be reloaded with a pre-defined ''initial state''.

The ''additive descrambler'' is just the same device as the additive scrambler.

Additive scrambler/descrambler is defined by the polynomial of its LFSR (for the scrambler on the picture above, it is <math>1+z^{-14}+z^{-15}</math>) and its ''initial state''.

=== Multiplicative (self-synchronizing) scramblers ===
[[File:Scrambler randomizer multiplicative scrambler.png|right|thumb|350px|A multiplicative scrambler used in V.34 recommendation]]

[[File:Scrambler randomizer multiplicative descrambler.png|right|thumb|350px|A multiplicative descrambler used in V.34 recommendation]]

''Multiplicative scramblers'' (also known as ''feed-through'') are called so because they perform a ''multiplication'' of the input signal by the scrambler's [[transfer function]] in [[Z-transform|Z-space]]. They are discrete [[Linear time-invariant system|linear time-invariant]] systems.
A multiplicative scrambler is recursive, and a multiplicative descrambler is non-recursive. Unlike additive scramblers, multiplicative scramblers do not need the frame synchronization, that is why they are also called ''self-synchronizing''. Multiplicative scrambler/descrambler is defined similarly by a polynomial (for the scrambler on the picture it is <math>1+z^{-18}+z^{-23}</math>), which is also a ''transfer function'' of the descrambler.

=== Comparison of scramblers ===
Scramblers have certain drawbacks: 
* Both types may fail to generate random sequences under worst-case input conditions. 
* Multiplicative scramblers lead to error multiplication during descrambling (i.e. a single-bit error at the descrambler's input will result in ''w'' errors at its output, where ''w'' equals the number of the scrambler's feedback taps). 
* Additive scramblers must be reset by the frame sync; if this fails, massive error propagation will result, as a complete frame cannot be descrambled. (Alternatively if you know what was sent, the scrambler can be synchronized)
* The effective length of the random sequence of an additive scrambler is limited by the frame length, which is normally much shorter than the period of the PRBS. By adding frame numbers to the frame sync, it is possible to extend the length of the random sequence, by varying the random sequence in accordance with the frame number.