Scrambler (randomizer)
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In telecommunications and recording, a scrambler (often erroneously referred to as a randomizer) is a device that manipulates a data stream before transmitting. The manipulations are reversed by a descrambler at the receiving side. Scrambling is widely used in satellite, radio relay communications and PSTN modems. A scrambler can be placed just before a FEC coder, or it can be placed after the FEC, just before the modulation or line code. A scrambler in this context, has nothing to do with encrypting, as the intent is not to render the message unintelligeable, but to give the transmitted data useful engineering properties.
A scrambler replaces sequences into other sequences without removing undesirable sequences, and as a result it changes the probability of occurrence of vexatious sequences. Clearly it is not foolproof as there are input sequences that yield all-zeros, all-ones, or other undesirable periodic output sequences. A scrambler is therefore not a good substitute for a line code, which, through a coding step, removes unwanted sequences.
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[edit] Purposes of scrambling
There are two main reasons why scrambling is used:
- It facilitates the work of a timing recovery circuit, an automatic gain control and other adaptive circuits of the receiver (eliminating long sequences consisting of '0' or '1' only).
- It eliminates the dependence of a signal's power spectrum upon the actual transmitted data, making it more dispersed to meet maximum power spectral density requirements (because if the power is concentrated in a narrow frequency band, it can interfere with adjacent channels due to the cross modulation and the intermodulation caused by non-linearities of the receiving tract).
[edit] Types of scramblers
- Additive (synchronous) scramblers
- Multiplicative (self-synchronizing) scramblers
[edit] Additive (synchronous) scramblers
Additive scramblers (they are also referred to as synchronous) transform the input data stream by applying a 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 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). 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 1 + x14 + x15) and its initial state.
[edit] Multiplicative (self-synchronizing) scramblers
Multiplicative scramblers are called so because they perform a multiplication of the input signal by the scrambler's transfer function in Z-space. They are discrete 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 1 + x18 + x23), which is also a transfer function of the descrambler.
[edit] 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 into 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.
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.
