Linear Recursive Sequence - LRS Flashcards
Why are linear recursive sequences used at a basic level?
To help maintain synchronicity
Where are linear recursive sequences used
Over the horizon radars
How do linear recursive systems help over the horizon radars ?
They given each radar pulse a unique sequence so that the receiver terminal can calculate the timings of the original data stream.
What are the uses of linear recursive sequences?
Selcal - selective calling Encryption Code division multiple access - CDMA Frequency hopping But error test rate Elint Randomisation Direct sequence spread spectrum Synchronisation Echo cancellation Forward error correction / error detection and correction
How is a linear recursive sequence generated ?
A shift register generator (SRG) known commercially as a linear feedback shift register (LFSR)
What is a shift register generator made up of ?
An xor gate
Clock
Shift register
What is a a shift register made of ?
What can they hold ?
Bistable cells
Which can independently hold a 1 or a 0
Is the length of a shift register fixed ?
No, it is dependant on the size of the LRS being generated
Where will there always be a tap point ?
The first cell
What is the initial start condition of the shift register called ?
The fill
What do the tapped cells link to ?
They are used to feed the xor gate
How is the output of the xor gate calculated
They are modulo 2 added 00 = 0 01 = 1 10= 1 11 = 0
Where does the put out of the xor gate go ?
Feeds back into the shift register
What can the initial fill not be ?
All 0’s
How can the arrangement of cells and tap points be defined ?
Numerically 1+2 = 5
Algebraic / generating polynomial PG - pg = x 0 + x 1 + x 4 = 0
Standard form R4(0,1,4)
What is the equation for a maximal length linear recursive sequence ?
2 n - 1
N = the number of cells in the shift register
What is the minimum number of tap points for a maximal linear recursive sequence?
Will it be an even or odd amount of tap points ?
Two
Even
What is the equation for a non maximal length linear recursive sequence?
< 2n -1
How does an additive randomiser work ?
It generates a linear recursive sequence of a given length and modulo - 2 adds it to the data repeatedly.
The data to be transmitted is modulo 2 added to the Lrs data
What is the result of an error within an additive randomiser ?
However many errors in the transmission will also be the amount of errors in the output data
What are the advantages of an additive randomiser ?
They are not prone to burst errors
What are the disadvantages of an addictive randomiser ?
An external sync area is required which adds over head
The frame width is still evident in the transmitted data
What are the two randomiser associated with linear recursive sequences?
The additive randomiser and the feed trough randomiser
Where is the input of a feed through randomiser ?
It is modulo 2 added with an Lrs after the first xor gate from which feeds the shift register
What are the advantages of a feed through randomiser ?
They are self synchronising and the data appears random
What are the disadvantages of a feed through randomiser ?
They are prone to producing errors or burst errors
One error = 1 x the number of tap points
What are two methods of error detection and correction?
Cyclic redundancy checks
A checksum
What similarities and differences do checksums and cyclic redundancy checks have to a linear recursive sequence?
They both employ a data stream generated in the same way as an Lrs
However they are used for error detection and correction rather than synchronisation
What is a checksum ?
It is a fixed sized datum or data code that is generated from the data to be sent.
It can be regenerated at anytime to compare with the stored checksum, to check for errors in the data
What is the procedure that produces a checksum called ?
A checksum function or a checksum algorithm
What is a cyclic redundancy check ?
It is a non secure function designed to detect accidental changes in raw communications or computer data
Where are cyclic redundancy checks often used ?
On digital networks and storage devices
What is a feature of a cyclic redundancy check ?
The check code adds zero information to the data
How does a cyclic redundancy check work ?
It calculates a short fixed length of binary sequence for each block of data.
It then sends and Stores them both together
How does a device check for errors using a cyclic redundancy check?
It repeats the initial calculation that generated the first cyclic redundancy check and compares the stored one with the new one
Why are cyclic redundancy checks popular ?
3 advantages
Because they are easily implemented in binary hardware
Easy to analyse mathematically
Useful in detecting common errors cause by noise
What are the disadvantages of a cyclic redundancy checks ?
They are not suitable in detecting intentional alteration of data.
There is no authentication and a crc and data could be easily edited even when encrypted
