Linear Recursive Sequence - LRS

Question 1

Why are linear recursive sequences used at a basic level?

Answer 1

To help maintain synchronicity

Question 2

Where are linear recursive sequences used

Answer 2

Over the horizon radars

Question 3

How do linear recursive systems help over the horizon radars ?

Answer 3

They given each radar pulse a unique sequence so that the receiver terminal can calculate the timings of the original data stream.

Question 4

What are the uses of linear recursive sequences?

Answer 4

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

Question 5

How is a linear recursive sequence generated ?

Answer 5

A shift register generator (SRG) known commercially as a linear feedback shift register (LFSR)

Question 6

What is a shift register generator made up of ?

Answer 6

An xor gate
Clock
Shift register

Question 7

What is a a shift register made of ?

What can they hold ?

Answer 7

Bistable cells

Which can independently hold a 1 or a 0

Question 8

Is the length of a shift register fixed ?

Answer 8

No, it is dependant on the size of the LRS being generated

Question 9

Where will there always be a tap point ?

Answer 9

The first cell

Question 10

What is the initial start condition of the shift register called ?

Answer 10

The fill

Question 11

What do the tapped cells link to ?

Answer 11

They are used to feed the xor gate

Question 12

How is the output of the xor gate calculated

Answer 12

They are modulo 2 added 
00 = 0
01 = 1
10= 1
11 = 0

Question 13

Where does the put out of the xor gate go ?

Answer 13

Feeds back into the shift register

Question 14

What can the initial fill not be ?

Answer 14

All 0’s

Question 15

How can the arrangement of cells and tap points be defined ?

Answer 15

Numerically 1+2 = 5
Algebraic / generating polynomial PG - pg = x 0 + x 1 + x 4 = 0
Standard form R4(0,1,4)

Question 16

What is the equation for a maximal length linear recursive sequence ?

Answer 16

2 n - 1

N = the number of cells in the shift register

Question 17

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 ?

Answer 17

Two

Even

Question 18

What is the equation for a non maximal length linear recursive sequence?

Answer 18

< 2n -1

Question 19

How does an additive randomiser work ?

Answer 19

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

Question 20

What is the result of an error within an additive randomiser ?

Answer 20

However many errors in the transmission will also be the amount of errors in the output data

Question 21

What are the advantages of an additive randomiser ?

Answer 21

They are not prone to burst errors

Question 22

What are the disadvantages of an addictive randomiser ?

Answer 22

An external sync area is required which adds over head

The frame width is still evident in the transmitted data

Question 23

What are the two randomiser associated with linear recursive sequences?

Answer 23

The additive randomiser and the feed trough randomiser

Question 24

Where is the input of a feed through randomiser ?

Answer 24

It is modulo 2 added with an Lrs after the first xor gate from which feeds the shift register

Question 25

What are the advantages of a feed through randomiser ?

Answer 25

They are self synchronising and the data appears random

Question 26

What are the disadvantages of a feed through randomiser ?

Answer 26

They are prone to producing errors or burst errors

One error = 1 x the number of tap points

Question 27

What are two methods of error detection and correction?

Answer 27

Cyclic redundancy checks

A checksum

Question 28

What similarities and differences do checksums and cyclic redundancy checks have to a linear recursive sequence?

Answer 28

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

Question 29

What is a checksum ?

Answer 29

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

Question 30

What is the procedure that produces a checksum called ?

Answer 30

A checksum function or a checksum algorithm

Question 31

What is a cyclic redundancy check ?

Answer 31

It is a non secure function designed to detect accidental changes in raw communications or computer data

Question 32

Where are cyclic redundancy checks often used ?

Answer 32

On digital networks and storage devices

Question 33

What is a feature of a cyclic redundancy check ?

Answer 33

The check code adds zero information to the data

Question 34

How does a cyclic redundancy check work ?

Answer 34

It calculates a short fixed length of binary sequence for each block of data.

It then sends and Stores them both together

Question 35

How does a device check for errors using a cyclic redundancy check?

Answer 35

It repeats the initial calculation that generated the first cyclic redundancy check and compares the stored one with the new one

Question 36

Why are cyclic redundancy checks popular ?

3 advantages

Answer 36

Because they are easily implemented in binary hardware

Easy to analyse mathematically

Useful in detecting common errors cause by noise

Question 37

What are the disadvantages of a cyclic redundancy checks ?

Answer 37

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