Page 366 - Satellite Communications, Fourth Edition

346 Chapter Eleven

repeat ARQ, where only a correct version of the corrupted block is
retransmitted, and not the subsequent blocks. This creates a storage
requirement at the receiver because it must be able to store the sub-
sequent blocks while waiting for the corrected version of the corrupted
block.
It should be noted that in addition to the ACK and NAK signals, the
transmitter operates a timeout clock. If the acknowledgement signal
(ACK or NAK) for a given block is not received within the timeout
period, the transmitter puts the ARQ mechanism into operation. This
requires the receiver to be able to identify the blocks so that it recog-
nizes which ones are repeats.
The throughput of an ARQ system is defined at the ratio of the aver-
age number of data bits accepted at the receiver in a given time to the
number of data bits that could have been accepted if ARQ had not been
used. Let P be the probability that a block is accepted; then, as shown
A
in Taub and Schilling (1986), the throughputs are
k P A
Go back N (11.29)
n P N(1 P )
A
A
k
Selective repeat P (11.30)
n A
Typically, for a BCH (1023, 973) code and N 4, the throughput for
go back N is 0.915, and for selective repeat, 0.942.
It is also possible to combine ARQ methods with FEC in what are
termed hybrid ARQ systems. Some details will be found in Pratt and
Bostian (1986).

11.13 Problems and Exercises
11.1. Explain in your own words how error detection and error correction differ.
Why would FEC normally be used on satellite circuits?

11.2. A transmission takes place where the average probability of bit error is
8
6
10 . Given that a message containing 10 bits is transmitted, what is the
average number of bit errors to be expected?
11.3. A transmission utilizes a code for which k 7 and n 8. How many
codewords and how many datawords are possible?

11.4. A triple redundancy coding scheme is used on a transmission where the
5
probability of bit error is 10 . Calculate the probability of a bit error occurring
in the output when (a) error detection only is used and (b) when error correction
with majority voting is implemented.