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where n k is the number of redundant bits in a codeword For example, a (15, 11) code has an upper bound of approximately 006, while a (64, 32) code has an upper bound of approximately 23 10 10 It will be assumed, therefore, that the data are sent in coded blocks (referred to simply as blocks in the following) The receiver acknowledges receipt of each block by sending back a positive acknowledgment or ACK signal if no errors are detected in the block and a negative acknowledgment or NAK signal if errors are detected In what is termed stop and wait ARQ, the transmitter stores a copy of the block just transmitted and waits for the acknowledgment signal If a NAK signal is received, it retransmits the block, and if an ACK signals is received, it transmits the next block.

In either case, the delay between transmissions is about half a second, the round-trip time to and from a geostationary satellite This would be unacceptable in many applications What is required is continuous transmission of blocks incorporating the retransmission of corrupted blocks when these are detected Go back N ARQ achieves this by having the blocks and the acknowledgment signals numbered The transmitter must now be capable of storing the number of blocks N transmitted over the round-trip time and updating the storage as each ACK signal is received If the receiver detects an error in block i, say, it transmits an NAKi signal and refuses to accept any further blocks until it has received the correct version of block i The transmitter goes back to block i and restarts the transmission from there This means that block i and all subsequent blocks are retransmitted.

It is clear that a delay will only be encountered when an NAK signal is received, but there is the additional time loss resulting from the retransmission of the good blocks following the corrupted block The method can be further improved by using what is termed selective.

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 subsequent 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 recognizes which ones are repeats. The throughput of an ARQ system is defined at the ratio of the average 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 PA be the probability that a block is accepted; then, as shown in Taub and Schilling (1986), the throughputs are Go back N Selective repeat k n PA k n PA PA N(1 PA) (11.29) (11.30)

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

A price index relates prices in a speci c year, month, or quarter to prices during a reference period. For example, the consumer price index (CPI), the most frequently quoted price index, relates the prices that urban consumers paid for a xed basket of approximately 400 goods and services

In some situations you ll want your program to step through each item in a collection perhaps to check or alter some property of every element. This is termed iteration. Like all collections in VBA, Layers has built-in support for iteration using a For ... Each loop. The following example iterates the Layers collection, printing each Layer name to the Immediate or Debug window: Public Sub ListLayers() Dim objLayer As AcadLayer For Each objLayer In ThisDrawing.Layers Debug.Print objLayer.Name Next End Sub