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Figure 11.14 Shannon limit (BPSK) TPC 4K blocks TPC 16K blocks Reed-Solorn on/Vlterbi LDPC 30K LDPC 16K

15 Fruit ies are being bred in an enclosure that can hold a maximum of 640 ies If the ies grow exponentially with growth constant K = 005 per day, how long will it take an initial population of 20 to ll the enclosure (Recall that ln 2 06931) 3616 A certain chemical decomposes exponentially Assume that 200 grams become 50 grams in 1 hour How much will remain after 3 hours 3617 If 100 bacteria in a colony reproduce exponentially and in 12 hours there are 300 bacteria, how many bacteria are in the colony after 72 hours 3618 If the world population in 1990 was 45 billion and it is growing exponentially with growth constant K = 1 ln 2 when time 5 is measured in years, nd the population in the year 2020 36.

FEC performance of Comtech AHA 4701 LDPC coder. (Courtesy of A. Summers Comtech AHA.)

RobotBASIC does not display the simulated robot in three-dimensional graphics, however, you will nd that the robot has all of the sensors you would expect to nd on a hobby robot as well as a few that most people wish they had the means to implement. Other simulators may have sophisticated graphics but displaying the robot in three dimensions does not enhance the functionality of simulations for a robot that moves in two dimensions. RobotBASIC is easy to use. It is a BASIC-like language that is easy to learn, even for people who have never programmed before. A teacher can utilize RobotBASIC to make even sixth graders excited and productive in only a few hours, and they won t just be learning to play with a robot, they will be developing signi cant problem solving skills and learning the principles needed to program a computer in any language. RobotBASIC can be used to create challenges appropriate to various age groups. Even though RobotBASIC is easy enough for beginners, you will nd it is also powerful enough to be used by sophisticated hobbyists and experienced programmers. It has all the standard ow-control structures and a virtually unlimited space for variables and arrays. As a RobotBASIC programmer you have a full complement of graphics commands and functions for manipulating strings. The mathematic functions available include the ones you would expect in any powerful scienti c calculator, but you will also nd matrix operations seldom found in any language.

be noticed that the estimate from any given parity node is not included in the new estimate sent to that parity node. This process is repeated a number of times (iterated) before a final hard decision is made. Turbo codes and LDPC codes are being employed in a number of satellite systems with a resulting improvement in channel performance, for example the Digital Video Broadcast S2 standard (DVB-S2) employs LDPC as the inner code in its FEC arrangement (Breynaert, 2005, Yoshida, 2003), and the DVB-RCS plans to use turbo codes (talk Satellite, 2004). The performance of a number of codes is shown in Fig. 11.14. 11.12 Automatic Repeat Request (ARQ) Error detection without correction is more efficient than FEC in terms of code utilization. It is less complicated to implement, and more errors can be detected than corrected. Of course, it then becomes necessary for the receiver to request a retransmission when an error has been detected. This is an automatic procedure, termed automatic repeat request (ARQ). The request for retransmission must be made over a low-bit-rate channel where the probability of bit error can be kept negligibly small. Because of the long round-trip delay time, on the order of half a second or more, encountered with geostationary satellites, ARQ is only suitable for transmission that is not sensitive to long delays. ARQ is normally used with block encoding. An estimate of the probability of an error remaining undetected can be made. With an (n, k) block code, the number of datawords is 2k, and

19 Bacteria in a culture growing exponentially increase from 100 to 400 in the rst hour (a) What will be the population in 15 hours (b) What is the average number present in the rst 2 hours 3620 Prove Cauchy s extended mean-value theorem: If f and g are differentiable in (a, b) and continuous on [a, b], and if g (x) = 0 for all x in (a, b), then there exists a point c in (a, b) such that f (c) f (b) f (a) = g(b) g(a) g (c).

8.5 Summary