Reference no: EM131100443
(Run-length coding) Suppose X1, X2 . is a sequence of binary random symbols with pXa = 0
9 and pXb = 0.1. We encode this source by a variableto-variable-length encoding technique known as run-length coding. The source output is first mapped into intermediate digits by counting the number of occurrences of a between each
b. Thus an intermediate output occurs on each occurence of the symbol b. Since we do not want the intermediate digits to get too large, however, the intermediate digit 8 is used on the eighth consecutive a, and the counting restarts at this point. Thus, outputs appear on each b and on each eighth
a. For example, the first two lines below illustrate a string of source outputs and the corresponding intermediate outputs: ba
The final stage of encoding assigns the codeword 1 to the intermediate integer 8, and assigns a 4 bit codeword consisting of 0 followed by the 3 bit binary representation for each integer 0 to 7. This is illustrated in the third line above.
(a) Show why the overall code is uniquely decodable.
(b) Find the expected total number of output bits corresponding to each occurrence of the letter
b. This total number includes the 4 bit encoding of the letter b and the 1 bit encodings for each consecutive string of eight occurrences of a preceding that letter b.
(c) By considering a string of 1020 binary symbols into the encoder, show that the number of occurrences of b per input symbol is, with very high probability, very close to 0.1. (d) Combine parts (b) and (c) to find L, the expected number of output bits per input symbol.
|
What change occurs organizationally
: What Change Occurs Organizationally? A community liaison officer (CLO) in each police precinct. Job duties of the CLO will include attending community meetings and listening to community concerns in order to determine an appropriate response.
|
|
Find the mean and variance of na
: One point of this exercise is to illustrate that the Chebyshev inequality used in bounding PrT in the text is very weak (although it is a strict bound, whereas the Gaussian approximation here is relatively accurate but not a bound). Another point..
|
|
Prepare a report to be distributed internally to department
: Prepare a 2- to 3-page report to be distributed internally to department employees on "Centervale Policing, a Community-Based Approach."
|
|
Civilization broadcasting a signal
: Consider a civilization broadcasting a signal with a power of 1.4×104 watts. The Arecibo radio telescope, which is about 300 meters in diameter, could detect this signal if it is coming from as far away as 118 light-years. Suppose instead that the..
|
|
Show why the overall code is uniquely decodable
: By considering a string of 1020 binary symbols into the encoder, show that the number of occurrences of b per input symbol is, with very high probability, very close to 0.1. (d) Combine parts (b) and (c) to find L, the expected number of output bi..
|
|
Pairs of jeans to the cost of the jeans
: Look at the table that reprecents the local store (1 pair or jean $24 ,2 pair of jean $48 , 3 pair of jean $72 ) for each row in the table , find the ratio of the number of pairs of jeans to the cost of the jeans.
|
|
The good homes construction
: Reconsider Prob. 10.5-4 involving the Good Homes Construction Co. project to construct a large new home. Michael Dean now has generated the plan for how to crash this project (as given as an answer in the back of the book).
|
|
Expected profit per warranty
: If the store charges $15 for the extended warranty, what will their expected profit per warranty be? If the company sells 100,000 projectors and 15% of the customers purchase the extended warranty, what will their expected profits from extended wa..
|
|
Obtaining future contracts for defense work
: Reconsider the Lockhead Aircraft Co. problem presented in Prob. 10.4-6 regarding a project to develop a new fighter airplane for the U.S. Air Force. Management is extremely concerned that current plans for this project have a substantial likelihoo..
|