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Overhead instead is a function of the decoding algorithm used and is de ned as the number of output symbols that the decoder needs to collect in order to recover the input symbols with high probability Different types of Raptor codes can be obtained depending on the type of erasure code C which is used for precoding and the particular degree distribution used in the second level encoding Hence, a complex precoding6 can be combined with a simple degree distribution of the LT encoder, or vice versa a simple precoding algorithm can be combined with a complex degree distribution In between these two extremes, other solutions are also possible Optimized Raptor codes applied to k original input symbols have the potential to generate an in nite stream of output symbols.

for ( int index = 0; index < 512; ++index ) ;

[PAA1996] C. Paar, A new architecture for a parallel nite eld multiplier with low complexity on composite elds. IEEE Trans. Comput., 45(7):856 861 (1996). [ULL1984] J. Ullman, Computational Aspects of VLSI, Computer Science Press, Maryland, 1984. [WOO2000] A. D. Woodbury, D. V. Bailey, and C. Paar, Elliptic curve cryptography on smart cards without coprocessors. IFIP CARDIS 71 92 (2000).

The first problem is readability What does it mean to test index against 512 What is the loop doing that is, what makes 512 matter (In this example, 512 is referred to as a magic number, one whose significance is not evident within the context of its use It is as if the number had been plucked from thin air) The second problem is maintainability Imagine that the program is 10,000 lines The use of the value 512 occurs in 4% of the code Of the 400 occurrences, 80% must be converted to 1024 To do that, we must understand which ones are to be converted and which are not Getting even one instance wrong breaks the program and requires us to go back and reexamine each use The solution to both problems is the use of an object initialized to 512 By choosing a mnemonic name, perhaps bufSize, we make the program more readable The test is now against the object rather than the literal constant:

The 320 occurrences no longer need to be found and converted in case bufSize is changed Rather, only the one line that initializes bufSize requires change Not only does this approach require significantly less work, but also the likelihood of making an error is reduced significantly The cost of the solution is one additional variable The value 512 is now said to be localized

int bufSize = 512; // input buffer size // for ( int index = 0; index < bufSize; ++index ) //

Any subset of symbols of size k(1 + ), for some > 0, is then suf cient to recover the original k input symbols with high.

file:///F|/WinDDK/resources/CPPPrimer/c++primerhtm (101 / 1065) [2001-3-29 11:32:03]

The problem with this solution is that bufSize is an lvalue It is possible for bufSize to be accidentally changed from within the program For example, here is a common programmer error:

// accidentally changes the value of bufSize if ( bufSize = 1 ) //

In C++, "=" is the assignment operator and "==" is the equality operator The programmer has accidentally changed bufSize's value to 1, and that results in a difficult-to-trace program error (Such an error is difficult to find because the programmer generally does not see the code as being wrong, and that is why many compilers issue a warning for this kind of assignment expression) The const type qualifier provides a solution It transforms an object into a constant For example,

6 Sometimes complex erasure codes can be used when intermediate symbols (code words in C) can be calculated of ine via preprocessing.

Type& Queue<Type>::remove() { }

A program that uses a member function instantiation need only include the header file before using the instantiation:

There are many data processing applications (e.g., image and voice processing), which use a large range of values and need a relatively high precision. In such cases, instead of encoding the information in the form of integers or xed-point numbers, an alternative solution is a oating-point representation ( 3). In the rst section of this chapter, a method is proposed for de ning a particular oating-point representation system as a function of the application speci cation. The next section is devoted to the algorithms for executing the basic arithmetic operations. The two following sections de ne the main rounding methods and introduce the concept of guard digit. Finally, the last few sections propose basic implementations of the arithmetic operations, namely, addition and subtraction, multiplication, division, and square root.

// ----- UserC ----#include "Queueh" int main() { // instantiation of Queue<int> Queue<int> *p_qi = new Queue<int>; int ival; // // ok: instantiation of Queue<int>::add( const int & ) p_qi->add( ival ); // }