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empty() returns the bool constant true if the string contains no characters; otherwise, it returns false A third form of string construction initializes one string object to a second For example,

string st3( st );

initializes st3 to be a copy of st How can we check that The equality operator compares two strings for equality, returning true if they are equal:

How can we copy one string to another The simplest method uses the assignment operator For example,

first deletes the storage containing the characters associated with st2, allocates the storage needed to contain the characters associated with st3, and then copies the characters associated with st3 It is also possible to concatenate two or more strings through the use of either the plus operator (+) or the somewhat strange-looking compound assignment operator (+=) For example, given the two strings

The advantage of a systematic code is that it simpli es reconstruction of the source words in case very few losses are expected In Figure 43 for example, two out of the k code-words arrived at destination are actual original words Hence, the system of equations that must be solved to reconstruct the original words includes k 2 equations instead of k By using xi GF (q = pr ), it is possible to construct encoding matrices with up to q 1 rows corresponding to the total number of non-null xi s of the eld The number of columns of the encoding matrix is instead k corresponding, as usual, to the total number of original source words, and the relation q 1 k must hold true As a result, the maximum size of the encoding matrix is (q 1) (q 1)..

string s1( "hello, " ); string s2( "world\n" );

signal state: state_type; begin --data_path f<=irreducible; f_n<=irreducible_n; process (clk) begin if clk event and clk= 1 then if load= 1 then u<=next_u; v<=next_v; c<=next_c; e<=next_e; m<=next_m; t<=next_t; u_m<=next_u_m; end if; end if; end process; process (mux_control, f_n, f, v, r, a, e, cc, t, deg_v, k, v_t_inverted, uu_m) begin case mux_control is when "00"=>next_u<=f; next_v<=a; next_c<=zero_polynomial; next_e<=one_polynomial; next_m<=conv_std_logic_vector(n, logn); next_t<=deg_v; next_u_m<=f_n; r_a<=a; k_v<=k; when "01";=>next_u<=v; next_v<=r; next_c<=e; next_e<=cc; next_m<=t; next_t<=deg_v; next_u_m<=uu_m; r_a<=r; k_v<=k; when "10"=>next_u<=r; next_v<=v; next_c<=cc; next_e<=e; next_m<=deg_v; next_t<=t; next_u_m<=uu_m; r_a<=r; k_v<=k; when others=>next_u<=r; next_v<=v; next_c<=cc; next_e<=e; next_m<=deg_v; next_t<=t; next_u_m<=uu_m; r_a<=r; k_v<=v_t_inverted; end case; end process; j<=m - t; selector1: selector port map (next_u, m, uu_m); selector2: selector port map (v, t, v_t); inverter: coef cient_inverter port map (v_t, v_t_inverted); multiplier1: coef cient_multiplier port map (u_m, v_t_inverted, k); multipliers1: for i in 0 to n-1 generate multiplier2: coef cient_multiplier port map (v(i), k, k_by_v(i)); end generate; shifter1: shifter port map (k_by_v, j, k_by_v_shifted); subtractors1: for i in 0 to n-1 generate subtractor1: subtractor port map (u(i), k_by_v_shifted(i), r(i)); end generate; multipliers2: for i in 0 to n-1 generate

we can concatenate the two strings to create a third string as follows:

file:///F|/WinDDK/resources/CPPPrimer/c++primerhtm (97 / 1065) [2001-3-29 11:32:03]

string s3 = s1 + s2;

Figure 4.3. The encoding/decoding process in matrix form, for systematic code (the top k rows of G constitute the identity matrix Ik ). y and G correspond to the grey areas of the vector and matrix on the right.

If, rather, we wanted to append s2 to s1 directly, then we would use the += operator:

s1 += s2;

Our initialization of s1 and s2 is made somewhat awkward by our including a blank space, a comma, and the newline Their presence limits the reusability of these string objects, although it serves our immediate need An alternative is to mix string objects and C-style character strings as follows:

const char *pc = ", "; string s1( "hello" ); string s2( "world" ); string s3 = s1 + pc + s2 + "\n";

The encoding matrix can further be extended with the identity matrix Ik to generate systematic codes that help simplify the decoding process Hence, the nal maximum size of the encoding matrix is as follows ((q 1) + kmax ) kmax = ((q 1) + (q 1)) (q 1) = 2(q 1) (q 1) where kmax is the maximum number of source words that can be encoded over GF(q) Applications A major hurdle in implementing a digital fountain through standard Reed Solomon codes (RS codes) is the unacceptably high computational time caused by both encoding and decoding It is of order O(n2 ), where n corresponds to the number of generated code-words The large decoding time for RS codes arises from the dense system of linear equations which is generated However, ef cient implementations of RS codes are actually feasible as has been shown in references 22 and 23.