Mobile Wireless Communications in .NET Encode Code 128C in .NET Mobile Wireless Communications

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Mobile Wireless Communications using .net framework todraw code-128c on web,windows application How to Use Visual Studio 2010 deinterleaver c*0 c ML decoder 1 interleaver ML decoder 2 interleaver c *2. deinterleaver output Figure 7.15 Iterative turbo decoder for turbo encoder of Fig. 7.14 fed to both encoders, a s well as to the decoders used at the receiver to retrieve the input bit sequence. Pseudo-random scrambling, using a long block size, is found to provide the best interleaver performance: the longer the interleaver size, the better the performance (Vucetic and Yuan, 2000). The performance of turbo codes is again found to depend on a Hamming-type free distance (Berrou and Glavieux, 1996; Vucetic and Yuan, 2000).

Good codes can therefore be found through a search procedure involving the Hamming distance (Vucetic and Yuan, 2000). A maximum-likelihood approach similar to the procedure mentioned in our discussion of convolutional decoding is used to determine the form of the decoder at the receiver. The resultant decoder appears as a serial concatenation of two decoders with the same interleaver as used at the transmitter separating the two (Berrou et al.

, 1993; Berrou and Glavieux, 1996; Vucetic and Yuan, 2000). Successive iteration is required to attain the best performance. As an example, the decoder for the case of the rate-1/3 turbo encoder of Fig.

7.14 appears in Fig. 7.

15 (Vucetic and Yuan, 2000). The symbols c0 , c1 , and c2 are used, respectively, to represent the received signals corresponding to the three transmitted signals shown in Fig. 7.

14. The transmitted signals are assumed to have passed through a channel of known properties such as one producing random fading, additive gaussian noise, etc. The speci c form of the two maximum-likelihood decoders ML1 and ML2 shown connected in series in Fig.

7.15 depends on the channel properties, as well as the form of the encoders RSC1 and RSC2 of Fig. 7.

14. Note that received signals c0 and c1 are fed into the rst decoder ML1; the received signal c2 is fed into the second decoder ML2. ML2 also receives as inputs the interleaved output.

Coding for error detection and correction of ML1 as well as the interleaved form of received signal c0 . The output of ML2 is fed back to ML1 to form the (iterated) third input to that device. It is this feedback loop that gives the name turbo coder to this coding system, based on the principle of the turbo engine.

Delays introduced by the ML decoders, interleavers, and the deinterleaver must be accounted for, but are not shown in Fig. 7.15.

Iteration continues until convergence to the best possible performance is attained. For large size interleavers of 4096 bits or more, 12 to 18 iterations are typically needed to attain convergence (Vucetic and Yuan, 2000). The effect of using turbo codes on Rayleigh fading channels has been presented in Hall and Wilson (1998) and is summarized as well in Vucetic and Yuan (2000).

Simulation results for rate-1/3 turbo codes show that in this environment they can achieve a performance within 0.7 dB of the capacity possible for this channel. This represents a coding gain of over 40 dB, as contrasted to uncoded PSK! (Recall from 6 that PSK operating over a fading channel requires Eb /N0 = 24 dB to achieve a bit error probability of 0.

001. This increases to 44 dB to achieve a bit error probability of 10 5 .) Vucetic and Yuan (2000) contains as well information on some of the turbo coders adopted for use with the third-generation cellular systems to be discussed in 10.

. Problems 7.1 (a) Show that one p arity-check bit, chosen to be the mod-2 sum of a block of k information bits, can be used to detect an even number of errors among the information bits. Check this result with a number of bit patterns of varying size.

(b) Repeat (a) for the case of odd-parity checking. Consider the (7, 3) code of equation (7.2).

(a) Show that this code generates the eight codewords of Table 7.1. (b) Show that this code is represented by the P, G, and H matrices of (7.

6), (7.7), and (7.15), respectively.

(c) Write the HT matrix of this code. (d) Find the syndrome s of each of the codewords of Table 7.1 if the received code vector has an error in its second digit.

Compare this vector with the appropriate column of the H matrix. The systematic (7, 4) block code has the generator matrix G written below. 1 0 0 0 1 0 1 0 1 0 0 1 1 1 G= 0 0 1 0 1 1 0 0 0 0 1 0 1 1 (a) Find the P matrix of this code and compare with that of the (7, 3) code.

(b) Find the parity-check matrix H and its transpose HT and compare with those of the (7, 3) code..
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