G Leija-Hernández et al.: Análisis de Desempeño de la Codif. Convolucional en Sist. de Com. CDMA
Diciembre, 2009
Fig. 2 Process of a Convolutional Encoder (2,1,9) for r=1/2 and (3,1,9) for r=1/3
In consequence, each frame of k-bits produces an output frame of n-bits. The redundancy foreseen at the output is because of nb. Figure 2 shows a convolutional encoder (2,1,9), and the reason for these values is to maintain the probability of error below 10-2 and to obtain a coding rate of 1/2 and of 1/3. A reduced value of the coding velocity r points to a high degree of redundancy; this brings a more effective error control at the cost of incrementing the coded signal’s bandwidth [7]. To obtain an effective convolutional code with constraint length K and rate r, the following expression is suggested [6].
Pf <
L T (Z ) 2
(3)
T(Z) is the code generating function, and Z is obtained from (2):
Z = 2 1− R 0 − 1
(4)
Now, a wireless personal communication system with CDMA access technique, that uses convolutional coding with M-ary orthogonal signaling is considered [8]. Let b bits flowing through the input of the register, to select n successive M-ary signals generating a coding rate of R=b/n bits/symbol. The frame error probability of the L-bits, for a constraint length register of bK bits, is given by [6]:
Pf <
L 2
⎛ 2b −1 ⎞ 2 − bKRo / R ⎜⎜ ⎟⎟ − b [( Ro / R )− 1 ] ⎝ b ⎠1− 2
(5)
Using expression (5) we can find the frame error probability with respect to α = R0/R. In disperse spectrum modulation there exists a coding redundancy. Consequently, no limitation is imposed on the code rate. The convolutional code is convolutioned over another, i.e., redundancy bits are added to a block of data at the input.
JVR 4 (2009) 4 1-9
©Journal of Vectorial Relativity
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