3.3 Convolutional Encoder

Another step in the CDMA "hardening" process is what is referred to as a Convolution Encoder, which effectively convolves the energy of several bits together in such a way that it is possible to extract that bit energy back out of the group using the reverse process. In other words, the convolutional encoding process maps a bit out across several of its adjoining neighbors so that the decoding process at the receiver is able to extract the original value of this bit back out of these adjoining bits if necessary (e.g., bit error due to noise corruption) provided they are not themselves corrupted. Figure 3.12 shows two possible convolutional encoders, as well as the convolution of a segment of a bit stream over several clock cycles (note that there is some flexibility about where we place the taps in the encoder which feeds into the Modulo-2 adders, and therefore, such encoders can be drawn in a variety of different ways). The "K" parameter specifies the number of bits involved in the convolution process (i.e., the number of registers in our shift register), while the "rate ¹/ ₂" refers to the fact that for every bit injected into the encoder, we get two bits out (here, u1 and u2). This is an indication of the amount of the redundancy created in the output bit stream by the encoding process. IS-95 mobiles use a rate ¹/ ₃ encoder, which indicates that for every bit injected into...