Fig. 1.19 Conditional probability distribution of the received bit position. Finally, notice that in normal applications there is no error-checking capability provided within CCITT recommendation G.704. However, if there is a need to provide additional protection against imitation of frame alignment signals or where there is a need for an enhanced error-monitoring capability, then the international bit can be used for the cyclic redundancy check (CRC). Higher-order multiplexing is accomplished by multiplexing the standard TDM frames. In this case each of the PCM 64-kbit/s channels is referred to as DSO in the United States and 0-order system (or E0) in Europe. Table 1.2 summarizes the American and European digital hierarchies. Because multiplexing of the tributaries needs very accurate synchroniza- tion, it is necessary to bring all the bits to exactly the same rate, which is achievable by employing retiming buffers. Transmission Performance After the speech data is converted into a multiplexed bitstream, it is transmitted over a communication channel. This section discusses the issues and challenges related to the transmission of digital speech signals over error-prone transmission channels. Digital Data Transmission After an analogue voice signal is converted to digital format, it is transmitted to the receiver through a communication channel where random noise is added to the PCM signal. The impact of this noise can appear as erroneous digits in the codeword, which can mislead the decoder. Figure 1.19 shows the conditional probability distribution of the received bit posi- Transmission Performance tion where P(x I X0) represents the probability distribution when 0 bits are sent and P(x X1) corresponds to the case where a marked bit is sent. Assuming an equal frequency of 0 and marked bits, the optimum performance is achieved when the decision threshold, S, is placed exactly in the middle of the two constellation points (i.e., The shaded parts of the figure represent the area where an erroneous decision is made