Communications I Dr. Mohammed Hawa Introduction to Digital - FET

8. M-ary CodingAll the line coding schemes discussed above are called binary codes, since thenumber of bits per second is identical to the number of symbols per second (calledbaud rate). We say that for binary signaling:f0, data bit rate [in units of bit/s] = fsymb, symbol rate [in units of baud]Notice that a symbol is defined as a waveform pattern that the line code has for acertain period of time before switching to another waveform pattern (i.e., anothersymbol).In M-ary signaling, on the other hand, a cluster of bits is grouped to represent onesymbol. For example, in the 4-ary (also called Quaternary) case, two bits are groupedinto one symbol. The two bits can be in one of 4 possible states, which means that thesymbol can take M=4 different symbols. The following table shows a possiblemapping of two bit values to four symbols of a Quaternary signal. Thecorresponding line code for this Quaternary signal representing the bit stream1110110001001 is shown next.Bits Symbol00 -5 V01 -10 V10 5 V11 10 VM=4levelsClockData10 V1 1 1 0 1 1 0 0 0 1 0 0 15 VCode-5 V0-10 VT 0 Bit TimeT symb Symbol TimeT sSampling Time (assuming 8 bits per sample)Quaternary CodeNotice that a symbol time Tsymb is now twice the bit time T0. This means that there arehalf as much symbol transitions as there are bit transitions. We can say that:symbol rate [in units of baud] = (½) × data bit rate [in units of bit/s]For a general M-ary line coding scheme, we have:symbol rate [in units of baud] = (1/log2 (M)) × data bit rate [in units of bit/s]16