6.22 Subtlies of coding

In the Huffman code, the bit sequences that represent individual symbols can have differing lengths so the bitstream index $m$ does not increase in lock step with the symbol-valued signal's index $n$ . To capture how often bits must be transmitted to keep up with the source's productionof symbols, we can only compute averages. If our source code averages $\langle B(A)\rangle$ bits/symbol and symbols are produced at a rate $R$ , the average bit rate equals $\langle B(A)\rangle R$ , and this quantity determines the bit interval duration $T$ .

A subtlety of source coding is whether we need "commas" in the bitstream. When we use an unequal number of bits to representsymbols, how does the receiver determine when symbols begin and end? If you created a source code that required a separation marker in the bitstream between symbols, it would be very inefficient sinceyou are essentially requiring an extra symbol in the transmission stream.

However, having a prefix code does not guarantee total synchronization: After hopping into the middle of a bitstream,can we always find the correct symbol boundaries? The self-synchronization issue does mitigate the use of efficientsource coding algorithms.

Another issue is bit errors induced by the digital channel; if they occur (and they will), synchronization can easily be losteven if the receiver started "in synch" with the source. Despite the small probabilities of error offered by good signalset design and the matched filter, an infrequent error can devastate the ability to translate a bitstream into a symbolicsignal. We need ways of reducing reception errors without demanding that $p_e$ be smaller.