symbols in a second and each of them carries 3 bits (with 4 bits, the maximum bit rate would be Transmission exceeded). The number of different symbols that can be used is 23 = 8 and this depends only on the S/N maximum, not on bandwidth. 4.4 Coding We have described modulation as the processing of a signal for efficient trans- mission in a different frequency band than where the information originally exists. Coding is a digital symbol processing operation in which the digital form of the information is changed for improved communication. In general, coding contains many different processes, such as ciphering, compression, and error control coding. For ciphering, the transmitter and the receiver may simply perform an exclusive-or operation with data and a ciphering sequence known only by the transmitter and receiver. An eavesdropper is not able to detect information content without knowing the ciphering sequence. Most modern systems use error control codes for handling of transmis- sion errors. By appending extra check digits to the transmitted data, we can detect or even correct errors that occur on the line. Error control coding increases both the required bandwidth (data rate increases) and the hardware and software complexity, but it pays off in terms of nearly error-free digital communication even when the S/N is low. Still another purpose for coding is for compressing information. By using data compression we can reduce the disk space needed to store data in a computer. In the same way we can decrease the required data rate on the line to a small fraction of the original information data rate. We could, for exam- ple, use very short codes for the most common characters instead of the full seven-bit ASCII code. Rarely needed characters would use long codes and the total data rate would be reduced. Some compression schemes for voice and video information were introduced in Chapter 3. The study of compression methods is a complex matter and will not be covered in any detail here. From now on we concentrate on