g to send a message; this is not very economical if the number of useful words per minute received is compared to channel occupancy. This illustrates the tradeoff between redundancy and channel efficiency. Redundancy can be increased such that the error rate could approach zero. Meanwhile, the information transfer across the channel would also approach zero. Thus unsystematic redundancy is wasteful and merely lowers the rate of useful communication. On the other hand, maximum efficiency could be obtained in a digital transmission system if all redundancy 10.5 ERRORS IN DATA TRANSMISSION and other code elements, such as "start" and "stop" elements, parity bits, and other "overhead" bits, were removed from the transmitted bit stream. In other words, the channel would be 100% efficient if all bits transmitted were information bits. Obviously, there is a tradeoff of cost and benefits somewhere between maximum efficiency on a data circuit and systematically added redundancy. There is an important concept here that should not be missed. An entirely error-free channel does not exist. It is against the laws of nature. We may have a channel with an excellent error performance, but some few errors will persist. A performance parameter in these circumstances would be residual error rate. 10.5.2 Nature of Errors In binary transmission, an error is a bit that is incorrectly received. For instance, suppose a 1 is transmitted in a particular bit location and at the receiver the bit in that same location is interpreted as a 0. Bit errors occur either as single random errors or as bursts of errors. Random errors occur when the signal-to-noise ratio deteriorates. This assumes, of course, that the noise is thermal noise. In this case noise peaks, at certain moments of time, are of sufficient level as to confuse the receiver's decision, whether a 1 or a 0. Burst errors are commonly caused by fading on radio circuits. Impulse noise can also cause error bursts. Impulse noise can derive from lightning, car ignitions, electrical machine