ddition and subtraction are not equivalent, SO the distinction matters. For nonbinary systems, multiplication and addition operations can be implemented using simple logic. Types of Error If the physical cause of digit errors is such that any digit is as likely to be affected as any other, the errors are described as random. A typical cause of random errors is thermal noise in the received signal. Other types of interference, however, might make it likely that when an error occurs, several symbols in succession will be corrupted; this is known as a burst error. A typical cause of burst errors is interference. Although the true behavior of the channel can be more complex than either of these simple models, the random error and burst error models are simple, effective, and universally used for describing channel char- acteristics and ECC performance. A channel used for transmitting binary digits is known as a binary channel, and if the probability of error is the same for Os and 1s, the channel is called a binary symmetric channel. The probability of error in binary digits is known as the Bit Error Rate (BER). Coding Gain Coding gain is a parameter commonly used for evaluating the effectiveness of an error correcting code and hence for comparing codes. It is defined as the saving in energy per source bit of information for the coded system, relative to an uncoded system delivering the same BER, and is expressed as a ratio in dB. The effects of both error correction and the increase in transmission rate by a factor of n/k must be included when calculating the coding gain. Chapter 4 Coding Criteria for Choosing a Code The primary objective of ECC is to achieve a desired end-to-end probability of either uncorrected or undetected digit errors. The choice of code will depend on the error characteristics of the channel (particularly the random and burst error probabilities). The other important factors are likely to be the value of n/k (the increase in transmission rate over the channel) and the implementation complexity