Appendix 4.A
Modified Chernoff Bound and Some Applications
One of the most important problems in analysis of communication systems is error probability evaluation. The exact computation of error probability for coded system is a hard, if not irresolvable, task for many practical situations. That is why the upper bounding of error probability is a common method in system performance estimation. In many cases the error probability can be computed using probability of large deviation of a random variable. One of the most powerful techniques is based on usage of so called Chernoff bound. This bound is very well-known and it is mentioned and referenced practically in any monograph and textbook on coding, information and communication theory.
Let Z be a random value. It is necessary to evaluate the value of probability P = Pr[Z 
0]. This probability is equal by definition to:
where wZ (·) is probability density function of the random value Z. Straightforward computation of P by (4.A1) can be difficult or even not possible. For example, the explicit expression for probability density function wZ (·) might be unknown. The following inequality gives the expression for common Chernoff bound for probability ...
