• Journal of Advanced Navigation Technology
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• v.11 no.4
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• pp.447-453
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• 2007

In this letter, we derive the Gallager random coding bound for discrete memoryless channels purely by simple manipulations of algebraic inequalities rather than invoking conceptually difficult random coding arguments. Gallager random coding bound is a very useful tool in information and coding theory due to its applicability to situations in which it is difficult to determine the decision regions and due to the fact that it can be used to derive the channel coding theorem. The readers will find it relatively easy to apply to many practical problems of interest the step-by-step algebraic derivations of the Gallager random coding bound with appropriate modifications.