  Random coding, expurgated and sphere packing bounds are derived by method of
types and method of graph decomposition for $E$-capacity of discrete memoryless
channel (DMC). Three decoding rules are considered, the random coding bound is
attainable by each of the three rules, but the expurgated bound is achievable
only by maximum-likelihood decoding. Sphere packing bound is obtained by very
simple combinatorial reasonings of the method of types. The paper joins and
reviews the results of previous hard achievable publications.
