  This work studies the deviations of the error exponent of the constant
composition code ensemble around its expectation, known as the error exponent
of the typical random code (TRC). In particular, it is shown that the
probability of randomly drawing a codebook whose error exponent is smaller than
the TRC exponent is exponentially small; upper and lower bounds for this
exponent are given, which coincide in some cases. In addition, the probability
of randomly drawing a codebook whose error exponent is larger than the TRC
exponent is shown to be double-exponentially small; upper and lower bounds to
the double-exponential exponent are given. The results suggest that codebooks
whose error exponent is larger than the error exponent of the TRC are extremely
rare. The key ingredient in the proofs is a new large deviations result of type
class enumerators with dependent variables.
