Universal random access error exponents for codebooks with different word-lengths

Csiszár's channel coding theorem for multiple code-books is generalized allowing the codeword lengths differ across codebooks. Also in this case, for each codebook an error exponent can be achieved that equals the random coding exponent for this codebook alone, in addition, the overload detection failure probability tends to 0. This is proved even for sender and receiver not knowing the channel. As a corollary, a substantial improvement is obtained when the sender knows the channel.