Universal Random Access Error Exponents for Codebooks of Different Word-Lengths

Csisz\'ar's channel coding theorem for multiple codebooks is generalized allowing the codeword lenghts 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, erasure 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.