Universal Random Access Error Exponents for Codebooks of Different Blocklengths

Csiszár's channel coding theorem for multiple codebooks is generalized allowing the code word 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, when the rate and code word-type of the employed codebook do not admit reliable transmission over the given channel, overload is detected with probability approaching 1. This is proved even for a sender and receiver not knowing the channel beyond the alphabets. A substantial improvement is obtained when the sender knows the channel while the receiver still does not.