Universal rateless coding with finite message set

Universal rateless coding over unknown discrete memoryless channels (DMC) is considered. In rateless codes each codeword is infinitely long, and the decoding time depends on the confidence level of the decoder. This work considers the finite message set case where a finite number of bits are transmitted over an unknown discrete memoryless channel, with a fix allowed error probability. Using rateless codes along with sequential universal decoding that utilizes a mixture probability law instead of the unknown channel law, an optimal universal scheme is obtained. The analysis specifies explicitly the attainable rate, at each message set size and allowed error probability, which reflects the cost of universality.