Efficient variable length channel coding for unknown DMCs

We present a strategy for the reliable communication of a message, in a variable number of channel uses, over an unknown discrete memoryless channel (DMC). The decoder periodically tests the received sequence and, when it can decode, sends an acknowledgment to the transmitter, which then stops transmitting. By choosing the size of the codebook large enough, the rate that is reliably realized by the strategy can be made to approach arbitrarily closely the mutual information between channel input and output induced by the user-chosen input distribution. The strategy presented can be considered as a generalization to arbitrary unknown DMCs of earlier variable length coding schemes, such as digital fountain codes for binary erasure channels (BECs), and a coding strategy for binary symmetric channels (BSCs) presented by Tchamkerten and Telatar