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One of the simplest, yet most effective schemes thus far devised for the correction of errors on compound channels is the adaptive decoding scheme invented by Gallager. In this paper we present a generalization of this scheme which, at a modest sacrifice in rate, enables the decoder to correct a burst even when the guard space following the burst contains random errors. This is accomplished with the use of two convolutional codes, and , where contains . At the encoder, the information sequence is first encoded with and then, after a fixed delay, is encoded with a "shortened" version of , which is added to the parity sequences of . At the decoder there are two modes of operation, a random mode and a burst mode. In the random mode errors are corrected with in a manner similar to that of the Gallager scheme. In the burst mode, the information bits in the bursty blocks are recovered from the later blocks where they have been superimposed on the parity bits. In this mode a decoder for , which precedes the decoder for , removes random errors from these later blocks, thereby greatly increasing the probability of recovery from the burst.