Generalization of Gallager's adaptive error control scheme

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, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C^ {}</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C^ {}</tex> contains <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> . At the encoder, the information sequence is first encoded with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> and then, after a fixed delay, is encoded with a "shortened" version of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C^ {}</tex> , which is added to the parity sequences of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> . At the decoder there are two modes of operation, a random mode and a burst mode. In the random mode errors are corrected with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> 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 <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C^ {}</tex> , which precedes the decoder for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">C</tex> , removes random errors from these later blocks, thereby greatly increasing the probability of recovery from the burst.