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GENERALIZED TAIL-BITING CONVOLUTIONAL CODES (THRESHOLD DECODING, UNEQUAL ERROR PROTECTION)
Generalized tail-biting (GTB) convolutional encoding has been presented as a means to ameliorate the rate deficiency caused by zero-tail convolutional encoding. This GTB encoding provides a block structure for convolutional codes without sacrificing any rate loss. Two special schemes of GTB are discussed. The first scheme uses the full constraint length (m) of information blocks as tails and is called full tail-bating (FTB) encoding. The second scheme uses m' (0 < m' < m) information blocks as tails and is called partial tail-biting (PTB) encoding.^ Using the generator matrix characterization, an equivalence relationship is developed between binary rate k/n convolutional codes and quasi-cyclic block codes of period n. This relationship is utilized to design both good systematic convolutional codes and block codes. These codes are then compared with existing good codes.^ Maximum likelihood (optimum) Viterbi-like decoding is developed for the classes of FTB and PTB codes. This scheme basically performs exhaustive searches (by Viterbi decoding trials) for the code word that satisfies the FTB or PTB encoding constraint. Therefore, two suboptimum decoding schemes are proposed to reduce the decoding complexity of the FTB codes. They are both focused upon the important task of estimating the starting state of the transmitted sequence.^ The decoding performance of both optimum and suboptimum decoding schemes for the binary symmetric channel are then evaluated using a transfer function technique, a Viterbi FTB decoding analysis method, and simulations.^ A design procedure is presented for synthesizing threshold decodable, rate 1/n and n/(n + 1), self-orthogonal block codes obtained from truncating convolutional codes by GTB. When GTB is applied to an equal error protection threshold decodable convolutional code, the result is a class of unequal error protection threshold decodable block codes. These codes are related to a class of unequal error protection codes previously described by Mandelbaum 75 . Furthermore, the codes of Mandelbaum are generalized. Finally, a relationship between quasi-cyclic self-orthogonal blocks codes and tail-biting self-orthogonal convolutional codes is discussed. ^
MA, HOWARD H, "GENERALIZED TAIL-BITING CONVOLUTIONAL CODES (THRESHOLD DECODING, UNEQUAL ERROR PROTECTION)" (1985). Doctoral Dissertations Available from Proquest. AAI8509576.