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On Non-Linear Finite State Digital Channel Coding

Hermawan Kresno Dipojono

Abstract. A discrete-time digital channel coding, in which the encoder and decoder are both time-invariant finite state machines, is investigated. The channel is assumed to be memoryless. Two measures of performance are considered: the probability of error and the minimum free distance. Greater emphasis is placed on the minimum free distance since it is easier to evaluate than the probability of error criterion, and for small channel crossover probability it is a very good indicator of system performance; it is defined as the Hamming distance between two possible output sequences that correspond to distinct state sequences of the same length that are identical at both the start and finish. An algorithm to calculate the distance between such possible output sequences was developed; it also identifies all such pain of output sequence. Another algorithm, based on the finite state machine properties of the encoder, was found to generate the finite state decoder. Finally, after having found the pairs of encoder-decoder finite state machines, we simulated the communication system.


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