Usage of Markov Metric in Decoding of Convolutional Codes in Two-State Channels

The article discusses the data transmission using convolutional codes over channels where the noise process can be described by a Markov chain with two states: a simple binary Markov channel and the Gilbert channel. Using the classical Viterbi algorithm with the Hamming metric for these channels does not guarantee low error probabilities. Additionally, the use of an interleaver can introduce delays in the transmission process. The article discusses a Markov metric that is consistent with a simple Markov channel, provided a set of conditions are met. The article proposes a modification to the Viterbi algorithm that uses this metric. While this modification does not increase the number of trellis nodes in the algorithm, it does lead to a slight increase in its computational complexity. Experiments were conducted to evaluate the decoding error probability using the convolutional code (171,133) in both the Markov and Gilbert channels. The results show that the proposed algorithm significantly reduces the error probability in a simple Markov channel, even when the Markov metric is not matched with the channel. In the Gilbert channel, the proposed modification reduces the decoding error probability compared to using the Hamming metric only at high values of the bit error probability in a bad state of the channel. The results obtained can be used to improve the reliability of data transmission over channels described by a simple Markov model. However, when changing the probabilities of bit errors in channel states, more complex decoding functions are required.