Fast Joint Source-Channel Decoding of Convolutional Coded Markov Sequences with Monge Property

We address the problem of joint source-channel maximum a posteriori (MAP) decoding of a Markov sequence which is first encoded by a source code, then encoded by a convolutional code, and sent through a noisy memoryless channel. The existing joint source-channel decoding algorithm for the case of general convolutional encoder has O(M K² N) time complexity, where M is the length in bits of the information sequence, K is the size of the Markov source alphabet and N is the number of states of the convolutional encoder. We show that for Markov sources satisfying the so-called Monge property the decoding complexity can be decreased to O(M K N) by applying a fast matrix search technique.