Fast joint source-channel decoding of convolutional coded Markov sequences with Monge property

This work addresses the problem of joint source-channel 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. It is shown that for Markov sources satisfying the so-called Monge property, both the maximum a posteriori probability (MAP) sequence decoding, as well as the soft output Max-Log-MAP decoding can be accelerated by a factor of K without compromising the optimality, where K is the size of the Markov source alphabet. The key to achieve a higher decoding speed is a convenient organization of computations at the decoder combined with a fast matrix search technique enabled by the Monge property. The same decrease in complexity follows, as a by-product of the development, for the soft output Max-Log-MAP joint source channel decoding in the case when the convolutional coder is absent, result which was not known previously.