On Optimal Index Assignment for MAP Decoding of Markov Sequences

Index assignment and maximum a posteriori (MAP) decoding are two well-known techniques for error-resilient multimedia communications. If the two techniques are used in tandem, how they interact with each other will greatly affect the system performance. An important problem in this regard is, which has seemingly evaded attention, the design of index assignment to achieve the best possible performance of joint source-channel MAP decoding, given the source and channel statistics and given a distortion metric. In a first attempt on this design challenge, we pose the index assignment of a scalar quantizer for MAP decoding of Markov sequences coded by this quantizer as a quadratic programming problem. For Gaussian Markov sequences we derive a locally optimal index assignment by exploring some properties of the objective function. Experimental results show that the proposed scheme can find optimal or near-optimal solutions. The optimized index assignment can achieve much lower average symbol error rate than conventional schemes.