Channel-optimized index assignment of source codewords is arguably the simplest way of improving transmission error resilience, while keeping the source and/or channel codes intact. But optimal design of index assignment is an instance of quadratic assignment problem (QAP), one of the hardest optimization problems in the NP-complete class. In this work we make a progress in the research of index assignment optimization. We apply some recent results of QAP research to compute the strongest lower bounds so far for channel distortion of BSC among all index assignments. The strength of the resulting lower bounds is validated by comparing them against the upper bounds produced by heuristic index assignment algorithms.
Xiaolin Wu, H. Mittelmann, Xiaohan Wang
IEEE Transactions on Communications