This paper addresses the joint quantization and control problem for hidden Markov chains with variable-length block-coding. The aim is to understand the impact of communication bandwidth and information delay (due to block-coding) on the control performance. A heuristic algorithm is developed to solve the dynamic programming (DP) equation through the introduction of a metric on the discrete observation space. Numerical results are presented demonstrating the attention division in block-coding and the tradeoffs between control performance and communication bandwidth.