How do you encourage your marketing and communication department to be more creative and productive?

I want them to do a short survey and get customer feedback about their product so we can provide what customer actually need.

Listen to your existing customers and identify the ways they approach when there is a need. When you knew it you can identify more customers from that perspective.

SHOULD SIT TOGETHER, DISCUSS, EXCHANGE VIEWS, BRING OUT SHORTCOMINGS, KNOW CUSTOMER  DEMANDS AND THEIR COMPLAINTS(IF ANY). GIVE IMPROVED  PRODUCTS, GIVE EFFICENCY BONUS TO CONCERN EMPLOYEES , ENCOURAGE AND GIVE   RIGHT DIRECTION FOR MOTIVATION.

analyse the product and study the market and  how to approach the customer in a attractive way

Firstly i'll research on my marketing company or department after case study i'll be able to convince others about my department. Yes,  innovative ideas for the betterment of your company is a symbolic point. Think out of the box and promote advancement into the organization.As a manager should highlight pull factors to the employees and give them more benefits in the light of their previous performance into the organization.

Firstly sitdown with them and discuss about the market, shortcoming, customer demand, segments approching and exchange views to provide them best tools to satisfy the customer from which they will be getting confidence and create better business.