Is it possible for a Central Bank to escape from a deflation trap by 'hiding' information? I'm reading this book on macroeconomics.

When determining the nominal interest rate, the Central Bank has in mind its real interest rate goal. By the Fisher Equation: $i_t=r_t+\pi^{E_{CB}}_{t+1}$, since at time $t$, I would need to know the price level at time $t+1$ to know inflation for next period, we use an expected value for inflation. I put the superscript $^{E_{CB}}$ to denote that the expectancy is formed by the central bank.

In the usual Philips Curve, we have $\pi_{t+1}=\pi^{E_{SS}}_{t+1}+\alpha(y_{t+1}-y_e)$ I put the superscript $^{E_{SS}}$ to denote that the expectancy is formed by the Supply Side (wage and price setters, i.e., with all available public information).

Recently, from a talk with someone who worked at a central bank, I learned that there's some difference in amount/quality of information that it's publicly available to wage and price setters, and that which is available to the Central Bank.

In the book I'm reading, the authors state one possible way of escaping a deflation trap, even if in practice it will not always work, is that to have higher expectations so that the minimum threshold for the real interest rate is lower enough to increase output until equilibrium. 

Now I was wondering if it was not possible for, in some situation, the CB publicly divulged information lead to workers and firms have higher expected inflation, while the CB would know those expectations to be a bit too optimistic, such that in reality that period real interest rate would be much lower to be enough to get out of deflation trap?

I think I must be making some errors in this reasoning. 

Any help would be appreciated
It is certainly possible for a central bank to move the economy away from liquidity trap or deflation trap by proper signals. Signals and targets are undoubtedly effective, as this NBER paper discusses http://www.nber.org/papers/w13932. I read an article, which I cannot find now, saying that signalling and targeting by central banks are sometimes more effective than actual policy changes. The problem is that the economy and financial markets have a huge amount of different players with different interests and goals so it is hard to predict with certainty the effect of the CB revealing certain information. 

One thing I have to disagree with is that signalling higher expectations would reduce real interest rates and move the economy away from deflation trap. The equation  it=rt+πt+1 would be more accurate as it+1=rt+1+πt+1. If you write it like that, then you can see that signalling higher inflation expectations would also signal an incoming interest rate hike, given that any central bank has the policy to keep inflation low and stable. When markets expect a rate hike, they reduce their equity and commodity positions (sell stocks, oil, gold etc.) and move into bonds and other cash positions. This sucks the money out of economy and creates more deflation. So if the CB wants to reduce deflation, the ideal strategy would be the opposite: signal sluggish growth and prolonged low interest rates. This is just what Fed has been doing for several years now and, arguably, it has worked. 

I can also add, as @ChingG noted in comments, the CB has to maintain credibility and not lie. On top of hurting its reputation, the central bank board members are also liable to the government for saying the truth. For example, if the Fed Chairwoman lied to Congress, she would be breaking the law. It makes more sense for the CB disclose the true data and to interpret the information the way the CB sees fit and give the signals and targets it deems necessary, but not "hide" information.