Assume I have signal $y[n]$ which is a result of convolution between $h[n]$ and $x[n]$. which means: 

$y[n] = h[n] * x[n]$ , where $*$ is the convolution operation 

In normal case, $h[n]$ should be known in order to extract $x[n]$ using deconvolution process. 

My question what about if I only know that $h[n] ∈ [1 , -1]$, it means $h[n]$ is either $1$ or $-1$, it's a vector and each value in the vector is $1$ or $-1$. for example if its length is $4$ , it could be $[1,-1,-1,1]$ or $[1,1,1,1]$ and so on. Is it possible in that case to perform any way, for example  deconvolution or any other method to estimate $x[n]$ ?