  This paper concentrates on the recovery of block-sparse signals, which is not
only sparse but also nonzero elements are arrayed into some blocks (clusters)
rather than being arbitrary distributed all over the vector, from linear
measurements. We establish high-order sufficient conditions based on block RIP
to ensure the exact recovery of every block $s$-sparse signal in the noiseless
case via mixed $l_2/l_p$ minimization method, and the stable and robust
recovery in the case that signals are not accurately block-sparse in the
presence of noise. Additionally, a lower bound on necessary number of random
Gaussian measurements is gained for the condition to be true with overwhelming
probability. Furthermore, the numerical experiments conducted demonstrate the
performance of the proposed algorithm.
