Does a noisy version of Conway's game of life support universal computation? Quoting Wikipedia, "[Conway's Game of Life] has the power of a universal Turing machine: that is, anything that can be computed algorithmically can be computed within Conway's Game of Life."

Do such results extend to noisy versions of Conway's Game of Life? 
The simplest version is that after every round every live cell dies with a small probability $t$ and every dead cell becomes alive with a small probability $s$ (independently).

Another possibility is to consider the following probabilistic variant of the rule of the game itself.


Any live cell with fewer than two live neighbours dies with probability $1-t$.
Any live cell with two or three live neighbours lives with probability $1-t$ on to the next generation.
Any live cell with more than three live neighbours dies with probability $1-t$.
Any dead cell with exactly three live neighbours becomes a live cell with probability $1-t$. 


Question: Do these noisy versions of the Game of Life still support universal computations? If not, what can be said about their "computational power"?

Related information on the computational power of cellular automata and noisy versions of cellular automata will be also much appreciated.

(This question developed from this question on MathOverflow. Vincent Beffara's answer on MO gave interesting references for related results on computational aspects of noisy cellular automata.)
Here are some "nearby best" references, for what it's worth. It would seem the way to go on this question is to reduce it to a question on "noisy Turing machines", which have been studied (somewhat recently), and which are apparently the nearest relevant area of the literature. The basic/general/reasonable answer seems to be that if the TM can resist/correct for noise (as is demonstrated in these references), it's quite likely the CA can also, within some boundaries/thresholds.

The question of how to reduce a "noisy CA" to a "noisy TM" (and vice versa) is more open. It may not be hard but there does not appear to be published research in the area. Another issue is that the noisy TM is a new model and therefore there may be multiple (natural?) ways to represent a noisy TM. For example, the following papers look at disruptions in the state transition function, but another natural model is disruptions in the tape symbols (the latter being more connected to noisy CAs?). There may be some relation between the two.


Fault-tolerant Turing Machine by Ilir Capuni, 2012 (PhD thesis)


  The Turing machine is the most studied universal model of computation. This thesis studies the question if there is a Turing machine that can compute reliably even when violations of its transition function occur independently of each other with some small probability.
  
  In this thesis, we prove the existence of a Turing machine that with a polynomial overheadcan simulate any other Turing machine, even when it is subject to faults of the above type, thereby answering the question that was open for 25 years.
  A Turing Machine Resisting Isolated Bursts Of
  Faults by Ilir Capuni and Peter Gacs, 2012
  Noisy Turing Machines by Eugene Asarin and Pieter Collins, 2005
  
  (Another question: could there be some connection between noisy TMs and probabilistic Turing Machines?)