FEC decoder processing delays
Well, yes, everything that you can calculate needs some time to calculate. Viterbi is quite well-behaved with respect to that, since you can decode up to the last couple of bits (only the last constraint length bits are relevant to the current decision), and you can already prepare the path metrics while receiving sequentially, and only need to do the backtracking after reception of the last code bit.
However, in most practical systems, you'd want some sort of interleaving. Also, you'll have filtering and all sorts of operations with inherent delay before you even decode. So, there's group delay and processing latency in your system anyway.
That, together with the fact that Viterbi is not an overly complex method and typically not used with convolutional codes with very large constraint lengths, and that 1 ms is a rather long time for a modern processing system:
You are probably barking up the wrong tree. You haven't defined acceptable latency yet, nor the length of your burst, nor the degree of error correction you need.
Start with that, and figure out (we'll be glad to help) whether processing delays will be a problem or not, before worrying about your decoder.