That is, to abstract, our security issue exists because:
A) There is complex compression/decompression software/code;
B) To implement this compression/decompression -- there are one or more lookup tables in effect;
C) The software implementing those lookup tables and the decompression side of things were never properly fuzzed, bound-checked, and/or mathematically proven not to create out-of-bounds errors, that is, for every potential use of the lookup table to be guaranteed as correct mathematically given any possibility, any combination of data in an input stream.
Also -- Didn't stuff like this already happen in GIF and PNG formats? Weren't there past security vulnerabilities for those formats?
Isn't this just (I dare to say) -- computer history repeating itself ?
Point: Software Engineering Discipline:
If you as a Software Engineer implement a decompressor for whatever format (or hell, more broadly and generically something that uses lookup tables on incoming streams of data) -- then the "burden of proof" is on you, to prove (one way or another) that it does not have vulnerabilities.
Fuzzing can help, mathematics and inductive/deductive logic can help, testing can help, and paranoid coding (always bounds-checking array accesses, etc.) can help, running in virtual machines and other types of limited environments and sandboxes can help. Running as interpreted code (albeit slower) could help. Deferring decompression to other local network attached resources running in limited execution environments could help.
In short... a monumental challenge... summed up as:
"Prove that all code which uses lookup tables can not generate hidden/unwanted states."