So they set aside 2 32-bit patterns; when these patterns appear at the end of a 64-byte cache line, they indicate a compressed line; otherwise, the line is literal.
This smells an awful lot like an impossible infinite compression claim; any real compressor must increase the length of at least some inputs due to the pigeonhole principle.
Their solution is to add a 16-entry table to track "lines that look like they have the compressed-line marker, but are not actually compressed" (and they also store such lines inverted in DRAM, but this seems inessential). They claim 16 entries is enough based on probabilistic arguments, but they should be thinking of storing data generated by an adversarial process; one such process would be to choose 60 incompressible bytes followed by the 4-byte compressed line indicator.
Including just one bit of metadata per cache line of memory is 32MiB, more than the 0.75 bits/line (24MiB) calculated on page 5 for the scheme they would like to replace.
Their next bit of handwavium is that they use "DES" to choose line markers in a way dependent on a secret key which can be changed in case of a LUT overflow. I wasn't immediately able to find a modern figure on how fast hardware "DES" is, but a 2003 paper gives a figure of "21 to 37 cycles of latency" https://www.intopix.com/Ressources/WPs_and_Sc_Pub/intoPIX%20... -- will this fit into the time budget or will it slow memory accesses? (They first say this is off the critical path but then that the marker is per-line, I don't see how both are true)
When the limited table is exhausted, a new key is chosen and all of memory must be updated (so you really don't want to do that) They dismiss this by again appealing to the rarity as "1-in-2^512" but if that's true you might as well just design the chip to blow up when the condition arises. If any timing information about "line appears in LUT" is visible to a program, then it is just 16 * 2^32 instead for an adversarial program (you can tweak line 1 until it needs a LUT entry, which takes just 2^32 writes; then repeat for the next line)