New Bounds and Constructions for Variable Packet-Error Coding

In this work, we consider the problem of variable packet-error coding, which emerges in network communication scenarios where a source transmits information to a destination through multiple disjoint paths. The objective is to design codes with dynamic error-correcting capabilities that adapt to a varying number of errors. Specifically, we first provide a bound on the rate-distortion trade-off for general variable packet-error coding schemes. Then, we present a construction that uses higherorder MDS codes and provides a variable packet-error coding scheme that achieves a better rate-distortion trade-off compared to known results for general parameter regimes.