Core Concepts
The authors establish an achievable rate region for distributed approximate computing with constant decoding locality by designing a layered coding scheme. They show that the rate region is optimal under mild regularity conditions, indicating the need for more rate to achieve lower coding complexity.
Abstract
Considered a fundamental problem in distributed computing, this paper introduces a novel approach to achieve efficient distributed approximate computing with constant decoding locality. By designing a layered coding scheme, the authors establish an achievable rate region and prove its optimality under certain conditions. The study highlights the trade-off between rate and reconstruction quality while emphasizing the importance of decoding complexity in achieving lower rates. Through detailed analysis and proofs, the paper provides insights into the challenges and solutions in distributed computing scenarios.
Stats
For many applications, lossless computing incurs a high cost.
A (n, 2nR1, 2nR2, t) code is defined by encoding functions.
An outer bound for Rloc(ǫ) is characterized by R1 ≥I(X1, U1), R2 ≥I(X2; U2), R1 + R2 ≥I(X1, X2; U1, U2).
The rate region for distributed lossless computing is easily obtained as follows.
The rate region for the distributed approximate compression problem is characterized by R1 ≥ min p(u1|x1):∃g1 P[d1(X1,g1(U1))≤ǫ]=1 I(X1, U1).
Quotes
"The proof mainly relies on the reverse hypercontractivity property and a rounding technique to construct auxiliary random variables."
"We also develop graph characterizations for the above rate regions."
"The rest of the paper is organized as follows."