A Unified Adaptive Recoding Framework for Batched Network Coding

TL;DR

This paper introduces a unified adaptive recoding framework for batched network coding that optimizes packet recoding based on expected rank, accommodating various packet loss models and ensuring robustness against measurement errors.

Contribution

It develops a general framework with an algorithm for optimal recoding solutions under stationary stochastic packet loss models, enhancing robustness and flexibility.

Findings

Expected rank functions are concave under stationary packet loss.

Existence of solutions that minimize recoding randomness and tolerate errors.

Proposed algorithms can find and tune optimal recoding solutions.

Abstract

Batched network coding is a variation of random linear network coding which has low computational and storage costs. In order to adapt to random fluctuations in the number of erasures in individual batches, it is not optimal to recode and transmit the same number of packets for all batches. Different distributed optimization models, which are called adaptive recoding schemes, were formulated for this purpose. The key component of these optimization problems is the expected value of the rank distribution of a batch at the next network node, which is also known as the expected rank. In this paper, we put forth a unified adaptive recoding framework with an arbitrary recoding field size. We show that the expected rank functions are concave when the packet loss pattern is a stationary stochastic process, which covers but not limited to independent packet loss and Gilbert-Elliott packet loss model. Under this concavity assumption, we show that there always exists a solution which not only can minimize the randomness on the number of recoded packets but also can tolerate rank distribution errors due to inaccurate measurements or limited precision of the machine. We provide an algorithm to obtain such an optimal optimal solution, and propose tuning schemes that can turn any feasible solution into a desired optimal solution.