Layered Subspace Codes for Network Coding

Abstract

Subspace codes were introduced by K\"otter and Kschischang for error control in random linear network coding. In this paper, a layered type of subspace codes is considered, which can be viewed as a superposition of multiple component subspace codes. Exploiting the layered structure, we develop two decoding algorithms for these codes. The first algorithm operates by separately decoding each component code. The second algorithm is similar to the successive interference cancellation (SIC) algorithm for conventional superposition coding, and further permits an iterative version. We show that both algorithms decode not only deterministically up to but also probabilistically beyond the error-correction capability of the overall code. Finally we present possible applications of layered subspace codes in several network coding scenarios.