Subspace codes

Abstract

For the noncoherent transmission model for random linear network coding, that is, neither the source node nor sink nodes were assumed to have knowledge of the channel transfer characteristic, a totally different framework is formulated for network error correction co, which is called subspace codes. In this case, the source information is encoded as a subspace rather than a specific matrix, and the sink nodes also receive a subspace spanned by the received packets. In this chapter, we will introduce the basic theory of subspace codes, particularly, constant-dimension codes in which all codewords have the same dimension. Specifically, we describe the channel model, the basic theory of subspace codes including encoding and decoding principle, the bounds on subspace codes, code construction and decoding algorithms.