1. A vector coding apparatus, comprising: a decomposing unit configured to decompose an initial vector into a sign vector and an initial absolute vector; a sign coding unit configured to obtain a sign code by coding the sign vector; a multi-level permutation-based coding unit configured to obtain an absolute vector code by performing multi-level permutation-based coding on the initial vector; and a combining unit configured to obtain an initial vector code by combining the sign code and the absolute vector code.