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; the multi-level permutation-based unit including: an element removing unit configured to remove an element of the initial absolute vector which has a value satisfying a preset condition, wherein the element removing unit is further configured to remove any element in the new absolute vector which does not satisfy the preset condition if a number of an element value in the new absolute vector is larger than 1; an element retaining unit configured to retain any element not satisfying a preset condition in a new absolute vector; a position coding unit configured to code the position of any element not satisfying the preset condition in the initial absolute vector; an absolute vector code unit configured to obtain an absolute vector code by combining the position codes if a number of an element values in the new absolute vector is larger than 1; and a combining unit configured to obtain an initial vector code by combining the sign code and the absolute vector code.