Low Density Lattice Codes: from Theory to Practice

Recently, lattice theory has been considered as useful tool for information theory. It has been also shown that lattice codes can be a strong competitor to traditional capacity achieving coding schemes such as LDPC or Turbo codes. Lattice codes are also attractive due to the fact that code space and signal space are equal, instead of traditional codes, where these spaces are different. However, all results were proved under too ideal constraint – infinite codeword dimensionality. Therefore, some practical concepts viable in real world are needed. The family of Low Density Lattice Codes (LDLC) seems to be a suitable candidate to achieve desired results. Although original LDLC decoding procedure has linear complexity, this algorithm is still memoryconsuming and difficult to implement. This paper describes LDLC code design including practical algorithms with linear complexity for encoding and decoding with effort to save memory as possible. This paper also introduces design of check matrix with structure allowing nested lattice shaping procedure with linear complexity.