Low density Lattice Codes: From Theory to Practice

CALIT2 3008
By: Prof. Meir Feder, Tel-Aviv University


Low density lattice codes (LDLC) proposed recently are lattice codes that can be decoded by linear-time iterative decoding close to the capacity. In LDLC a codeword x is generated directly at the n-dimensional Euclidean space as a linear transformation of a corresponding integer message vector b, i.e., x = Gb, where H=G^{-1} is restricted to be sparse. In LDLC the messages are pdf's of the component of the real codeword x. In order to make LDLC practical for application we proposed parametric representation of the pdf's, making the decoding algorithm very efficient in storage and computations.
Furthermore, for practical application, the infinite lattice should be combined with a shaping algorithm, that maps information bits to lattice points and ensures that the power of the lattice codewords is properly constrained. This work also proposes several efficient and practical shaping algorithms for LDLC. One technique establishes the notion of "systematic lattice codes". It is desired to use LDLC's not only in the AWGN channel but also in fading channels. For this to be practical,  it is shown that the prior "shaping" constraint should be taken into consideration as a prior knowledge in the iterative algorithm. In summary, then,, LDLC's are not only interesting theoretically, but can practically outperform any other proposed scheme for spectrally efficient communication, can be used in fading channels and can be considered for any case where lattice were shown theoretically to be useful.


Meir Feder received the B.Sc and M.Sc degrees from Tel-Aviv University,
Israel and the Sc.D degree from the Massachusetts Institute of Technology
(MIT) Cambridge, and the Woods Hole Oceanographic Institution, Woods
Hole, MA, all in electrical engineering in 1980, 1984 and 1987, respectively.
After being a research associate and lecturer in MIT he joined in 1989
the Department of Electrical Engineering - Systems, Tel-Aviv University,
where he is now a Professor. He had visiting appointments at the Woods
Hole Oceanographic Institution, Scripps Institute, Bell laboratories and in
1995/1996 he has been a visiting professor at MIT. He is also extensively in-
volved in the high-tech industry and co-founded several companies including
Peach Networks, a developer of a unique server-based interactive TV solution
which was acquired on March 2000 by Microsoft and Amimon a leading
provider of ASIC's for wireless high-denition A/V connectivity at the home.
Prof. Feder received numerous awards, including the 1993 IEEE Information Theory Best
Paper Award and the 1978 "creative thinking" award of the Israeli Defense Forces.