Universal criteria for blind deconvolution

We present necessary and sufficient conditions for blind equalization/deconvolution (without observing the input) of an unknown, possible non-minimum phase linear time invariant system (channel). Based on that, we propose a family of optimization criteria and prove that their solution correspond to the desired response. These criteria, and the associated gradient-search algorithms, involve the computation of high order cumulants. The proposed criteria are universal in the sense that they do not impose any restrictions on the probability distrbution of the input symbols. We also address the problem of additive noise in the system and show that in several important cases, e.g. when the additive noise is Gaussian, the proposed criteria are unaffected.Funding was provided by the Office of Naval Research under Grant Number NOO014-90-J-1109

Low Density Lattice Codes

Low density lattice codes (LDLC) are novel lattice codes that can be decoded efficiently and approach the capacity of the additive white Gaussian noise (AWGN) channel. 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, the inverse of G, is restricted to be sparse. The fact that H is sparse is utilized to develop a linear-time iterative decoding scheme which attains, as demonstrated by simulations, good error performance within ~0.5dB from capacity at block length of n = 100,000 symbols. The paper also discusses convergence results and implementation considerations.Comment: 24 pages, 4 figures. Submitted for publication in IEEE transactions on Information Theor

Signal Codes

Motivated by signal processing, we present a new class of channel codes, called signal codes, for continuous-alphabet channels. Signal codes are lattice codes whose encoding is done by convolving an integer information sequence with a fixed filter pattern. Decoding is based on the bidirectional sequential stack decoder, which can be implemented efficiently using the heap data structure. Error analysis and simulation results indicate that signal codes can achieve low error rate at approximately 1dB from channel capacity.Comment: Submitted to IEEE Transactions on Information Theor