Efficient Decoding of Low Density Lattice Codes

Abstract

Low density lattice codes (LDLC) are a family of lattice codes that can be decoded efficiently using a messagepassing algorithm. In the original LDLC decoder, the message exchanged between variable nodes and check nodes are continuous functions, which must be approximated in practice. A promising method is Gaussian approximation (GA), where the messages are approximated by Gaussian functions. However, current GAbased decoders share two weaknesses: firstly, the convergence of these approximate decoders is unproven; secondly, the best known decoder requires O(2 d ) operations at each variable node, where d is the degree of LDLC. It means that existing decoders are very slow for long codes with large d. The contribution of this paper is twofold: firstly, we prove that all GA-based LDLC decoders converge sublinearly (or faster) in the high signal-tonoise ratio (SNR) region; secondly, we propose a novel GAbased LDLC decoder which requires only O(d) operations at each variable node. Simulation results confirm that the error correcting performance of proposed decoder is the same as the best known decoder, but with a much lower decoding complexity.

Neural Fuzzy Extractors: A Secure Way to Use Artificial Neural Networks for Biometric User Authentication

“…Our implementation of the LDLC decoder is based directly on the method proposed in [49], which is known to be rather inefficient. Many subsequent works have proposed much more efficient techniques for decoding LDLCs, see for example [5,35,61,66]. For example, when considering decoding parameters similar to In this paper, we presented a secure architecture for biometric user authentication (or identification), which avoids the storage of information (such as neural network weights or specific biometric data) that could be used by malicious entities for constructing artificial biometric inputs able to pass the authentication tests.…”

Efficient Decoder Design for Low-Density Lattice Codes From the Lattice Viewpoint

“…The shuffled version is out of the scope of this paper. To further reduce decoding complexity, a faster decoder was proposed in [17] with complexity O(n • t • d). Each variable node message is approximated with a mixture containing at most two Gaussian functions.…”

“…Each variable node message is approximated with a mixture containing at most two Gaussian functions. However, compared to the 2-Gaussian decoder, the decoder in [17] has performance loss of 0.2 dB and 0.3 dB in the waterfall region for n = 10 3 and n = 10 4 , respectively (see Fig. 3 in [17]).…”

“…Several LDLC message passing decoders [4], [13]- [17] have been proposed in the past two decades. The decoder in [4] exhibits the best-known error performance.…”

Hardware Implementation of Fixed-Point Decoder for Low-Density Lattice Codes

“…There are other efficient Gaussian mixture reduction techniques available in literature, e.g., [68]. The technique in [68] applies to the Gaussian mixtures with two mixture components only while the work in this thesis explores a larger design space.…”