Fast Decoding of Low Density Lattice Codes
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Low density lattice codes (LDLC) are a family of lattice codes that can be decoded efficiently using a message-passing 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 GA-based 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-to-noise ratio (SNR) region; secondly, we propose a novel GA-based 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.
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