Signal codes: Convolutional lattice codes

Ofir Shalvi*, Naftali Sommer, Meir Feder

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


The coded modulation scheme proposed in this paper has a simple construction: an integer sequence, representing the information, is convolved with a fixed, continuous-valued, finite impulse response (FIR) filter to generate the codeword-a lattice point. Due to power constraints, the code construction includes a shaping mechanism inspired by precoding techniques such as the Tomlinson-Harashima filter. We naturally term these codes convolutional lattice codes or alternatively signal codes due to the signal processing interpretation of the code construction. Surprisingly, properly chosen short FIR filters can generate good codes with large minimal distance. Decoding can be done efficiently by sequential decoding or for better performance by bidirectional sequential decoding. Error analysis and simulation results indicate that for the additive white Gaussian noise (AWGN) channel, convolutional lattice codes with computationally reasonable decoders can achieve low error rate close to the channel capacity.

Original languageEnglish
Article number5961819
Pages (from-to)5203-5226
Number of pages24
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2011


FundersFunder number
Israeli Science Foundation634/09


    • Achieving AWGN capacity
    • coded modulation
    • convolutional lattice codes
    • lattice codes
    • sequential decoding
    • shaping


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