TY - JOUR
T1 - Signal codes
T2 - Convolutional lattice codes
AU - Shalvi, Ofir
AU - Sommer, Naftali
AU - Feder, Meir
N1 - Funding Information:
Manuscript received June 25, 2008; revised January 19, 2011; accepted March 13, 2011. Date of current version July 29, 2011. The work was supported by the Israeli Science Foundation by Grant 634/09. The material in this paper was presented at the IEEE Information Theory Workshop, Paris, France, 2003. O. Shalvi is with the Department of Electrical Engineering–Systems, Tel-Aviv University, Tel-Aviv, Israel, and also with Anobit Technologies, Herzlia, Israel. N. Sommer is with the Department of Electrical Engineering–Systems, Tel-Aviv University, Tel-Aviv, Israel, and also with Anobit Technologies, Herzlia, Israel. M. Feder is with the Department of Electrical Engineering–Systems, Tel-Aviv University, Tel-Aviv, Israel. Communicated by H.-A. Loeliger, Associate Editor for Coding Techniques. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TIT.2011.2158876
PY - 2011/8
Y1 - 2011/8
N2 - 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.
AB - 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.
KW - Achieving AWGN capacity
KW - coded modulation
KW - convolutional lattice codes
KW - lattice codes
KW - sequential decoding
KW - shaping
UR - http://www.scopus.com/inward/record.url?scp=79960990912&partnerID=8YFLogxK
U2 - 10.1109/TIT.2011.2158876
DO - 10.1109/TIT.2011.2158876
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AN - SCOPUS:79960990912
SN - 0018-9448
VL - 57
SP - 5203
EP - 5226
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 8
M1 - 5961819
ER -