Parallel Concatenated Convolutional Lattice Codes With Constrained States

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Abstract
Convolutional lattice codes, also known as signal codes, have been proposed as a technique to generate structured codes that have good performance. While in principle optimal decoding can be achieved using the Viterbi Algorithm, in practice due to Tomlinson-Harashima precoding, the size of the state space is too large, and one must resort to suboptimal techniques such as sequential decoding. In this paper, we take an alternate approach. By employing a judicious selection of tap coefficients and in combination with precoding, we show that the state space can be constrained to a relatively small set such that Viterbi decoding is practical. The performance of such codes still exhibits a large gap to capacity, and we further propose a parallel concatenation similar to that of turbo codes, resulting in a “turbo signal code.” Due to the relatively small state space, iterative decoding based on the BCJR algorithm is now possible. The gaps between the SNR for a frame error rate of 1% and the optimal performance theoretically achievable for a code of the same rate over an AWGN channel are found by simulation to be within 0.75-0.85 dB with a block length of 8192.
Funding Information
  • JSPS Invitation Fellowships for Research in Japan program
  • Shared Hierarchical Academic Research Computing Network (SHARCNET:www.sharcnet.ca) and Compute/Calcul Canada
  • Natural Sciences and Engineering Research Council of Canada (NSERC)

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