A Serial Concatenation of Binary-Input Nonbinary-Output Convolutional Code and Recursive Convolutional Lattice Code

The recently proposed recursive convolutional lattice code (RCLC) can form a signal with pseudo-Gaussian constellations, and their parallel concatenation is shown to approach the Shannon limit. A practical limitation is that its input symbol is limited to L²-ary quadrature amplitude modulation (QAM), which has non-power-of-two constellation points when L is chosen from the odd numbers. Therefore, encoding binary information by the RCLC is not straightforward. Furthermore, the information rate is limited to log₂L bits per complex dimension due to their parallel concatenation. In this paper, we tackle these issues by introducing a serial concatenation of binary-input nonbinary-output convolutional code (CC) and the RCLC, where the outer CC outputs an L-ary symbol that is matched to the input of the inner RCLC. We demonstrate that even with L = 3, the proposed approach can achieve 2 bits per complex dimension and still is able to approach the Shannon limit with lower decoding complexity compared with its parallel concatenation counterpart. As is demonstrated through theoretical analysis, the major practical drawback of the constellation generated by the RCLC is its Gaussian-like distribution, which has large peak-to-average power ratio. Therefore, we further introduce an approach to reduce the signal dynamic range for the proposed system. It is shown that a remarkable gain can be achieved in terms of capacity compared with the conventional QAM signals under the constraint of comparable power amplifier efficiency.