Doubly-Irregular Repeat-Accumulate Codes over Integer Rings for Multi-user Communications
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Structured codes based on lattices were shown to provide enlarged capacity for multi-user communication networks. In this paper, we study capacity-approaching irregular repeat accumulate (IRA) codes over integer rings ℤ_2^m for 2^m-PAM signaling, m=1,2,⋯. Such codes feature the property that the integer sum of K codewords belongs to the extended codebook (or lattice) w.r.t. the base code. With it, structured binning can be utilized and the gains promised in lattice based network information theory can be materialized in practice. In designing IRA ring codes, we first analyze the effect of zero-divisors of integer ring on the iterative belief-propagation (BP) decoding, and show the invalidity of symmetric Gaussian approximation. Then we propose a doubly IRA (D-IRA) ring code structure, consisting of irregular multiplier distribution and irregular node-degree distribution, that can restore the symmetry and optimize the BP decoding threshold. For point-to-point AWGN channel with -PAM inputs, D-IRA ring codes perform as low as 0.29 dB to the capacity limits, outperforming existing bit-interleaved coded-modulation (BICM) and IRA modulation codes over GF(2^m). We then proceed to design D-IRA ring codes for two important multi-user communication setups, namely compute-forward (CF) and dirty paper coding (DPC), with 2^m-PAM signaling. With it, a physical-layer network coding scheme yields a gap to the CF limit by 0.24 dB, and a simple linear DPC scheme exhibits a gap to the capacity by 0.91 dB.
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