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 $\mathbb{Z}_{2^{m}}$ for $2^m$-PAM signaling, $m=1,2,\cdots$. 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, \emph{% 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 \emph{irregular multiplier distribution} and \emph{irregular node-degree distribution}, that can restore the symmetry and optimize the BP decoding threshold. For point-to-point AWGN channel with $% 2^m $-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.
翻译:基于 lattices 的结构性代码显示为多用户通信网络提供更大的能力。 在本文中, 我们研究在整数环上使用不规则重复累积代码的能力处理。 $\ mathbb ⁇ 2 ⁇ 2 m $$, $2 m美元- PAM 信号, $m= 1, 2,\ cddocks$。 这些代码包含一个属性, $K 的整数是扩展代码簿( 或 lattice) w.r. t. 基数。 有了它, 就可以利用基于 lattice 的网络信息理论所承诺的收益。 在设计 IRA 环形代码时, 我们首先分析整数圈零divisors对迭接的信仰- 解析( BP) 的效应, 显示符号高比值的接近值。 然后, 我们提出一个比值的 IRA (D-IRA) 低调( ) 键值, 由 emph =正值 正常的 倍 倍化 倍化的 网络信息发布 和 IMDIM 。