Two encoding methods and a decoding algorithm for Construction D' coding lattices that can be used with shaping lattices for power-constrained channels are given. We construct nested lattice codes which are good for coding, good for shaping, and have low-complexity encoding and decoding. An indexing method for nested lattice codes is modified to avoid an integer overflow problem at high dimension. Convolutional code generator polynomials for Construction A lattices with the greatest shaping gain are given, the result of an extensive search. It is shown that rate 1/3 convolutional codes provide a more favorable performance-complexity trade-off than rate 1/2 convolutional codes. For a given dimension, tail-biting convolutional codes have higher shaping gain than that of zero-tailed convolutional codes. A design for quasi-cyclic low-density parity-check (LDPC) codes to form Construction D' lattices is presented, where their parity-check matrices can be easily triangularized, thus enabling efficient encoding and indexing. The resulting LDPC Construction D' lattices are evaluated using four shaping lattices: the $E_8$ lattice, the $BW_{16}$ lattice, the Leech lattice and our best-found convolutional code lattice, showing a shaping gain of approximately 0.65 dB, 0.86 dB, 1.03 dB and 1.25 dB at dimension 2304.
翻译:提供两种编码方法,并使用一种解码算法,用于构建受电力限制的频道的拉特层。 我们建造了适合编码、 有利于塑造、 且具有低复杂度编码和解码功能的嵌套拉特代码。 为避免高尺寸的整数溢出问题, 修改了嵌套拉特代码的索引方法。 给出了具有最大成份收益的建筑一个拉特层的革命代码生成器多位值。 显示1/3 的平比值代码提供了比1/2 的更有利的性能兼容性交易。 对于给定的尺寸, 尾比平差的调调和解码具有更高的成型收益。 提供了一种准循环低密度对等化的代码(LDPC), 以构建 D'lattical $, 它们的平比校准矩阵可以很容易三角化, 从而能够高效地进行编码和索引化。 由此产生的LDEC dtrace ddtical_ ddrice ddrace ddrace 。