Trellis complexity versus the coding gain of lattices II
Trellis complexity versus the coding gain of lattices II
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网格复杂度与网格 II 的编码增益
DOI：
10.1109/18.556676
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
I. Blake
中科院分区：
文献类型：
--
作者：
V. Tarokh;I. Blake
关于PT，见同上，第42卷，第6期，第1796 -1802页，1996年。每一个有理格都有一个有限格图，它可以用于通过Viterbi算法在加性白色高斯噪声信道上进行最大似然解码。对于具有增益/spl gamma/的任意有理格L，L的任何给定格图中的状态（分别为分支）的平均数量由/spl gamma/的函数下界。证明了这个函数在/spl gamma/中指数增长。在相反的方向上，证明了给定/spl isin/>0，对于任意大的/spl gamma/值，存在增益/spl gamma/的晶格，其平均分支数和状态数小于exp（/spl gamma//sup（1+/spl isin//））。从截断卷积码得到的块码的网格图表明，在网格模型内，解码格的问题并不比指数困难得多。
For pt.I see ibid., vol. 42, no.6, p.1796-1802, 1996. Every rational lattice has a finite trellis diagram which can be employed for maximum-likelihood decoding over the additive white Gaussian noise channel via the Viterbi algorithm. For an arbitrary rational lattice L with gain /spl gamma/, the average number of states (respectively, branches) in any given trellis diagram of L is bounded below by a function of /spl gamma/. It is proved that this function grows exponentially in /spl gamma/. In the reverse direction, it is proved that given /spl isin/>0, for arbitrarily large values of /spl gamma/, there exist lattices of gain /spl gamma/ with an average number of branches and states less than exp(/spl gamma//sup (1+/spl isin//)). Trellis diagrams of block codes obtained from truncated convolutional codes are employed to show that, inside the trellis model, the problem of decoding lattices is not much harder than exponential.