Every bad code has a good subcode: A local converse to the coding theorem
Every bad code has a good subcode: A local converse to the coding theorem
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每个坏代码都有一个好的子代码：编码定理的局部逆向
DOI：
10.1007/bf00535683
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发表时间：
1976
期刊：
影响因子：
--
通讯作者：
G. Dueck
中科院分区：
文献类型：
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作者：
R. Ahlswede;G. Dueck
局部匡威具有字母表5 F和Y/的离散无记忆信道（DMC）的传输概率P由下式给出：P（y”]x”）= ~ w（y t 1 x，）（1）t= 1 n n其中x”=（x 1.，x，）~ 2F”= 1~ 5F，y”=（y~ .....其中w是IX[ x 1 - 1-随机矩阵，z 1]。DMC的An（n，N，2）-码是对{（u，D-）[i= 1，...，..，N），并将此结果在[1]中作为定理12陈述（未加证明）。不等式limifn-1 logN（n，1）=C，0<2<1（4）noD oD（编码定理）在[3]和[5]中得到了证明.在[2]中证明了（弱匡威）inflimsup n-1 log N（n，2）< C（5）2>0 n-，oo，最后在[4]中证明了强匡威成立，即limsup n-1 log N（n，2）< C，0 < 2 < 1。
The Local Converse The transmission probabilities P of a discrete memoryless channel (DMC) with alphabets 5F and Y/are given by P(y"]x")= ~ w(ytlx,) (1) t=l n n where x" = (x 1 .... , x,) ~ 2F" = 1~ 5F, y" = (y~ ..... y,) ~ ~d" = I~ @', and where w is a IX[ x l~l-stochastic matrix, z 1 An (n, N, 2)-code for the DMC is a system of pairs {(u~, D~)[i= 1, ..., N} with ui~Y' and pairwise disjoint subsets D i of ~" (i= 1 .... , N), and with This result was stated (without proof) in [1] as Theorem 12. The inequality liminf n-1 log N(n, ' > /~)=C, 0<2<1 (4) noD oD (the coding theorem) was proved in [3] and in [5]. It was shown in [2] that (weak converse) inf limsup n-1 log N(n, 2)< C (5) 2>0 n-,oo and finally in [4] that the strong converse holds, i.e. limsup n-1 log N(n, 2) < C, 0 < 2 < 1.