We derive a new upper bound on the reliability function for channel coding over discrete memoryless channels. Our bounding technique relies on two main elements: (i) adding an auxiliary genie-receiver that reveals to the original receiver a list of codewords including the transmitted one, which satisfy a certain type property, and (ii) partitioning (most of) the list into subsets of codewords that satisfy a certain pairwise-symmetry property, which facilitates lower bounding of the average error probability by the pairwise error probability within a subset. We compare the obtained bound to the Shannon-Gallager-Berlekamp straight-line bound, the sphere-packing bound, and an amended version of Blahut's bound. Our bound is shown to be at least as tight for all rates, with cases of stricter tightness in a certain range of low rates, compared to all three aforementioned bounds. Our derivation is performed in a unified manner which is valid for any rate, as well as for a wide class of additive decoding metrics, whenever the corresponding zero-error capacity is zero. We further present a relatively simple function that may be regarded as an approximation to the reliability function in some cases. We also present a dual form of the bound, and discuss a looser bound of a simpler form, which is analyzed for the case of the binary symmetric channel with maximum likelihood decoding.
翻译:在离散的内存性信道的频道编码的可靠性功能上,我们得出一个新的上限。我们的捆绑技术依赖于两个主要要素:(一) 添加一个辅助的精灵接收器,向原始接收者显示一份包括传送的特性在内的编码词清单,该编码词清单满足某一类型属性,以及(二) 将清单分成符合某种对称对称对称对称约束特性的编码词组子组,这有利于降低对称误差概率在子集中的平均误差概率的界限。我们将获得的编码与香农-加拉格-贝莱坎普直线绑定、球包装约束和修正版布拉胡特约束的编码清单进行比较。我们的界限显示至少与所有费率一样紧紧,与上述所有三个界限相比,在一定范围的低率范围更加紧紧。我们的衍生以统一的方式进行,对任何比率有效,以及广泛的添加分解码度度度指标组,只要对应的零度能力为直线绑定线,以及修正版版版版版版版版版版本的Blahututbroutbly 函数相对简单,我们也可以对质地对质地讨论一个简单的版本。我们还可以的轨道的分解剖式,对立的分解剖式,对立为一个比较,对立的分法,对立的分法,对立的分法例的分。