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引用次数: 0
摘要
虽然偏长码可以看作是一种编码方案，但从组合的角度来看，将其视为加权的Kneser图更为方便。有效码字对应于此图中某些较大的(实际上是最大的)独立集。定义5.1对于偏差参数p∈(0,1)，字母Σ，加权Kneser图Gp[Σ]的顶点集为p (Σ)，即Σ的所有子集的族。一个顶点的重量⊆Σμp (a) = p | |(1−p) |Σ|−| |。边集为{(A, B) | A, B≤Σ， A∩B = φ}。对于一个族F (Σ)，设μp(F)为其在μp下的权值。
5.1 Biased Long Code While the biased long code can be viewed as an encoding scheme, it is more con venient to take a combinatorial view and treat it as a weighted Kneser graph. Valid codewords correspond to certain large (in fact the largest) independent sets in this graph. Definition 5.1 For a bias parameter p ∈ (0, 1) and alphabet Σ, the vertex set of weighted Kneser graph Gp[Σ] is P(Σ), the family of all subsets of Σ. The weight of a vertex A ⊆ Σ is μp(A) = p|A|(1 − p)|Σ|−|A|. The edge set is { (A, B) | A, B ⊆ Σ, A ∩ B = φ}. For a family F ⊆ P(Σ), let μp(F ) denote its weight under μp.
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