二维非对称受限编码信道容量的证明

摘要

To determine whether the channel capacity of two-dimensional asymmetric constrained code is positive or zero, scanning method is proposed. If each location in (d1, k1, d2, k2) -constrained matrix can be determined by known signs and is able to be scanned, then channel capacity is 0. Some specific constraints are used to verify scanning method is more validated than algebraic and combinatorial methods. The common technology for proofing channel capacity positive is used to find two distinct m X n matrices satisfying (d1, k1, d2, k2) constraints. If these two matrices satisfy (d1, k1, d2, k2) constraints under eachtransformation, then the channel capacity Cd1,k1,d2,k2≥1/mn . This method is used to expand positive capacity region.%为了判断二维非对称受限编码的信道容量是否为正,提出了扫描方法.若满足限制(d1,k1,d2,k2)矩阵中的每个位置都可以通过已知的标志来决定并且被扫描,则限制(d1,k1,d2,k2)的信道容量为0.通过对特定二维受限编码信道容量的证明,验证了扫描方法比代数与组合方法更为有效.同时采用证明信道容量大于零常用的技术,找到满足(d1,k1,d2,k2)受限的两个m×n矩阵,若两矩阵在各种变形下都满足(d1,k1,d2,k2)限制,则信道容量Cd1,k1,d2,k2≥1/mn.这一方法对信道容量为正的区域进行扩展.