Research On The Channel Capacity Of Constrained Code

Constrained binary strings or words are ubiquitous in codes for magnetic and optical recording. The most common constrained codes is so-called RLL ( d ,k )codes which are the codes over bianry alphabet (0, 1) where d (k) is the minimum (maximum) permitted number of 0's separating consecutive 1's. In information theory channel capacity is the important parameters to measure channel properties, reflecting the channel can transfer the biggest information. But for fixed channel, there is always a source that gains transmission biggest information closing to channel capacity. So how effective coding to achieve or close to the channel capacity is an important aspect of our study. So research on the channel capacity of two-dimensional constrained code is very important. If transmission information of two-dimensional in channel is zero, then the coding is pointless. Therefore, in the coding process must determine whether the channel capacity of two-dimensional constrained code is positive or is zero.The concept and features of the channel capacity of constrained code are introduced in this paper , and three methods of calculation channel capacity are summarized. To determine whether the channel capacity of two-dimensional asymmetric constrained code is positive or is zero, scanning method is proposed on the basis of these theories. 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 combinatorial method. The common technology for proofing channel capacity positive is used to find two distinct m×n matrices satisfying ( d₁ , k₁ , d₂ , k₂)constraints. If these two matrices satisfy ( d₁ , k₁ , d₂ , k₂)constraints under each transformation, then the channel capacity C_d1k1d2k2≥1／mm. This method is used to expand positive capacity region.