On the Girth of Tanner ( 5,7) Quasi?Cyclic LDPC Codes

TN911; The girth plays an important role in the design of LDPC codes. In order to determine the girth of Tanner (5,7) quasi?cyclic (QC) LDPC codes with length 7p for p being a prime with the form 35m + 1, the cycles of lengths 4,6,8,and 10 are analyzed. Then these cycles are classified into sixteen categories,each of which can be expressed as an ordered block sequence,or a certain type. It is also shown that the existence of these cycles is equal to polynomial equations over Fp who has a 35th unit root. We check if these polynomial equations have a 35th unit root and obtain the girth values of Tanner (5,7) QC LDPC codes.