Convolutional cylinder-type block-circulant cycle codes

Abstract

In this paper‎, ‎we consider a class of column-weight two‎ ‎quasi-cyclic low-density parity check codes in which the girth can be large enough‎, ‎as an‎ ‎arbitrary multiple of 8‎. ‎Then we devote a convolutional form to these codes‎, ‎such that‎ ‎their generator matrix can be obtained by elementary row and‎ ‎column operations on the parity-check matrix‎. ‎Finally‎, ‎we show that the free distance of the convolutional codes is equal to the minimum distance of‎ ‎their block counterparts‎.