Recoverability of Variable Nodes in Periodically Punctured LDPC Convolutional Codes

The concept of transformed codes is introduced to algebraically evaluate the recoverability of punctured nodes for periodically punctured low-density parity-check convolutional codes (LDPC-CCs) by a simple matrix-based approach. The proposed very efficient algorithm allows to identify and exclude those candidate puncturing patterns in a computer search that contain unrecoverable nodes that would lead to bad error-correction performance. Moreover, a novel upper bound on the maximum punctured code rate is obtained, above which any punctured code must contain unrecoverable punctured nodes.