Analysis and design of rate compatible LDPC codes

The main concern in nowadays digital communications standards, such as IEEE802.11n, 802.16e (Wi-MAX), 100BaseT Ethernet, and Digital Video Broadcasting (DVB), is the need of adaptive and flexible communication techniques. The request for higher efficiency, both in bandwidth use and power consumption, increases the need for limit-achieving, flexible techniques of channel coding. Low Density Parity Check (LDPC) Codes are very interesting because of their high performances and potential flexibility introduced by puncturing. In this paper, the design of rate-compatible LDPC is addressed. A class of punctured LDPC codes is defined through their equivalent parity check matrices. A formal analysis is provided, based on a simplified approach on the decoding belief propagation algorithm, i.e., considering a Gaussian approximation for message densities under density evolution. A suitable design criterion for the puncturing patterns is then addressed.