Generator matrix design and degree-oriented scheduling for the fast decoding convergence of rateless codes

In the encoding of Luby transform (LT) codes, information bits (variable nodes) are randomly connected to the check nodes. Although the check-node degrees have been optimized for error-rate performance, the arbitrary connections in the code graph cannot guarantee efficient propagation of the channel information (intrinsic messages), and may slow down the convergence speed of the iterative decoding. This paper presents a design for a generator matrix such that the intrinsic messages can be efficiently propagated through the arranged connections. In addition, the convergence speed of rateless codes can also be accelerated using the proposed degree-oriented scheduling (DOS), where the intrinsic messages are propagated based on the order of check node degrees. An improvement in the convergence speed can be achieved without sacrificing the error-rate performance. In the case of Raptor codes, the BER performance can be significantly improved.