Rateless Coding with Feedback

Abstract

The erasure resilience of rateless codes, such as Luby-Transform (LT) codes, makes them particularly suitable to a wide variety of loss-prone wireless and sensor network applications, ranging from digital video broadcast to software updates. Yet, traditional rateless codes usually make no use of a feedback communication channel, a feature available in many wireless settings. As such, we generalize LT codes to situations where receiver(s) provide feedback to the broadcaster. Our approach, referred to as Shifted LT (SLT) code, modifies the robust soliton distribution of LT codes at the broadcaster, based on the number of input symbols already decoded at the receivers. While implementing this modification entails little change to the LT encoder and decoder, we show both analytically and through real experiments, that it achieves significant savings in communication complexity, memory usage, and overall energy consumption. Furthermore, we show that significant savings can be even achieved with a low number of feedback messages (on the order of the square root of the total number of input symbols) transmitted at a uniform rate. The practical benefits of Shifted LT codes are demonstrated through the implementation of a real over-the-air programming application for sensor networks, based on the Deluge protocol.