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. A version of this paper appeared as:• A. Hagedorn, S. Agarwal, S. Starobinski, and A. Trachtenberg, "Rateless Coding with Feedback", IEEE INFOCOM 2009.I. INTRODUCTION Point-to-multipoint wireless data communication, i.e., from a broadcaster to multiple downstream receivers, is gaining popularity with emerging wireless broadcast channels like digital video broadcast and cellular data broadcast [1] that support digital data broadcasting to multiple receivers. Broadcast scenarios also appear naturally in wireless sensor networks, most notably during software updates. Unlike analog broadcast, digital broadcast may also allow a back channel for receivers to communicate with the broadcaster, enabling interactive applications and protocols such as (n)ack-based data dissemination.Point-to-multipoint wireless communication poses several unique challenges. First, wireless channels are prone to lost packets (packet erasures) due to interference, occlusion, multi-path, etc.; as a result, different receivers may, and often do, receive different subsets of the transmitted data packets. Second, energy constraints often require receivers to be off during various (often differing) time periods during a given broadcast, again leading to the reception of different subsets of broadcast packets at each receiver. The same energy constraints also typically limit computation and memory on receiver units, thus providing a natural limit on the complexity of error coding for the communication channel. Finally, receivers are usually heterogeneous, with the least capable device dictating, or at least heavily influencing, the broadcast protocols.Erasure codes, which have the rateless property of being applicable to any channel loss p...

Delete-and-Conquer: Rateless coding with constrained feedback

“…In the Real Time (RT) oblivious codes [3], the encoder starts with degree one symbols and the encoded symbol degree increases based upon feedback messages containing the number of recovered symbols. Shifted LT codes (SLT) [4] use the same type of feedback information as RT codes, but instead of increasing the encoded symbols degree explicitly, SLT shift the Robust Soliton distribution according to the number of decoded symbols. The authors in [14] study the problem of minimizing the amount of feedback in broadcast scenarios by combining extreme value theory with rate less coding.…”

“…The authors in [3] propose real-time oblivious erasure codes, which utilize feedback messages to send the number of decoded symbols to the broadcaster. Shifted LT codes [4] utilize a similar approach by shifting the LT codes' Robust Solution distribution [1] according to the number of decoded symbols noted through the receiver's feedback channel. The authors in [5] use more informative feedback messages to notify the transmitter of which input symbols have been decoded, and this information is then applied to modify the degree distribution.…”

Rateless feedback codes

“…With this information the transmitter chooses a fixed degree for future encoded symbols, which maximizes the probability of decoding new symbols. The same type of feedback is applied in [5], but with the purpose of minimizing the redundancy.…”

Doped LT Decoding with Application to Wireless Broadcast Service

“…However, if limited feedback is allowed, the data recovery performance can be improved. Some works that have considered rateless codes over a feedback channel include [2] and [3]. In [2], rateless coding with feedback is proposed in the form of hybrid automatic repeat request (ARQ), called doped rateless decoding.…”

“…In [2], rateless coding with feedback is proposed in the form of hybrid automatic repeat request (ARQ), called doped rateless decoding. On the other hand, in [3], the transmitter adjusts the degree distributions of the LT code to improve performance based on the feedback of the number of correctly decoded bits. In this paper, following [2], we propose several improved doping methods for LT codes to reduce the number of doping iterations (or the doping rate) required for correct decoding.…”