Raptor Codes for Hybrid ARQ Emina Soljanin, Nedeljko Varnica and Phil Whiting Abstract— An incremental redundancy hybrid ARQ (IR- HARQ) scheme based on recently introduced Raptor codes is proposed and analyzed. A number of important issues, such as rate and power control, and error rate performance after each transmission on time varying binary-input, symmetric-output channels are addressed by analyzing performance of Raptor codes on parallel channels. A set of rules for incrementing redundancy and setting the signal power at each transmission in order to maximize the throughput are derived. The theoretical results obtained for random code ensembles are tested on several practical code examples by simulation. Both theoretical and simulation results show that Raptor codes are suitable for HARQ schemes. I. I NTRODUCTION In conventional automatic repeat request (ARQ) schemes, frame errors are examined at the receiving end by an error detecting (usually cyclic redundancy check (CRC)) code. If a frame passes the CRC, the receiving end sends an acknowledgement (ACK) of successful transmission to the receiver. If a frame does not pass the CRC, the receiving end sends a negative acknowledgement (NAK) requesting retransmission. In communications systems, user data may be additionally protected by an error correcting code, which increases the probability of successful transmission. The transmission mechanisms that combine the ARQ protocol with error control coding are known as hybrid ARQ (HARQ) schemes. A standard measure of ARQ protocol efficiency is throughput, defined as the average number of user data bits accepted at the receiving end in the time required for transmission of a single bit. Therefore the level of redundancy of the error correcting code employed in an HARQ scheme has two opposing effects on the scheme efficiency, because with increased redundancy the probability of successful transmission increases while the percentage of user data in the frame decreases. Usually, a fixed rate code well suited to the channel characteristics and throughput requirements is selected. Emina Soljanin and Phil Whiting are with Bell Labs, Lucent Murray Hill NJ 07974, USA, emina,pwhiting@research.bell-labs.com. Nedeljko Varnica is with Marvell Semiconductor, Inc., Santa Clara, CA 95054 USA, nvarnica@marvell.com. In applications with fluctuating channel conditions within a range of signal-to-noise ratios (SNRs), such as mobile and satellite packet data transmission, the so called incremental redundancy (IR) HARQ schemes achieve higher throughput efficiency by adapting their error correcting code redundancy to different channel conditions. At the transmitter, the infor- mation and CRC bits are encoded by a systematic “mother” code. Initially, only the systematic part of the codeword and a selected number of parity bits are transmitted. The selected parity bits together with the systematic bits form a codeword of a punctured mother code. Decoding of this code is performed at the receiving end. If a retransmission is requested, the transmitter sends additional parity bits, possibly under different channel conditions or at different power. Decoding is again attempted at the receiving end, where the new parity bits are combined with those previously received. The procedure is repeated after each subsequent retransmission request until all the parity bits of the mother code are transmitted. A historic overview of hybrid ARQ schemes up to 1998, can be found in [2]. Recent interest in the schemes comes from the quest for reliable and efficient transmission under fluctuating conditions in wireless networks. An information- theoretic analysis of some HARQ protocols, concerning throughput and average delay for block-fading, Gaussian, collision channels have been reported in [3]. Another line of recent work on HARQ is concerned with the mother code and its puncturing since the throughput in these schemes is strongly affected by the properties of the mother code used in the system and the family of codes obtained by puncturing [1], [4], [5], [6]. The HARQ scheme of the third generation wireless stan- dards is based on powerful turbo codes. There are two crucial questions in this application of HARQ: 1) how to evaluate the error rate performance after each transmission (which is equivalent to evaluating performance of punctured codes on time varying channels [7]), and 2) how to choose the signal power and the number of bits for transmission after a failed transmission . In [8], both questions were successfully addressed by analyzing performance of IR- HARQ schemes averaged over certain ensembles of turbo Forty-Fourth Annual Allerton Conference Allerton House, UIUC, Illinois, USA Sept 27-29, 2006 WIIC.220 438