Abstract— We present a new class of irregular low-density parity-check (LDPC) codes for finite block length (up to a few thousand symbols). The proposed codes are efficiently encodable and have a simple rate-compatible puncturing structure which is suitable for incremental redundancy hybrid automatic repeat request (IR-HARQ) systems. The codes outperform optimized irregular LDPC codes and (extended) irregular repeat- accumulate codes for rates 0.67~0.94, and are particularly good at high puncturing rates where good puncturing performance has been previously difficult to achieve. These characteristics result in good throughput performance over time-varying channels in IR-HARQ systems. I. INTRODUCTION Many wireless broadband systems require flexible and adaptive transmission techniques since they operate in the presence of time-varying channels. For these systems, incremental redundancy hybrid automatic repeat request (IR- HARQ) schemes are often used, whereby parity bits are sent in an incremental fashion depending on the quality of the time-varying channel [1]. Careful design of an adaptive forward error correction (FEC) code can improve data throughput in such systems. Incremental Redundancy systems require the use of rate-compatible punctured codes (RCPC) [2]. These codes can be operated at different rates by using the same encoder-decoder pair. Depending on the rate requirement, an appropriate number of parity bits are sent by the transmitter. The receiver decodes by treating the parity bits that are not transmitted (called punctured bits) as erasures. In addition, the set of parity bits of a higher rate code forms a subset of the parity bits of a lower rate code. Thus in an IR-HARQ system if the receiver fails to decode at a particular rate it only needs to request additional parity bits from the transmitter. Low-Density Parity-Check (LDPC) codes are increasingly being considered as good candidates for the next-generation FEC codes in high throughput wireless and recording applications. Their excellent performance and parallelizable decoder make them appropriate for technologies such as DVB-S2, IEEE 802.16e, and IEEE 802.11n. To be useful in IR-HARQ systems LDPC codes need to (a) exhibit good performance under puncturing and (b) have an efficient encoder. Ha et al. introduced a good puncturing algorithm with rate-compatible fashion for finite length LDPC codes [3], [4]. This puncturing algorithm shows better puncturing performance than random puncturing for any given LDPC codes. However, the maximum puncturing rate is often limited when this algorithm is applied, so that high puncturing rates are difficult to achieve. Also, designing good mother codes for this puncturing algorithm is a crucial open problem. Efficient encoding of LDPC codes that have block length up to a few thousand bits may be hard unless the code has some algebraic structure. Random constructions of LDPC codes that are known to possess good performance do not have simple encoders in general. Some exceptions are irregular repeat accumulate (IRA) and extended IRA (eIRA) codes [5], [6]. In this work we present a class of efficiently- encodable rate-compatible LDPC codes, called E 2 RC codes that have good performance under puncturing as well as efficient encoding scheme [7]. We also present results that demonstrate the superior performance of these codes when used in an IR-HARQ system over time-varying channels. Previous work in IR-HARQ systems includes [8], [9], where the design of an ensemble of FEC codes is considered. IR-HARQ systems require good frame error rate (FER) performance, especially at high rate region to get good throughput performance. Through simulations, we verify that the E 2 RC codes have better throughput performance than other comparable LDPC codes since they have good performance at higher puncturing rate. II. INCREMENTAL REDUNDANCY HYBRID ARQ SYSTEMS The objective of IR-HARQ scheme is to improve the throughput by retransmitting the required fractional part of the parity bits rather than the whole information and parity bits when the previous transmission fails. The code combining process of our IR-HARQ scheme follows the Chase’s rule [10], and details of the steps are as follows: Code Combining Process for IR-HARQ Scheme STEP 1: Making a frame with cyclic redundancy check (CRC) STEP 2: LDPC encoding STEP 3: Ordering and grouping the parity bits STEP 4: Transmit the message and/or the required parity group At the receiver end, the frame is reconstructed with the message and parity groups of the previous frame after receiving the parity group of the current frame. Then, the frame is decoded with LDPC decoder. We detect errors with the help of CRC detection. If errors occur in the current frame, send the negative acknowledgement (NACK) signal to the transmitter, and the transmitter sends the next required parity group. Otherwise, Design of Rate-Compatible Irregular LDPC Codes for Incremental Redundancy Hybrid ARQ Systems Jaehong Kim†, Woonhaing Hur†, Aditya Ramamoorthy‡, and Steven W. McLaughlin† †School of Electrical and Computer Engineering, ‡Marvell Semiconductor Inc., Georgia Institute of Technology, Atlanta, GA, U.S.A. Sunnyvale, CA, U.S.A. E-mail: {onil, whhur2, swm}@ece.gatech.edu E-mail: adityar@marvell.com ISIT 2006, Seattle, USA, July 9  14, 2006 1139 1424405041/06/$20.00 ©2006 IEEE