An Adaptive Incremental Redundancy Scheme for LDPC Code Based on the Mutual Information Model Xiang Chen, Hui Jiang, Fei Zesong Room 301, Dept. of Information Technologies Hefei Electronic Engineering Institute Huangshan Road 460, Hefei, P. R. China Abstract-The spectrum efficiency will be improved obviously, if the least number of retransmitted check bits of traditional Incremental Redundancy (IR) scheme is adaptively changing to meet the target error probability according to the instantaneous channel state. Based on the mutual information (MI) model, as well as the new Rate Compatible (RC) LDPC code family whose check nodes can be changed one by one, the proposed Adaptive IR (AIR) scheme meets exactly the reliability requirement of a certain RC-LDPC coded system in a wide range of channel state, occupying the least radio resources. Thus the AIR scheme maximizes the throughput of the system. I. INTRODUCTION Link error prediction (LEP) is crucial for link adaptation (LA) design, as well as system level simulation. In the beyond 3G or 4G systems, coded and modulated data blocks are divided into several sub-blocks, or made a number of copies, to be transmitted by various radio resource elements, such as time-slots, sub-carriers, spatial sub-channels and so on. Therefore, a coded block often experiences several different channel states before it is picked by a receiver. The error probability is not only related to a certain Signal-to- Interference-plus-Noise Ratio (SINR), but a series of SINRs. This makes the LEP complex, thus an accurate and simple multi-state LEP model is critical. Lei Wan et al proposed the Mutual Information (MI) model for the turbo and convolutional codes [1]. We have extended the MI model to LDPC codes, and proved that it outperforms the other LEP models for LDPC codes, typically the minus Exponential Effective SINR Ratio Mapping (EESM) model [2]. Then we introduced the MI model to two adaptive hybrid ARQ schemes, the Adaptive Partial Chase Combining (APCC) scheme performs perfectly, yet the adaptive Incremental Redundancy (AIR) scheme doesn't work so well [3]. Now we improve the AIR scheme in two aspects, the RC-LDPC family and the prediction procedure. The improved AIR scheme is as spectrum efficient as the APCC strategy, and is capable of working in a much wider range of SINR than APCC. The rest of the paper is organized as follows. The MI model is described in brief in section II. We present the new RC- LDPC family and Look-up Tables (LUTs) of the MI model. The improved procedure is proposed in section III to predict the retransmission length T for adaptive IR (AIR) with the MI model. Simulation results verify the accuracy of MI model’s prediction in section IV. Section V concludes this paper. II. THE MUTUAL INFORMATION MODEL The MI model serves not only as a link to system interface, but a convenient LUT for LA. Fig. 1 shows the diagram of the MI link quality model, including two separate sub-models: the modulation sub-model and the coding sub-model. They are independent, the modulation sub-model merely relates to the demodulation algorithm and modulation order, while the coding model only relies on AWGN performance of the decoding algorithm, coding rate and block size. The parameter passed from the modulation sub-model to the coding sub-model is modulated symbol-level mutual information (SI) of each sub-carrier. Each SI corresponds to a channel state during one coding block. For M-ary modulation, with modulation order m, the SI of the channel symbol signal- to-interference-and-noise ratio (SINR) value g is defined as 2 2 ( | , ) (, ) log ( ) ( | , ) ( | , ) ( | , ) log ( ) ( | , ) R I XY X X I R Y Y X PY X SI m E PXPY X PY X E PY X dY Y PXPY X g g g g g g +¥ +¥ =-¥ =-¥  ü   =        ü   =            (1) Where the modulated symbol X belongs to a certain modulation constellation, and the received symbol ( * ) R I Y Y i Y = + . We assume as the a priori probability of X in this paper. ( | , ) PY X g is the probability density function of Y conditioned on the noise-free channel symbol X and parameterized by channel state g . Figure 1. Diagram of the MI link quality model structure