Abstract-This paper proposes a class of rate-compatible LDPC codes, called protograph-based Raptor-like (PBRL) codes. The construction is focused on binary codes for BI-AWGN channels. As with the Raptor codes, additional parity bits are produced by exclusive-OR operations on the precoded bits, providing extensive rate compatibility. Unlike Raptor codes, the structure of each additional parity bit in the protograph is explicitly designed through density evolution. The construction method provides low iterative decoding thresholds and the lifted codes result in excellent error rate performance for long-blocklength PBRL codes. For short-blocklength PBRL codes the protograph design and lifting must avoid undesired graphical structures such as trapping sets and absorbing sets while also seeking to minimize the density evolution threshold. Simulation results are shown in information block sizes of k = 192, 16368 and 16384. Comparing at the same information block size of k = 16368 bits, the PBRL codes outperform the best known standardized code, the AR4JA codes in the waterfall region. The PBRL codes also perform comparably to DVB-S2 codes even though the DVB-S2 codes use LDPC codes with longer blocklengths and are concatenated with outer BCH codes.

Abstract-Multiple reads of the same Flash memory cell with distinct word-line voltages provide enhanced precision for LDPC decoding. In this paper, the word-line voltages are optimized by maximizing the mutual information (MI) of the quantized channel. The enhanced precision from a few additional reads allows frame error rate (FER) performance to approach that of full-precision soft information and enables an LDPC code to significantly outperform a BCH code.A constant-ratio constraint provides a significant simplification in the optimization with no noticeable loss in performance.For a well-designed LDPC code, the quantization that maximizes the mutual information also minimizes the FER in our simulations. However, for an example LDPC code with a high error floor caused by small absorbing sets, the MMI quantization does not provide the lowest frame error rate. The best quantization in this case introduces more erasures than would be optimal for the channel MI in order to mitigate the absorbing sets of the poorly designed code.The paper also identifies a trade-off in LDPC code design when decoding is performed with multiple precision levels; the best code at one level of precision will typically not be the best code at a different level of precision.

Abstract-The main advantage of feedback in a point-to-point memoryless channel is the reduction of the average blocklength required to approach capacity. This paper presents a communication system with feedback that uses carefully designed nonbinary LDPC (NB-LDPC) codes and incremental transmissions to achieve 92−94% of the idealized throughput of rate-compatible sphere-packing with maximum-likelihood decoding (RCSP-ML) for average blocklengths of 150-450 bits. The system uses active feedback by carefully selecting each bit of additional incremental information to improve the reliability of the least reliable variable node. The system uses post processing in the decoder to further improve performance. The average blocklengths of 150-450 bits are small enough that feedback provides a throughput advantage but also large enough that overhead that might be associated with transmitter confirmation is more easily tolerated.

This paper presents a general approach for optimizing the number of symbols in increments (packets of incremental redundancy) in a feedback communication system with a limited number of increments. This approach is based on a tight normal approximation on the rate for successful decoding. Applying this approach to a variety of feedback systems using non-binary (NB) low-density parity-check (LDPC) codes shows that greater than 90% of capacity can be achieved with average blocklengths fewer than 500 transmitted bits. One result is that the performance with ten increments closely approaches the performance with an infinite number of increments. The paper focuses on binaryinput additive-white Gaussian noise (BI-AWGN) channels but also demonstrates that the normal approximation works well on examples of fading channels as well as high-SNR AWGN channels that require larger QAM constellations. The paper explores both variable-length feedback codes with termination (VLFT) and the more practical variable length feedback (VLF) codes without termination that require no assumption of noiseless transmitter confirmation. For VLF we consider both a two-phase scheme and CRC-based scheme.

Abstract-One advantage of incremental transmissions with feedback in point-to-point memoryless channels is a reduction in average blocklength required to approach capacity. This paper optimizes the size of each incremental transmission for nonbinary (NB) LDPC codes to maximize throughput in VLFT and two-phase VLF settings. The optimization problem uses an approximation based on the inverse-Gaussian p.d.f. of the blocklength required for successful decoding. By using the optimized incremental transmission lengths (with an average blocklength of less than 500 bits), NB-LDPC codes for VLFT setting limited to 5 transmissions achieve a throughput greater than 96% of that obtained by an unlimited-transmission VLFT scheme with the same average blocklength. With a similar average blocklength, a two-phase VLF system limited to five transmissions (with optimized lengths) using the binary image of NB-LDPC codes achieves greater than 90% of the capacity of binary-input AWGN channel with SNR=2 dB. Two-phase VLF does not match the throughput of VLFT, but it is more practical than VLFT because it does not assume noiseless transmitter confirmation.