The error floor performance of a low-density parity-check (LDPC) code is highly related to the presence of error-prone substructures (EPSs). In general, existing characterizations of the EPSs are inspired by the LDPC decoding behavior under simple binary erasure channel (BEC) and binary symmetric channel (BSC) models. In this work, we first introduce a new class of EPSs: the 1-shot EPSs and static EPSs for the binary-input ternary-output channel (BITOC). By focusing on BITOCs, which are a step closer to additive white Gaussian channels (AWGNC), the proposed EPS would better characterize the decoding behavior of the AWGNC than the existing BEC-or BSC-based definitions. We then develop an efficient search algorithm that can exhaustively enumerate all small BITOC EPSs. The new exhaustive algorithm enables us to order the harmfulness of the EPSs and distinguish within a given EPS which bits are more prone to what types of errors. The proposed algorithm can also be regarded as a unified search method for the existing EPSs such as cycles, codewords, stopping sets, and fully absorbing sets. The proposed methodology is potentially generalizable to the binary-input m-ary output channel.

This work provides an efficient exhaustive search algorithm for finding all small fully absorbing sets (FASs) of any arbitrary low-density parity-check (LDPC) code. The proposed algorithm is based on the branch-&-bound principle for solving NP-complete problems. In particular, given any LDPC code, the problem of finding all FASs of size less than t is formulated as an integer programming problem, for which a new branch-&-bound algorithm is devised with new node selection and tree-trimming mechanisms. The resulting algorithm is capable of finding all FASs of size <; 7 for LDPC codes of length <; 1000. When limiting the FASs of interest to those with the number of violated parity-check nodes <; 3, the proposed algorithm is capable of finding all such FASs of size <; 14 for LDPC codes of lengths <; 1000. The resulting exhaustive list of small FASs is then used to devise a new efficient post-processing low-error floor LDPC decoder. The numerical results show that by exploiting the exhaustive list of small FASs, the proposed post-processing decoder can significantly lower the error-floor performance of a given LDPC code. For various example codes of length <; 3000, the proposed post-processing decoder lowers the error floor by a couple of orders of magnitude when compared to the standard belief propagation decoder and by an order of magnitude when compared to other existing low error-floor decoders.

We consider practical schemes for binary dirty-paper channels and broadcast channels (BCs) with two receivers and varying channel quality. With the BC application in mind, this paper proposes a new design for binary dirty paper coding (DPC). By exploiting the concept of coset binning, the complexity of the system is greatly reduced when compared to the existing works. Some design challenges of the coset binning approach are identified and addressed. The proposed binary DPC system achieves similar performance to the state-of-the-art, superposition-coding-based system while demonstrating significant advantages in terms of complexity and flexibility of system design. For binary BCs, achieving the capacity generally requires the superposition of a normal channel code and a carefully designed channel code with non-uniform bit distribution. The non-uniform bit distribution is chosen according to the channel conditions. Therefore, to achieve the capacity for binary BCs with varying channel quality, it is necessary to use quantization codes of different rates, which significantly increases the implementation complexity. In this paper, we also propose a broadcast scheme that generalizes the concept of binary DPC, which we term soft DPC. By combining soft DPC with time sharing, we achieve a large percentage of the capacity for a wide range of channel quality with little complexity overhead. Our scheme uses only one fixed pair of codes for users 1 and 2, and a single quantization code, which possesses many practical advantages over traditional time sharing and superposition coding solutions and provides strictly better performance.

This work provides an exhaustive search algorithm for finding small fully absorbing sets (FASs) of arbitrary low-density parity-check (LDPC) codes. In particular, given any LDPC code, the problem of finding all FASs of size less than t is formulated as an integer programming problem, for which a new branch-&-bound algorithm is devised. New node selection and the tree-trimming mechanisms are designed to further enhance the efficiency of the algorithm. The proposed algorithm is capable of finding all FASs of size ≤ 11 with no larger than 2 induced odd-degree check nodes for LDPC codes of length ≤ 1000. The resulting exhaustive list of small FASs is then used to devise a new post-processing decoder. Numerical results show that by taking advantage of the exhaustive list of small FASs, the proposed decoder significantly lowers the error floor for codes of practical lengths and outperforms the state-of-the-art low-error-floor decoders.

We propose a practical scheme for binary dirty-paper channels. By exploiting the concept of random binning instead of superposition coding, the complexity of the system is greatly reduced. For comparison, the existing approaches require one of the native codes to be of non-uniform a priori distribution, which is generally achieved by combining a symbol mapper and high-order-alphabet low-density parity-check (LDPC) codes. Using high-order alphabets increases significantly the complexity and the resulting method is not flexible for designing systems of practical channel parameters. In contrast, we propose to implement the random binning concept using only binary LDPC and binary convolutional codes. In this work, some design challenges of this random binning approach are identified and addressed. Our systems are optimized by the joint use of density evolution (DE) and the extrinsic information transfer (EXIT) analysis. Simulation results using practical Quasi-Cyclic LDPC codes show that our system achieves similar performance to the state-of-the-art, high-order-alphabet LDPC-based systems while demonstrating significant advantages in terms of complexity and flexibility of system design.