Design & analysis for practical LDPC-coded systems from broadcast channel to low error-floor applications

Gyu Bum Kyung, Purdue University

Abstract

The application of low-density parity-check (LDPC) codes to classic point-to-point communication channels with independently and identically distributed noises has been well studied. Various results have demonstrated near-optimal performance with manageable complexity based on the sub-optimal but ultra-efficient belief propagation (BP) decoders. Nonetheless, the suboptimality of the BP decoder presents new challenges when applying LDPC codes to other non-traditional scenarios. This thesis considers two such problems: the code design for binary dirty paper coding (DPC) / broadcast channels, and the error-floor characterization/mitigation for low-error-rate applications. In the first part of this thesis, we consider practical schemes for binary dirty-paper channels and broadcast channels with two receivers and varying channel quality. We first propose a new design for binary DPC. By exploiting the concept of coset binning, the complexity of the system is greatly reduced when compared to the existing works, which used symbol mappers to design the non-uniformly distributed dirty paper code. Some unique design challenges of coset binning for binary DPC are identified and addressed. The proposed system achieves comparable performance to the state-of-the-art, superposition-coding-based binary DPC system while demonstrating significant advantages in terms of complexity and flexibility of system design. For the binary broadcast channel, achieving the capacity generally requires the superposition of a primary channel code and a carefully designed secondary error control code with non-uniform distribution, the latter of which is similar to the one used in binary DPC. Motivated by our results in binary DPC, we propose a new binary broadcast scheme that generalizes the concept of 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. Our scheme uses only one fixed pair of codes for users 1 and 2, and a single quantization code, which possesses several practical advantages over traditional time-sharing and superposition coding solutions and provides better performance. The second part of this thesis focuses on providing an exhaustive search algorithm for finding small error-prone substructures (EPSs) such as fully absorbing sets (FASs) of arbitrary regular LDPC codes and relaxed FASs (RFASs) and near FASs (NFASs) of arbitrary irregular LDPC codes. 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 EPSs of size less than s is formulated as an integer programming problem, for which a new branch-&-bound algorithm is devised. The proposed solution also incorporates new cut conditions that speed up the computation and reduce the memory usage. 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 (resp. NFASs) of size ≤13 with no larger than 2 induced odd-degree check nodes for regular (resp. irregular) LDPC codes of length ≤ 1000. The resulting exhaustive list of small EPSs is then used to devise a new efficient post-processing low-error floor LDPC decoder. Numerical results show that by taking advantage of the exhaustive list of small FASs, the proposed post-processing decoder significantly lowers the error floor by a couple of orders of magnitude for codes of practical lengths and outperforms the state-of-the-art low error-floor decoders. In addition, the list of EPSs can also be used to estimate the error floor when combined with the importance sampling techniques. Moreover, with the list of EPSs we can find the dominant EPSs and eliminate them using edge swapping to lower the error floor of any given LDPC codes. Finally, we introduce a new type of EPSs of LDPC codes called one-shot EPSs and static EPSs for the binary-input ternary-output (BITO) channel . The proposed new EPS is motivated by the observation that compared to binary erasure Channel (BEC) and binary symmetric channel (BSC), the decoder behavior of a BITO channel is a step closer to that of the additive white Gaussian noise channel (AWGNC). Therefore, the EPSs of a BITO would better characterize the EPSs of an AWGNC than the existing BEC- or BSC-based definitions. We develop a new exhaustive algorithm for these new EPSs for the BITO channel. The new exhaustive search algorithm enables us to order the harmfulness of EPSs and also distinguish the harmful bits of a given EPS. The algorithm can also be regarded as a unified search method for the existing EPSs such as codewords, stopping sets, FASs, and RFASs. The proposed algorithm is potentially generalizable to the binary-input m-ary output channel, which provides a concrete step towards understanding the notoriously complicated BP decoding behavior in the high-SNR (low FER) regime.

Degree

Ph.D.

Advisors

Wang, Purdue University.

Subject Area

Electrical engineering

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