Multiplicatively Repeated Non-Binary LDPC Codes

We propose non-binary LDPC codes concatenated with multiplicative repetition codes. By multiplicatively repeating the (2,3)-regular non-binary LDPC mother code of rate 1/3, we construct rate-compatible codes of lower rates 1/6, 1/9, 1/12,... Surprisingly, such simple low-rate non-binary LDPC codes outperform the best low-rate binary LDPC codes so far. Moreover, we propose the decoding algorithm for the proposed codes, which can be decoded with almost the same computational complexity as that of the mother code.Comment: To appear in IEEE Transactions on Information Theor

Low-Density Parity-Check Coded High-order Modulation Schemes

In this thesis, we investigate how to support reliable data transmissions at high speeds in future communication systems, such as 5G/6G, WiFi, satellite, and optical communications. One of the most fundamental problems in these communication systems is how to reliably transmit information with a limited number of resources, such as power and spectral. To obtain high spectral efficiency, we use coded modulation (CM), such as bit-interleaved coded modulation (BICM) and delayed BICM (DBICM). To be specific, BICM is a pragmatic implementation of CM which has been largely adopted in both industry and academia. While BICM approaches CM capacity at high rates, the capacity gap between BICM and CM is still noticeable at lower code rates. To tackle this problem, DBICM, as a variation of BICM, introduces a delay module to create a dependency between multiple codewords, which enables us to exploit extrinsic information from the decoded delayed sub-blocks to improve the detection of the undelayed sub-blocks. Recent work shows that DBICM improves capacity over BICM. In addition, BICM and DBICM schemes protect each bit-channel differently, which is often referred to as the unequal error protection (UEP) property. Therefore, bit mapping designs are important for constructing pragmatic BICM and DBICM. To provide reliable communication, we have jointly designed bit mappings in DBICM and irregular low-density parity-check (LDPC) codes. For practical considerations, spatially coupled LDPC (SC-LDPC) codes have been considered as well. Specifically, we have investigated the joint design of the multi-chain SC-LDPC and the BICM bit mapper. In addition, the design of SC-LDPC codes with improved decoding threshold performance and reduced rate loss has been investigated in this thesis as well. The main body of this thesis consists of three parts. In the first part, considering Gray-labeled square M-ary quadrature amplitude modulation (QAM) constellations, we investigate the optimal delay scheme with the largest spectrum efficiency of DBICM for a fixed maximum number of delayed time slots and a given signal-to-noise ratio. Furthermore, we jointly optimize degree distributions and channel assignments of LDPC codes using protograph-based extrinsic information transfer charts. In addition, we proposed a constrained progressive edge growth-like algorithm to jointly construct LDPC codes and bit mappings for DBICM, taking the capacity of each bit-channel into account. Simulation results demonstrate that the designed LDPC-coded DBICM systems significantly outperform LDPC-coded BICM systems. In the second part, we proposed a windowed decoding algorithm for DBICM, which uses the extrinsic information of both the decoded delayed and undelayed sub-blocks, to improve the detection for all sub-blocks. We show that the proposed windowed decoding significantly outperforms the original decoding, demonstrating the effectiveness of the proposed decoding algorithm. In the third part, we apply multi-chain SC-LDPC to BICM. We investigate various connections for multi-chain SC-LDPC codes and bit mapping designs and analyze the performance of the multi-chain SC-LDPC codes over the equivalent binary erasure channels via density evolution. Numerical results demonstrate the superiority of the proposed design over existing connected-chain ensembles and over single-chain ensembles with the existing bit mapping design

Design and Evaluation of the Efficiency of Channel Coding LDPC Codes for 5G Information Technology

This paper proposes a result of an investigation of a topical problem and the development of models for efficient coding in information networks based on codes with a low density of parity check. The main advantage of the technique is the presented recommendations for choosing a signal-code construction is carried out taking into account the code rate and the number of iterations decoding for envisaging the defined noise immunity indices. The noise immunity of signal-code constructions based on low-density codes has been increased by combining them with multi position digital modulation. This solution eventually allowed to develop a strategy for decoder designing of such codes and to optimize the code structure for a specific information network. To test the effectiveness of the proposed method, MATLAB simulations are carried out under for various Information channels binary symmetric channel (BSC), a channel with additive white Gaussian noise (AWGN), binary asymmetric channel (BAC), asymmetric channel Z type. In addition, different code rates were used during the experiment. The study of signal-code constructions with differential modulation is presented. The efficiency of different decoding algorithms is investigated. The advantage of the obtained results over the known ones consists in determining the maximum noise immunity for the proposed codes. The energy gain was on the order of 6 dB, and an increase in the number of decoding iterations from 3 to 10 leads to a gain in coding energy of 5 dB. Envisaged that the results obtained can be very useful in the development of practical coding schemes in 5G networks