Efficient LDPC Codes over GF(q) for Lossy Data Compression

In this paper we consider the lossy compression of a binary symmetric source. We present a scheme that provides a low complexity lossy compressor with near optimal empirical performance. The proposed scheme is based on b-reduced ultra-sparse LDPC codes over GF(q). Encoding is performed by the Reinforced Belief Propagation algorithm, a variant of Belief Propagation. The computational complexity at the encoder is O(.n.q.log q), where is the average degree of the check nodes. For our code ensemble, decoding can be performed iteratively following the inverse steps of the leaf removal algorithm. For a sparse parity-check matrix the number of needed operations is O(n).Comment: 5 pages, 3 figure

비신뢰 경로 검색 기법을 이용한 저밀도 패리티 체크 부호를 위한 저복잡도 복호 기법 연구

학위논문 (박사)-- 서울대학교 대학원 공과대학 전기·컴퓨터공학부, 2017. 8. 노종선.This dissertation contains the following contributions on the low-complexity decoding schemes of LDPC codes. Two-stage decoding scheme for LDPC codes – A new stopping criterion for LDPC codes – A new decoding scheme for LDPC codes with unreliable path search Parallel unreliable path search algorithm Analysis of two-stage decoding schemes – Validity and complexity analysis First, a new two-stage decoding scheme for low-density parity check (LDPC) codes to lower the error-floor is proposed. The proposed decoding scheme consists of the conventional belief propagation (BP) decoding algorithm as the first-stage decoding and the re-decodings with manipulated log-likelihood ratios (LLRs) of variable nodes as the second-stage decoding. In the first-stage decoding, an early stopping criterion is proposed for early detection of decoding failure and the candidate set of the variable nodes is determined, which can be partly included in the small trapping sets. In the second-stage decoding, the scores of the variable nodes in the candidate set are computed by the proposed unreliable path search algorithm and the variable nodes are sorted in ascending order by their scores for the re-decoding trials. Each re-decoding trial is performed by BP decoding algorithm with manipulated LLR of a selected variable node in the candidate set one at a time with the second early stopping criterion. Secondly, the parallel unreliable path search algorithm is proposed for practical application to the proposed unreliable path search algorithm. In order to reduce the decoding delay and computational complexity, an efficient method for the search algorithm based on the parallel message-passing algorithm in the LDPC decoding is proposed. The parallel unreliable path search algorithm significantly reduces the additional complexity without extra hardware requirements. Finally, the validity and the complexity analysis of the proposed unreliable path search algorithm is presented. The proposed algorithm effectively finds the variable nodes in small trapping sets much more faster than the previous random selection method. Also, it is verified that the additional complexity of the parallel unreliable path search algorithm is less than that of one iteration of iterative decoders.Abstract i Contents iii List of Tables v List of Figures vi 1 Introduction 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Overview of Dissertation . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Overview of LDPC Codes 9 2.1 Basic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Decoding of LDPC Codes . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Analysis of LDPC Codes . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.1 Density Evolution . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.2 Mean Evolution . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.4 Quasi-Cyclic LDPC Codes . . . . . . . . . . . . . . . . . . . . . . . 19 2.5 Error-Floor and Trapping Sets . . . . . . . . . . . . . . . . . . . . . 21 3 A New Two-Stage Decoding Scheme with Unreliable Path Search 23 3.1 Overview of The Proposed Two-Stage Decoding Scheme . . . . . . . 26 3.2 First-Stage Decoding with the First Early Stopping Criterion . . . . . 27 3.3 Second-Stage Decoding with Unreliable Path Search Algorithm . . . 36 3.3.1 Scoring by Unreliable Path Search Algorithm . . . . . . . . . 37 3.3.2 LLR Manipulation and Re-decoding with the Second Early Stopping Criterion . . . . . . . . . . . . . . . . . . . . . . . 42 4 Parallel Unreliable Path Search Algorithm 44 4.1 Description of Parallel Unreliable Path Search Algorithm . . . . . . . 44 4.2 Scoring by Parallel Unreliable Path Search Algorithm . . . . . . . . . 48 5 Analysis of the Unreliable Path Search Algorithm 51 5.1 Validity of the Unreliable Path Search Algorithm . . . . . . . . . . . 51 5.2 Complexity Analysis of the Unreliable Path Search Algorithm . . . . 56 6 Simulation Results 59 7 Conclusions 65 Abstract (In Korean) 73Docto

Short Block-length Codes for Ultra-Reliable Low-Latency Communications

This paper reviews the state of the art channel coding techniques for ultra-reliable low latency communication (URLLC). The stringent requirements of URLLC services, such as ultra-high reliability and low latency, have made it the most challenging feature of the fifth generation (5G) mobile systems. The problem is even more challenging for the services beyond the 5G promise, such as tele-surgery and factory automation, which require latencies less than 1ms and failure rate as low as $10^{-9}$. The very low latency requirements of URLLC do not allow traditional approaches such as re-transmission to be used to increase the reliability. On the other hand, to guarantee the delay requirements, the block length needs to be small, so conventional channel codes, originally designed and optimised for moderate-to-long block-lengths, show notable deficiencies for short blocks. This paper provides an overview on channel coding techniques for short block lengths and compares them in terms of performance and complexity. Several important research directions are identified and discussed in more detail with several possible solutions.Comment: Accepted for publication in IEEE Communications Magazin

Concatenated Turbo/LDPC codes for deep space communications: performance and implementation

Deep space communications require error correction codes able to reach extremely low bit-error-rates, possibly with a steep waterfall region and without error floor. Several schemes have been proposed in the literature to achieve these goals. Most of them rely on the concatenation of different codes that leads to high hardware implementation complexity and poor resource sharing. This work proposes a scheme based on the concatenation of non-custom LDPC and turbo codes that achieves excellent error correction performance. Moreover, since both LDPC and turbo codes can be decoded with the BCJR algorithm, our preliminary results show that an efficient hardware architecture with high resource reuse can be designe