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International Conference on Communications

Design of rate-compatible efficiently-encodable generalized LDPC codes

Tingjun Xie, Stephen G. Wilson

Published Jun 1, 2013• 0 citations
Publisher

Abstract

We study rate-compatible (RC) puncturing algorithms for efficiently-encodable (EE) generalized LDPC (GLDPC) codes of short-to-moderate blocklength. EE-GLDPC codes are systematic codes and well-suited for puncturing, thus they are able to address a rate constraint issue, which is an obvious disadvantage of traditional GLDPC codes. In this work, we propose systematic puncturing algorithms for EE-GLDPC codes. Simulation results show that the systematic puncturing has considerable performance improvement over random puncturing. In addition, the punctured codes, like their mother codes, have the advantage of good error floor performance, which can be a very important feature in practical applications. Finally, it is also demonstrated that, compared with LDPC codes, GLDPC codes have a better error floor performance, but suffer from a decoding threshold loss at high puncturing rates; nonetheless the tradeoff between error floor and decoding threshold loss can be conveniently implemented via the method of doping.

DOI
10.1109/icc.2013.6655050

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IEEE Journal on Selected Areas in Communications•Jul 29, 2009•66 citations
We study rate-compatible (RC) puncturing algorithms for efficiently-encodable (EE) generalized LDPC (GLDPC) codes of short-to-moderate blocklength. EE-GLDPC codes are systematic codes and well-suited for puncturing, thus they are able to address a rate constraint issue, which is an obvious disadvantage of traditional GLDPC codes. In this work, we propose systematic puncturing algorithms for EE-GLDPC codes. Simulation results show that the systematic puncturing has considerable performance improvement over random puncturing. In addition, the punctured codes, like their mother codes, have the advantage of good error floor performance, which can be a very important feature in practical applications. Finally, it is also demonstrated that, compared with LDPC codes, GLDPC codes have a better error floor performance, but suffer from a decoding threshold loss at high puncturing rates; nonetheless the tradeoff between error floor and decoding threshold loss can be conveniently implemented via the method of doping.
Finding coding schemes that approach the Shannon capacity limit has been the central theme during the development of error-control coding (ECC).In recent years low-density parity-check (LDPC) codes, due to their remarkable performance under iterative decoding, have received extensive study and have been adopted by many modern advanced communication systems.LDPC codes can be further extended to generalized LDPC (GLDPC) codes and doublygeneralized LDPC (DGLDPC) codes.GLDPC and DGLDPC codes are supersets of LDPC codes that possess more generic code structures.GLDPC and DGLDPC codes are more flexible than LDPC codes, since a richer variety of check nodes (CNs) or variable nodes (VNs) offers additional options and flexibility, which enable many advantages over LDPC codes in numerous scenarios.In this dissertation we focus on improved design methods for finite-length (FL) GLDPC and DGLDPC codes.The first research topic is the error floor behavior of FL-GLDPC and FL-DGLDPC codes.In GLDPC and DGLDPC codes, the existence of generalized CNs and VNs requires more careful management of edge connections for achieving low error floors.In this work the approximate cycle extrinsic message degree (ACE), a cycle parameter used in LDPC codes that reflects the resilience of the cycle to the noise, is generalized to extended ACE (eACE) for GLDPC and DGLDPC codes.By integrating eACE into the progressive-edge-growth (PEG) algorithm and adding more constraints on the connectivity of nodes, the error floor performance of GLDPC and DGLDPC codes can be greatly improved.In practice, designing codes capable of fast encoding is an important issue.Efficiently-encodable (EE) GLDPC and DGLDPC codes are studied and a self-consistent unified framework is proposed for constructing EE iteratively-decodable block codes, including EE-LDPC, EE-GLDPC and EE-DGLDPC codes.The competing nature of the fast encoding speed and the low error floor performance iv Abstract v is analyzed and verified via various simulation results.EE codes are systematic and suitable for puncturing; therefore, they are good candidates for rate-compatible (RC) data transmissions.Based on the characteristics of GLDPC and DGLDPC codes, we devise several systematic puncturing algorithms to provide good puncturing patterns for them.It is shown that we can significantly improve the code performance compared with random puncturing.Over a wide range of code rates, RC EE-GLDPC and EE-DGLDPC codes show advantages over EE-LDPC codes, especially at high signal-to-noise ratios (SNRs).
In this paper, we present an effective puncturing scheme for rate-compatible low-density parity-check (RC-LDPC) codes. Our scheme is based on the criterion of maximum average girth which is an important performance parameter for the construction of RC-LDPC codes. We select a pattern wherein the punctured bits are far apart from each other in the Tanner graph of the codes by sorting algorithm, and then puncture the bits with the maximum average girth. In the process, there is no need to do any optimization. By simulations, the proposed codes show good performance under puncturing over a wide range of rates. The introduced puncturing criterion results in lower bit error rate and error floor when compared with random puncturing. Moreover, the performance of proposed method is similar to the direct structured LDPC codes by progressive edge growth (PEG). But the scheme is very simple to implement and lowers the complexity of encoding and decoding.
A family of robust rate-compatible (RC) punctured low-density parity-check convolutional codes (LDPC-CCs) is derived from a time-invariant LDPC-CC mother code by periodically puncturing encoded bits (variable nodes) with respect to several criteria: (1) ensuring the recoverability of punctured variable nodes, (2) minimizing the number of completely punctured cycle trapping sets (CPCTSs), and (3) minimizing the number of punctured variable nodes involved in short cycles. The influence of (1) and (3) on iterative decoding performance is felt most strongly in the waterfall region of the bit-error-rate (BER) curve, while (2) has a larger effect in the error floor, or high signal-to-noise ratio (SNR), region. We show that the length of the puncturing period is an important parameter when designing high rate punctured codes and, moreover, that extending the puncturing period can improve the decoding performance and extend the range of compatible rates. As examples, we obtain families of RC LDPC-CCs from several time-invariant LDPC-CC mother codes with monomial and binomial entries in their polynomial syndrome former matrices.
Several kinds of non-binary rate-compatible LDPC codes with strong error-detecting ability and low complexity in encoding and decoding are studied and constructed.An efficient punctured encoding algorithm of parity bit is proposed,thus to get high-performance non-binary RC-LDPC codes.The punctured algorithm,based on the non-binary mother code with high performance and medium bit rate(1/2 rate),adopts efficient structured punctured algorithm and designs the high-performance error correction codes in a wide rate range(for example,from 1/10 to 9/10).The simulation results indicate that this algorithm is better in performance than the conventional random puncturing algorithm and the puncturing algorithm based on node grouping and sorting.
A class of rate-compatible (RC) quasi-cycle low-density parity-check (QC-LDPC) codes that have linear encodable complexity and low error floor is presented. To ensure linear encoding complexity, a lower triangular (LT) form for the parity part of the mother parity-check matrix is designed. By the designed LT form, a recursive encoding strategy is proposed. This encoding strategy can achieve linear encodable complexity, which is completely proportional to the code length. To guarantee good performances for a wide range of code rates, a layered short-cycle optimization algorithm is designed to obtain good girth distribution, and a layered density evolution algorithm is used to optimize degree distributions of each code rate. Then, a class of RC QC-LDPC codes can be obtained by both extension and puncturing from the optimized QC-LDPC mother code with rate 1/2. Simulation results show that no error floor is exhibited for the proposed RC QC-LDPC codes at FER=10-5. The practical performance at BER=10-6shows a gap of about 1.477 dB to the Shannon limit.
In this paper, families of rate-compatible protograph-based LDPC codes that are suitable for incrementalredundancy hybrid ARQ applications are constructed. A systematic technique to construct low-rate base codes from a higher rate code is presented. The base codes are designed to be robust against erasures while having a good performance on error channels. A progressive node puncturing algorithm is devised to construct a family of higher rate codes from the base code. The performance of this puncturing algorithm is compared to other puncturing schemes. Using the techniques in this paper, one can construct a rate-compatible family of codes with rates ranging from 0.1 to 0.9 that are within 1 dB from the channel capacity and have good error floors.