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Journal of Communications and Networks

A non-greedy puncturing method for rate-compatible LDPC codes

Lin Zhou, Wei‐Cheng Huang, Rui Zhao, Yucheng He

Published Feb 1, 2017• 5 citations
Publisher

Abstract

In this paper, we propose a non-greedy punctur- ing method for constructing binary rate-compatible low-density parity-check codes. First, we show that the recovery error prob- ability for a punctured variable node can be reduced by allocat- ing a small number of unpunctured variable nodes in the recovery tree. Then, we redefine the recovery tree according to the princi- ple of iterative decoding with the sum-product algorithm. The pro- posed non-greedy puncturing algorithm lies mainly in the dynam- ical minimization of the number of unpunctured variable nodes in the redefined recovery tree for the punctured variable nodes. Fi- nally, simulation results show that the proposed puncturing algo- rithm outperforms the existing best puncturing algorithms in bit error rate performances of iterative decoding.

DOI
10.1109/jcn.2017.000006

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In this paper, we propose a non-greedy punctur- ing method for constructing binary rate-compatible low-density parity-check codes. First, we show that the recovery error prob- ability for a punctured variable node can be reduced by allocat- ing a small number of unpunctured variable nodes in the recovery tree. Then, we redefine the recovery tree according to the princi- ple of iterative decoding with the sum-product algorithm. The pro- posed non-greedy puncturing algorithm lies mainly in the dynam- ical minimization of the number of unpunctured variable nodes in the redefined recovery tree for the punctured variable nodes. Fi- nally, simulation results show that the proposed puncturing algo- rithm outperforms the existing best puncturing algorithms in bit error rate performances of iterative decoding.
In this paper, we study and propose a puncturing algorithm of block-type low-density parity-check (B-LDPC) codes. This optimal puncturing algorithm is derived from the fact that puncturing of parity bits is equivalent to merging the check nodes. Furthermore, we propose a new decoding algorithm suitable for the punctured B-LDPC codes. This decoding algorithm needs not only smaller number of operations at each iteration, but also shows faster decoding convergence speed than the conventional erasure decoding algorithm. If the optimally punctured B-LDPC code is decoded by the new decoding algorithm, it results in the same performance as the unpunctured B-LDPC code of the same code rate.
While rate-compatible punctured low-density parity-check (RCP-LDPC) codes offer high flexibility in terms of code rate at a relatively low cost in implementation complexity, they are reported to require more decoding iterations than unpunctured LDPC codes. In this paper1we consider layered belief propagation decoding and propose efficient check node layering that significantly accelerates the decoding convergence of RCP-LDPC codes. We show that the proposed layering outperforms both random layering and conventional BP decoding. The performance improvements become more distinctive at high rates and they come at no additional implementation cost.
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.
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.
An iterative decoding algorithm of rate-compatible punctured low-density parity-check (RCP-LDPC) codes of high coding rates is developed. This algorithm performs a predetermined recovering process of punctured bits sums at the beginning of each iteration of the standard belief-propagation (BP) decoding algorithm. By propagating messages of two punctured bits sum, this algorithm can recover much more punctured bits than the standard BP decoding algorithm. It is shown that the proposed algorithm is applicable for RCP-LDPC codes of higher coding rates with little increase of decoding complexity.
In this paper, we introduce a new approach to puncturing irregular Low-Density Parity-Check (LDPC) mother codes. The proposed greedy approach constructs a single degree puncture sequence that identifies the variable-node degrees to puncture in a nested fashion. The construction is done one degree at a time choosing the variable-degree that requires the least amount of SNR for newly punctured ensemble. This approach takes into account the finite length of a particular LDPC code realization by adjusting the puncture probabilities using the finite granularity of each variable-degree available for puncturing given a codeword length. This greedy approach results in a single degree puncture sequence of encapsulating subsets for all possible code rates. Subsequently, a single variable-node sequence can be easily constructed from this degree sequence. In AWGN, the SNR gap performance of these rate-compatible LDPC codes varies little for a wide range of effective code rates with respect to the rate-distorted Shannon limit using binary source signalling.