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Communications technology

On Several Kinds of Non-binary Rate-compatible LDPC Codes

XU Jia-pin

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

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.

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IEEE Communications Letters•May 15, 2017•4 citations
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.
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.
In the wireless communication system, it is necessary to change the transmitted code word or code rate in real time according to the channel environment, designing and implementing rate compatible codes is of great practical significance. In allusion to the defects of algebraically constructed QC-LDPC codes algorithm and the time-varying characteristics of wireless channel, we propose an algorithm based on check matrix optimization puncturing technique to construct QC-LDPC codes in this paper. The algorithm selects a high rate matrix with excellent performance as the parent matrix, and then uses the backward node puncturing method to puncture the information bits in the code word from the last column of the check matrix by a multiple of the number of rows to obtain a low rate matrix. The simulation results show that the rate-compatible non-binary LDPC codes constructed by this algorithm not only reduces the complexity of hardware implementation, but also improves the error correction performance of the non-binary LDPC codes, realizes the rate-compatible coding at the same time, and improves the average effectiveness and reliability of the communication system.
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.
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.
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.
This letter presents a new method for constructing the multi-rate non-binary quasi-cyclic low-density parity-check codes by expurgating a high-rate mother code. A matrix-theoretic approach is applied to design the parity-check matrices of the proposed codes. The resulting codes possess a quasi-cyclic structure, which is desirable for hardware implementations of the encoder and decoder. The codes can also be encoded directly with parity-check matrices due to the block dual-diagonal structure. Simulation results show that the codes can achieve good performance within a wide range of code rates both in the waterfall region and in the error-floor region.