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International Symposium on Turbo Codes and Iterative Information Processing

A puncturing algorithm for rate-compatible LDPC convolutional codes

Hua Ren Zhou, David G. M. Mitchell, Norbert Goertz, Daniel J. Costello

Published Aug 1, 2012• 1 citation
Publisher

Abstract

A family of rate-compatible (RC) punctured low-density parity-check convolutional codes (LDPC-CCs) is derived from an LDPC-CC 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. As an example, a family of RC punctured LDPC-CCs with rates 4/9, 4/8, 4/7, 4/6, and 4/5 are obtained from the (21,3, 5) Tanner LDPC-CC.

DOI
10.1109/istc.2012.6325182

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A family of rate-compatible (RC) punctured low-density parity-check convolutional codes (LDPC-CCs) is derived from an LDPC-CC 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. As an example, a family of RC punctured LDPC-CCs with rates 4/9, 4/8, 4/7, 4/6, and 4/5 are obtained from the (21,3, 5) Tanner LDPC-CC.
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.
The concept of transformed codes is introduced to algebraically evaluate the recoverability of punctured nodes for periodically punctured low-density parity-check convolutional codes (LDPC-CCs) by a simple matrix-based approach. The proposed very efficient algorithm allows to identify and exclude those candidate puncturing patterns in a computer search that contain unrecoverable nodes that would lead to bad error-correction performance. Moreover, a novel upper bound on the maximum punctured code rate is obtained, above which any punctured code must contain unrecoverable punctured nodes.
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.
This paper presents an improvement of a puncturing technique for rate-compatible low density parity check (LDPC) codes originally proposed by Asvadi and Banihashemi. In the original technique, the puncturing bits are selected by progressively reducing the search space according to a certain sequence of criteria. The last criterion is based on the ACE (approximate cycle extrinsic message degree) values of the short cycles present in the Tanner graph of the code. In this paper, we propose to substitute the last criterion with one which is based on the absorbing sets of the code. Simulation results show that this scheme improves the performance compared to the original and some other scheme available in the literature.
This paper presents a cycle-based rate-compatible puncturing technique for non-binary (NB) low-density parity-check (LDPC) codes. The proposed puncturing technique is based on the connectivity of the short non-binary (NB) cycles present in the Tanner graph. The connectivity of a cycle is measured by the extrinsic message degree (EMD). The short cycles with low values of EMD degrade the performance of iterative decoders significantly. The proposed technique selects the variable nodes for puncturing by reckoning their involvements in the short NB cycles with a low EMD. Simulations in different contexts are performed to check the efficiency of the proposed technique.
In this paper, we study rate-compatible puncturing of finite-length Low-Density Parity-Check (LDPC) codes. First, we derive simple and yet good bounds on the expected performance of punctured codes (constructed by random puncturing) over Binary Erasure Channel (BEC) as a function of the performance of their parent LDPC code. We then present a novel rate-compatible puncturing scheme that is very easy to implement. Our scheme uses the idea that a more uniform distribution of punctured bits across the Tanner graph results in punctured codes with better performance. Although the puncturing scheme tailored to regular codes is presented, it is also directly applicable to irregular parent ensembles. By simulations, the proposed rate-compatible puncturing scheme is shown to be superior to the existing puncturing methods for both regular and irregular LDPC codes over BEC and Additive White Gaussian Noise (AWGN) Channel.