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IEEE Journal on Selected Areas in Communications

Design of rate-compatible structured LDPC codes for hybrid ARQ applications

Mostafa El‐Khamy, Jilei Hou, Naga Bhushan

Published Jul 29, 2009• 66 citations
Publisher

Abstract

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.

DOI
10.1109/jsac.2009.090814

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Applied Optics•Apr 13, 2015•1 citation
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.
Over time-varying wireless channel,it is necessary for error-correction codes to be rate-compatible.Protograph LDPC codes can achieve rate-compatibility through and extending;and solve the problem that the encoders of tradition LDPC codes are more complex.With the AR4JA code which can be represented by protograph,we construct a rate-compatible family of AR4JA codes with rates ranging from 0.5 to 0.8 using the algorithm of puncturing node by node.To obtain the lower rates from 0.5 to 0.25,matrix expansion is also used.Simulation results over AWGN channel show that using both and extending we can construct rate-compatible family of AR4JA codes which do not suffer from error floor when BER is 10-6.
We construct a protograph-based rate-compatible family of low-density parity-check (LDPC) codes that cover a very wide range of rates from 1/2 to 16/17, perform within about 0.5 dB of their capacity limits for all rates, and can be decoded conveniently and efficiently with a common hardware implementation. In contrast to alternative methods that create codes of different rates by puncturing, shortening, or expurgation, our method uses a combination of expurgation and lengthening (equivalent to an unusual extension) to produce lower-rate codes. Advantages compared to the alternative methods include roughly uniform utilization of common family decoder hardware for different rates, implementation with uniformly low maximum check node degrees despite high maximum rate, and a large fixed portion of the protograph that can be labeled with a fixed set of edge permutations for all rates. We apply this method to create a rate-compatible code family anchored by a particular code of (nominal) rate 7/8 and length n = 8176 designed by Kou, Lin and Fossorier [1] whose edge permutations are determined by Euclidean geometries (EG). All members of our family retain all of the EG-designed edges and circulant permutations of this anchor code, and this helps to avoid weak spots in the code graph that usually arise when edge permutations are assigned by greedy algorithms. There are also varying numbers of auxiliary and ancillary checks, variables, and edges, allowing realization of different rates, with fixed (nominal) dimension k = 8176 for all rates. Simulations show that all members of this family achieve steeply falling error rate curves without detectable error floors, at least to codeword error rates of about 10-6
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.
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.
The use of rate-compatible error correcting codes offers several advantages as compared to the use of fixed-rate codes: a smooth adaptation to the channel conditions, the possibility of incremental Hybrid ARQ schemes, as well as sharing of the encoder and decoder implementations between the codes of different rates. In this paper, the implementation of a decoder for rate-compatible quasi-cyclic LDPC codes is considered. Assuming the use of a code ensemble obtained through puncturing of a low-rate mother code, the decoder achieves significantly reduced convergence rates by merging the check node neighbours of the punctured variable nodes. The architecture uses the minsum algorithm with serial node processing elements to efficiently handle the wide spread of node degrees that results from the merging of the check nodes.
This work investigated the performance of a newly developed protograph-based low-density parity-check code (LDPC) families belonging to accumulate-repeat-4-jagged-accumulate codes. The proposed code has hierarchical irregularity and quasi-cyclic property that retains it to be suitable for fast encoder and decoder implementation. The code used in this work is a rate-compatible linearly punctured code. The modified iterative decoding algorithm as mentioned in the literature is used along with a newly proposed encoder and simulation has been done for proposed LDPC coded orthogonal frequency division multiplexing (OFDM) link over wireless and optical wireless channels with hard- and soft-decision decoding. The code relates to new methods for designing rate-compatible families of protographs of different rates, all having the linear minimum distance property showing small performance degradation compared with the threshold. The parity-check matrix is composed of small identical modules to reduce the routing complexity of the decoder. The main essence of this code lies in the fact that LDPC codes of arbitrarily large size can be built by expanding from individual protographs or rate-compatible protograph families.