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Evaluation of LDPC decoder with standardized codes

Jun Zhao

Published Jan 1, 2012• 0 citations
OpenAlex

Abstract

Low density parity check (LDPC) codes are one of the most popular channel codes.Based on traditional sum-product and max-product algorithms, various modified algorithms are tried to improve the performance of LDPC codes in terms of error rate, complexity and latency.Uniformly rweighted belief propagation (URW-BP) algorithm can offer better performance than traditional algorithm especially for regular LDPC codes.linear programming (LP) decoder is also competitive to traditional message passing algorithm.We describe two traditional message passing decoders, four reweighted message passing decoders based on URW-BP and LP decoder in this paper.Reweighted decoders can outperform traditional decoders especially when iteration number is limited.Considering complexity and latency, reweighted max product decoder of version 2 (R-MPD-II) is the most promising decoder.CONTENTS 4.3 Short regular LDPC codes . . . . . . . .

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Low density parity check (LDPC) codes are one of the most popular channel codes.Based on traditional sum-product and max-product algorithms, various modified algorithms are tried to improve the performance of LDPC codes in terms of error rate, complexity and latency.Uniformly rweighted belief propagation (URW-BP) algorithm can offer better performance than traditional algorithm especially for regular LDPC codes.linear programming (LP) decoder is also competitive to traditional message passing algorithm.We describe two traditional message passing decoders, four reweighted message passing decoders based on URW-BP and LP decoder in this paper.Reweighted decoders can outperform traditional decoders especially when iteration number is limited.Considering complexity and latency, reweighted max product decoder of version 2 (R-MPD-II) is the most promising decoder.CONTENTS 4.3 Short regular LDPC codes . . . . . . . .
Low density parity check (LDPC) codes can be decoded with a variety of decoding algorithms, offering a trade-off in terms of complexity, latency, and performance. We describe seven distinct LDPC decoders and provide a performance comparison for a practical regular LDPC code. Our simulations indicate that the best performance/latency trade-off is achieved by one version of the reweighted max-product decoder. When latency is not an issue, the traditional sum-product decoder yields the best performance.
The LDPC coded bit-interleaved coded modulation iterative decoding(BICM-ID)system was modeled by a normal factor graph.From the angle of the message update rule,uniformly reweighted belief propagation algorithm(URW-BP)and belief propagation algorithm(BP)are unified and interpreted as message passing algorithm by variation method.Combining the local nature of BP with the improved performance of URW-BP in graphs with cycles,the uniformly reweighted iterative decoding algorithm(URID)was derived and the impact of edge appearance probabilities(EAP)on its performance discussed. Simulation results for AWGN and Rayleigh fading channel and different modulation illustrate the performance improvement of URID compared with other iterative decoding algorithms such as BP and DifferenceMap BP(DMBP)algorithm.
Channel coding technique is a fundamental building block in any modern communication system to realize reliable, fast, and secure data transmission. At the same time, it is a challenging and crucial task, as the data transmission happens in a channel where noise, fading, and other impairments are present. The Low-Density Parity-Check (LDPC) codes give substantial results close to the Shannon limit when the complexity and processing delay time are unlimited. In this paper, the performance of the LDPC decoding with four algorithms was investigated. The investigated four algorithms were Belief Propagation (BP), Layered Belief Propagation (LBP), Normalized min-sum (NMS), and Offset min-sum (OMS). These algorithms were examined for code rates ranging from 1/3 to 9/10 and message block lengths (64, 512, 1024, and 5120) bits. The simulation results revealed the flexibility of these decoders in supporting these code rates and block lengths, which enables their usage in a wide range of applications and scenarios for fifth-generation (5G) wireless communication. In addition, the effect of the maximum number of decoding iterations on the error correction performance was investigated, and a gain of 5.6 dB can be obtained by using 32 decoding iterations at BER=2*10-3 instead of one decoding iteration. The results showed that the decoders performed better for longer message blocks than for short message blocks, and less power was required for transmitting longer messages. Finally, the comparison results of their performance in terms of bit error rate (BER) under the same conditions showed a gain of 0.8 dB using LBP at BER= 10-5 compared with the NMS decoding algorithm.
For decoding of LDPC codes two types of algorithms are frequently discussed in the literature. One type is based on belief propagation (BP) the other is based on linear programming (LP). Especially for short LDPC codes it has been observed that BP decoding often performs better at low SNR ranges, whereas LP decoding performs better at high SNR levels. A combined linear programming and belief propagation decoder is presented, which significantly outperforms both a pure LP and a pure BP decoder throughout the whole SNR range.
Many classes of high-performance Low-density parity check codes are based on parity check matrices composed of permutation sub matrices. The emulation-simulation framework further allows the algorithm and implementation to be iteratively redefined to improve the error floor performance of message passing decoder. Log-Like hood-Ratio (LLR) based Belief-Propagation (BP) algorithm is presented for Low Density Parity Check codes. Numerically accurate representation of check node update computation used in LLR-BP decoding is described. The implementation of Sum-Product algorithm (SPA) within Low Density Parity Check Code (LDPC) decoder is described in this paper and the correction term is used to improve the decoding performance of min-sum algorithm (MSA). Quantization and log-tanh function approximation in sum-product decoder strongly affect which absorbing set dominates in error floor region. For LDPC decoder, bit error rate (BER) decreases with increase in the signal to noise ratio.
Linear programming (LP) decoding is an alternative to iterative algorithms for decoding low density parity check (LDPC) codes. Although the practical performance of LP decoding is comparable to message-passing decoding, a significant advantage is its relative amenability to nonasymptotic analysis. Moreover, there turn out to be a number of important theoretical connections between the LP decoding and standard forms of iterative decoding. These connections allow theoretical insight from the LP decoding perspective to be transferred to iterative decoding algorithms. These advantages encouraged many researchers to work in this recent decoding technique for LDPC codes. In this paper, LP decoding for LDPC code is extensively reviewed and is discussed in different segmented areas.