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International Journal of Applied Research on Information Technology and Computing

New Optimizations for Layered Non-Binary LDPC Codes Decoding

Sanae El Hassani, Frédéric Guilloud, Ramesh Mahendra Pyndiah, Marie‐Hélène Hamon, Pierre Penard

Published Mar 5, 2013• 0 citations
Publisher

Abstract

Non-binary LDPC codes have interesting performances, especially for short to moderate blocklengths. The decoding schedule of these codes decoding, similarly to the binary case, has an important impact on the decoder's behaviour and should be carefully designed. This paper studies and optimizes the layered scheduling of non-binary LDPC codes following two approaches: A static approach, defining an optimized permanent scheduling for the decoder independently of its entries or state, and a dynamic approach adapting the scheduling on the fly following the decoder's convergence. These two approaches show either a reduction in the number of iterations of about 18% or a reduction in signal to noise ratio of about 0.05dB.

DOI
10.5958/j.0975-8070.3.1.005

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Non-binary LDPC codes have interesting performances, especially for short to moderate blocklengths. The decoding schedule of these codes decoding, similarly to the binary case, has an important impact on the decoder's behaviour and should be carefully designed. This paper studies and optimizes the layered scheduling of non-binary LDPC codes following two approaches: A static approach, defining an optimized permanent scheduling for the decoder independently of its entries or state, and a dynamic approach adapting the scheduling on the fly following the decoder's convergence. These two approaches show either a reduction in the number of iterations of about 18% or a reduction in signal to noise ratio of about 0.05dB.
Non-binary LDPC codes are promising error cor- recting codes for short and moderate block lengths. These codes demonstrate interesting performances in high order fields, though are more complex to decode. As for binary LDPC codes, decoding scheduling can be optimized to improve performance. In this paper, a simulation-based approach is used for different scheduling policies in the non-binary case in order to point out possible performance gains for these codes. An optimization of decoding scheduling is also proposed and exhibits about 20% complexity reduction in error-floor region, thus promising interesting gains if combined with advanced dynamic scheduling strategies. I. INTRODUCTION Channel coding has seen important developments over the last two decades. Thanks to the introduction of advanced error- correcting codes, initiated by Turbo-codes in the early 90's, and to the use of iterative decoding techniques, Shannnon- limit performance has been closely approached. Low-Density Parity-Check (LDPC) codes, first introduced by Gallager (1) in the 60's, were rediscovered by Mackay and Neal (2) in 1996. Excellent error-correcting performance for long block lengths (3) position LDPC codes as an important candidate for advanced communication systems, already adopted in different standards, such as DVB-S2, IEEE 802.16 and 802.11n. How- ever, as codewords become shorter, LDPC performance gains are generally less satisfying. Non-binary LDPC codes, though more complex, proved to significantly improve performance for moderate and short blocklengths (4), (5). The use of a high order alphabet also suggests matching it with the modulation alphabet: LDPC codes over a 16�elements Galois field for example can be naturally mapped in 16�QAM modulated symbols. This would avoid the bit-to-symbol performance loss, especially when having a frequency selective channel, as non- binary encoding can reduce channel memory effect (6). This use of non-binary LDPC codes is thus very promising for high data rate communications, especially when complexity reduc- tion techniques are adopted, either for decoding update rules or scheduling policy. Previous work on scheduling strategies for the binary case can be found in (7). In this paper, we will first address a brief overview of decoding techniques for LDPC codes over high order extension fields. Then, scheduling strategies and effects will be compared for the non-binary case. A simulation-based approach will also be detailed to suggest new scheduling policies, and results from an optimized scheduling will be presented. The paper will be concluded by some remarks and suggestions towards future works.
Non-binary LDPC codes are promising error correcting codes for short and moderate block lengths. These codes demonstrate interesting performances in high order fields, though are more complex to decode. As for binary LDPC codes, decoding scheduling can be optimized to improve performance. In this paper, a simulation-based approach is used for different scheduling policies in the non-binary case in order to point out possible performance gains for these codes. An optimization of decoding scheduling is also proposed and exhibits about 20% complexity reduction in error-floor region, thus promising interesting gains if combined with advanced dynamic scheduling strategies.
An efficient dynamic schedule for layered belief-propagation (LBP) decoding of low-density parity-check (LDPC) codes is presented, in which the check nodes connecting to a variable node with maximum relative message residual are chosen in each dynamic decoding iteration, and then LBP is performed for these check nodes. In this schedule we combined the features of lazy schedule and node-wise residual belief propagation (NWRBP) together while keeping the extra computational complexity very low. Simulation results show that the new schedule speeds up the convergence rate and greatly improves error performance at medium to high signal-to-noise ratio (SNR) when compared to the standard LBP decoding algorithm.
Low-density parity-check (LDPC) codes constructed over the Galois field GF(q) (q>;2), which are also called non-binary LDPC codes, are an extension of binary LDPC codes with significantly better performance. In this paper, an efficient column-layered decoding algorithm, which can reduce the message memory as well as the average number of iterations dramatically, is proposed for min-max decoding. In addition, a non-uniform quantization scheme is developed for reducing the word length while achieving similar performances compared to a conventional quantization scheme. Meanwhile, the corresponding decoder architecture is also proposed.
Recently, the concept of layered decoding schedule for Low-Density Parity-Check codes has been introduced. But the advantage of layered decoding schedule for irregular LDPC codes is not as obvious as regular LDPC codes. The major drawback of the layered irregular LDPC codes versus the layered regular LDPC codes is its comparative low convergence decoding speed. Simulation results show that different bit node degrees of irregular LDPC codes significantly contribute to the decoding performance. The decoding performance of bit nodes with different degrees is of great difference. Bit nodes with small degrees always converge slower than larger ones. In this paper, we propose an optimized decoding schedule for irregular LDPC codes to accelerate the decoding convergence rate. Meanwhile, for the irregular LDPC decoder, the faster decoding speed means a higher throughput and almost the same error performance.
Non-binary LDPC codes are promising error correcting techniques with very good performance, especially for high order fields. Using higher order fields enhances performance but, at the same time, increases decoding complexity. Several methods have been proposed to reduce this complexity, such as sub-optimal decoding algorithms or techniques aiming at reducing the number of iterations. In this paper, a technique for selective check nodes update is presented enabling a complexity reduction at the level of iteration in the non-binary case. More than 35% of complex updates can be saved in a large SNR region, with parameters that can be tuned according to the desired complexity/performance ratio.