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On the encoding complexity of Quasi-Cyclic LDPC Codes

IEEE TRANSACTIONS ON SIGNAL PROCESSING 2015年第22期63卷 6096-6108页

作者： Mahdi, Ahmed Paliouras, Vassilis Univ Patras Elect & Comp Engn Dept VLSI Design Lab Patras 26500 Greece

In this paper, we propose a parity check matrix (PCM) construction technique that reduces the encoding complexity of quasi-cyclic (QC)-LDPC codes. The proposed construction method is based on a constraint selection of shifting factors, shown here to reduce the density of an inverted matrix used in several encoding algorithms. Furthermore, it demonstrates that the complexity of encoding schemes involving inverted matrices, can be defined by the density of the small inverted binary base matrix and not by the extended QC-PCM. Comparisons of the proposed codes with codes employed in international standards and with randomly shifted QC-LDPC codes of comparable characteristics, show the low complexity of the corresponding hardware implementations and a BER performance equivalent to that of previously reported codes without increasing the decoding complexity. Furthermore, adoption of the proposed method can decrease the complexity of several encoding procedures;in particular, an area reduction of 40%-55% is reported for QC-LDPC encoders, while a reduction of 86% is reported for Multi-Level-QC-LDPC encoders.

关键词： BER performance density reduction encoding complexity hardware architecture LDPC encoding matrix inversion quasi-cyclic LDPC

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A Class of QC-LDPC Codes with Low encoding complexity and Good Error Performance

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IEEE COMMUNICATIONS LETTERS 2010年第2期14卷 169-171页

作者： Tam, Wai M. Lau, Francis C. M. Tse, Chi K. Hong Kong Polytech Univ Elect & Informat Engn Dept Hong Kong Hong Kong Peoples R China

We propose a novel approximate lower triangular structure for the parity part of the parity-check matrix of QC-LDPC codes. About half of the non-zero elements in the parity part are set to locate on the upper diagonal while the remaining non-zero elements can be located almost anywhere within the lower triangular area, provided certain rules are observed. Compared with the typical dual-diagonal structure, the proposed structure requires very similar encoding complexity and produces lower error rates over an AWGN channel.

关键词： Approximate lower triangular structure encoding complexity QC low-density-parity-check (LDPC) codes

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Rate Adaptive Non-Binary LDPC Codes with Low encoding complexity

Rate Adaptive Non-Binary LDPC Codes with Low Encoding Comple...

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45th Asilomar Conference on Signals, Systems and Computers (ASILOMAR)

作者： Chang, Nicholas B. MIT Lincoln Lab 244 Wood St Lexington MA 02420 USA

ISBN: (纸本)9781467303231

For error-correction codes, the optimal coding rate can vary and depend on factors including channel, time-varying fading, environmental interference, power, bandwidth allocation, communication content, and application. Rate adaptive coding schemes are thus important for robust communications. This writeup proposes and studies a rate adaptive low density parity check (LDPC) coding scheme using non-binary Galois fields (GF). The algorithm uses a single low complexity encoding structure, but maintains strong near-capacity performance at arbitrary rational rates. The rate adaptive encoder can be used in a space-time code for multiple-input multiple-output (MIMO) communication systems and is shown to achieve near capacity performance at various rates and different MIMO configurations.

关键词： error correction coding low-density parity-check encoding complexity outage capacity space-time coding multiple-input multiple-output rate-adaptive codes puncturing

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Video encoding complexity Characterization 14

Video Encoding Complexity Characterization

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14th International Conference on Quality of Multimedia Experience (QoMEX)

作者： Satti, Shahid Mahmood Obermann, Matthias Schmidmer, Christian Keyhl, Michael Optic GmbH Erlangen Germany

ISBN: (数字)9781665487948

ISBN: (纸本)9781665487948

Spatial/temporal information (SI/TI) is used to characterize the scene-complexity of videos. It is often hypothesized that SI/TI can also be used to measure the encoding-complexity of a video;although higher scene-complexity may not always mean a higher encoding-complexity for videos. In this paper, two alternative views on the video encoding-complexity are proposed. In the first view, a ground-truth of encoding-complexity is derived using the area-under-the-curve of a rate-quality plot. In the second view, constant rate-factor (CRF) video encoding is used to synthesize a measure of video encoding-complexity. Experimental evaluation on 734 UHD video sequences showed that the CRF based method, compared to SI/TI, yields better complexity characterization w.r.t. the ground-truth.

关键词： video quality encoding complexity rate distortion

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A Graph Theoretical Approach to Network encoding complexity

A Graph Theoretical Approach to Network Encoding Complexity

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International Symposium on Information Theory and its Applications (ISITA)

作者： Xu, Easton Li Shang, Weiping Han, Guangyue Univ Hong Kong Hong Kong Hong Kong Peoples R China Zhengzhou Univ Zhengzhou Peoples R China Univ Hong Kong Hong Kong Peoples R China

ISBN: (纸本)9784885522673

For an acyclic directed network with multiple pairs of sources and sinks and a group of edge-disjoint paths connecting each pair of source and sink, it is known that the number of mergings among different groups of edge-disjoint paths is closely related to network encoding complexity. Using this connection, we derive exact values of and bounds on two functions relevant to encoding complexity for such networks.

关键词： encoding complexity Sinks Network Paths Pairing

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Low-complexity encoding of Quasi-Cyclic Codes Based on Galois Fourier Transform

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IEEE TRANSACTIONS ON COMMUNICATIONS 2014年第6期62卷 1757-1767页

作者： Huang, Qin Tang, Li He, Shanbao Xiong, Zixiang Wang, Zulin Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China China Acad Space Technol Qian Xuesen Lab Space Technol Beijing 100094 Peoples R China China Acad Space Technol Beijing 100094 Peoples R China Texas A&M Univ Dept Elect & Comp Engn ECE College Stn TX 77843 USA

This paper presents two novel low-complexity encoding algorithms for quasi-cyclic (QC) codes based on Galois Fourier transform. The key idea behind them is making use of the block diagonal structure of the transformed generator matrix. The first one, named encoding by Galois Fourier transform, is equivalent to the fast implementations of the traditional encoding by Galois Fourier transform. The second one, named encoding in the transform domain (ETD), requires much less computational complexity for encoding binary QC codes. It skips the first step of the first algorithm and applies post-processing to save a large number of Galois field multiplications. Its application to QC-LDPC codes is also studied in this paper. Particularly, the hardware cost of the ETD for RS-based LDPC codes can be greatly reduced by short linear-feedback shift registers.

关键词： encoding complexity Galois Fourier transform (GFT) low-density parity-check (LDPC) codes matrix transformation quasi-cyclic (QC) codes redundant rows

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Low complexity encoding Algorithm of RS-based QC-LDPC Codes

Low Complexity Encoding Algorithm of RS-based QC-LDPC Codes

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Information Theory and Applications Workshop (ITA)

作者： Zhang, Mu Tang, Li Huang, Qin Wang, Zulin Beihang Univ Sch Elect & Informat Engn Beijing 100191 Peoples R China

ISBN: (纸本)9781479935901

This paper presents a novel encoding algorithm for QC-LDPC codes constructed from Reed-Solomon codes. The encoding is performed in the transform domain via Galois Fourier transformation. Message bits are encoded in sections corresponding to sub-matrices of the parity-check matrix in the transform domain. Because of the structure of the paritycheck matrices of these LDPC codes, the encoding can be easily implemented with some linear-feedback shift registers, thus efficiently reduces the hardware cost.

关键词： LDPC codes RS codes encoding complexity matrix transformation Galois Fourier transform

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Low-complexity MPEG-4 shape encoding towards realtime object-based applications

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ETRI JOURNAL 2004年第2期26卷 122-135页

作者： Jang, ES Hanyang Univ Coll Informat & Commun Software Div Seoul 133791 South Korea

Although frame-based MPEG-4 video services have been successfully deployed since 2000, MPEG-4 video coding is now facing great competition in becoming a dominant player in the market. Object-based coding is one of the key functionalities of MPEG-4 video coding. Real-time object-based video encoding is also important for multimedia broadcasting for the near future. Object-based video services using MPEG-4 have not yet made a successful debut due to several reasons. One of the critical problems is the coding complexity of object-based video coding over frame-based video coding. Since a video object is described with an arbitrary shape, the bitstream contains not only motion and texture data but also shape data. This has introduced additional complexity to the decoder side as well as to the encoder side. In this paper, we have analyzed the current MPEG-4 video encoding tools and proposed efficient coding technologies that reduce the complexity of the encoder. Using the proposed coding schemes, we have obtained a 56 percent reduction in shape-coding complexity over the MPEG-4 video reference software (Microsoft version, 2000 edition).

关键词： MPEG4 encoding complexity real-time video shape coding

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ON THE PERFORMANCE AND complexity OF CHANNEL-OPTIMIZED VECTOR QUANTIZERS

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IEEE TRANSACTIONS ON INFORMATION THEORY 1991年第1期37卷 155-160页

作者： FARVARDIN, N VAISHAMPAYAN, V TEXAS A&M UNIV SYST DEPT ELECT ENGN COLLEGE STN TX 77843 USA

The performance and complexity of channel-optimized vector quantizers are studied for the Gauss-Markov source. Observations on the geometric structure of these quantizers are made, which have an important implication on the encoding complexity. For the squared-error distortion measure, it is shown that an operation equivalent to a Euclidean distance measurement with respect to an appropriately defined set of points (used to identify the encoding regions) can be used to perform the encoding. This implies that the encoding complexity is proportional to the number of encoding regions. It is then demonstrated that for very noisy channels and a heavily correlated source, when the codebook size is large, the number of encoding regions is considerably smaller than the codebook size-implying a reduction in encoding complexity.

关键词： geometrical construction coding encoding complexity complexity quantizer codebook distance measurement

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Two-pass MPEG-2 variable-bit-rate encoding

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IBM JOURNAL OF RESEARCH AND DEVELOPMENT 1999年第4期43卷 471-488页

作者： Westerink, PH Rajagopalan, R Gonzales, CA IBM Corp Div Res Thomas J Watson Res Ctr Multimedia Technol Yorktown Heights NY 10598 USA Lucent Technol Bridgewater NJ 08807 USA IBM Digital Video Prod Grp Dev Org Yorktown Heights NY USA

Many MPEG-2 encoding applications are realtime;this implies that the video signal must be encoded with no significant lookahead. However, there exist non-real-time applications that do enable us to first analyze a video sequence entirely, and, using the analysis results, to optimize a second encoding pass of the same data. One example of such an application is the digital video disk (DVD), which is designed to facilitate a variable-bit-rate (VBR) output stream. In that case, it is possible to let the MPEG-2 encoder produce a video sequence with a constant visual quality over time. This is in contrast to constant-bit-rate (CBR) systems, where the rate is constant but the visual quality Varies with the coding difficulty. This paper describes a two-pass encoding system that has as its objective to produce an optimized VER data stream in a second pass. In a first pass, the video sequence is encoded with CBR, while statistics concerning coding complexity are gathered. Next, the first-pass data is processed to prepare the control parameters for the second pass, which performs the actual VER compression. In this off-line processing stage, we determine the target number of bits for each picture in the sequence, such that we realize the VER objective. This means that the available bits are appropriately distributed over the different Video segments such that constant visual quality is obtained. To be able to quantify the constant visual quality, perceptual experiments are described and a practical model is fitted to them. Exceptional cases such as scene changes and fades are detected and dealt with appropriately. We also ensure that the second-pass compression process does not violate the decoder buffer boundaries. Finally, the encoding is performed again, but now under control of the processed first-pass data. During the running of this second pass, a run-time bit-production control mechanism monitors the accuracy and validity of the first-pass data, correcting errors in pr

关键词： Video sequences Visualization coding encoding complexity control parameter Video signals variable Bit rate lining processes Coding systems

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