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Composite scheme LR+Th for decoding with erasures and its effective equivalence to Forney's rule

IEEE TRANSACTIONS ON INFORMATION THEORY 1999年第1期45卷 78-93页

作者： Hashimoto, T Univ Electrocommun Dept Elect Engn Chofu Tokyo 182 Japan

For decoding with erasures, Forney's scheme is known to be optimal in the sense that no other scheme can make the erasure probability P-ers and undetected error probability P-uer simultaneously smaller, me propose a scheme for erasure decision which tests the likelihood ratio as well as the likelihood itself and show that the attainable upper bounds on P-ers and P-uer are the same as those proved for the optimal scheme up to a constant factor. We also show that the scheme gives, when applied to convolutional codes, a bound which is related to the block-coding bound via Forney's inverse concatenation construction We show that,this bound is the same as the one which naturally arises when we apply Raghavan and Baum's optimal scheme to convolutional code.

关键词： convolutional code decoding with erasures erasure probability error exponent undetected error probability

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Anti-jamming Frequency Hopping System Using Multiple Hopping Patterns

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WIRELESS PERSONAL COMMUNICATIONS 2015年第3期81卷 1159-1176页

作者： Quan, Houde Zhao, Huan Cui, Peizhang Mech Engn Coll Dept Informat Engn Shijiazhuang 050003 Peoples R China

This paper deals with the follower jamming (FJ) and partial-band jamming (PBJ) resistance for the frequency hopping (FH) communication system with low hopping rate over AWGN channel. To gain a comprehensive FJ and PBJ rejection capability, we propose a multi-pattern frequency hopping (MPFH) scheme. In MPFH, the data channel and complementary channel are hopped on separate frequency slots determined by their respective frequency patterns, which will lure the follower jammer out of aiming at the complementary channel, thus mitigating the effect of FJ. Besides, narrow-band receiver is employed to ensure its PBJ rejection capability. We further enhance the proposed scheme by employing convolutional coding and maximum-likelihood decoding. Its upper bounds on bit error rate (BER) are derived under FJ and PBJ, respectively. Effects of three FJ parameters (tracking success probability, jamming duration ratio and jamming bandwidth ratio) and one PBJ parameter (jamming bandwidth ratio) on BER performance of MPFH are investigated versus the conventional FH/BFSK and recently developed differential frequency hopping (DFH) system. Numerical and simulation results show that when under the worst-case FJ, the proposed MPFH performs as well as DFH, but outperforms the conventional FH/BFSK by more than 5 dB;on the other hand, when under worst-case PBJ, the MPFH has the similar BER performance as conventional FH/BFSK, but outperforms DFH by more than 5 dB. The proposed MPFH shows superior jamming rejection performance under both PBJ and FJ.

关键词： Frequency hopping Multi-pattern frequency hopping Follower jamming Partial-band jamming convolutional code

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Coding techniques for link adaptation in multicarrier systems

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IET COMMUNICATIONS 2008年第7期2卷 895-902页

作者： Nagaraj, S. Bell, M. San Diego State Univ Dept Elect & Comp Engn San Diego CA 92182 USA Purdue Univ Dept Elect & Comp Engn W Lafayette IN 47907 USA

A novel technique for improving coding and diversity gains in orthogonal frequency division multiplexing (OFDM) systems is proposed. Multidimensional symbol design based on complex field codes with interleaving across frequency has been known for some time now. However, such symbols cannot be concatenated to convolutional codes owing to the prohibitive complexity of decoding. A novel way of designing multidimensional symbols that allow to concatenate them to convolutional codes while maintaining a low decoding complexity is shown. The proposed multidimensional symbols are based on tailbiting convolutional codes and the design of codes is discussed with desirable properties. Also the design of bit interleaved coded modulation-type and trellis-coded modulation-type codes over these multidimensional symbols is shown. Simulations show that the proposed coding scheme provides significant performance and/or complexity improvements over existing alternatives and also provides more degrees of freedom for channel-based link adaptation.

关键词： orthogonal frequency division multiplexing convolutional codes interleaved codes channel coding decoding convolutional code concatenated code OFDM system OFDM modulation channel-based link adaptation trellis coded modulation concatenated codes multicarrier system trellis-coded modulation adaptive codes telecommunication links interleaved code multidimensional symbol design

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Search and determination of convolutional self-doubly orthogonal codes for iterative threshold decoding

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IEEE TRANSACTIONS ON COMMUNICATIONS 2005年第5期53卷 802-809页

作者： Haccoun, D Cardinal, C Gagnon, F Ecole Polytech Dept Elect Engn Montreal PQ H3C 3A7 Canada Ecole Technol Super Dept Elect Engn Montreal PQ H3C 1K3 Canada

In this paper, we present new results on the search and determination of wide-sense convolutional self-doubly orthogonal codes ((CSOC)-C-2-WS) which can be decoded using a simple iterative threshold decoding algorithm without interleaving. For their iterative decoding, in order to ensure the independence of observables over the first two iterations without the presence of interleavers, these (CSOC)-C-2 must satisfy specific orthogonal properties of their generator connections. The error performances of (CSOC)-C-2, depend essentially on the number of taps J of the code generators but not on the code memory length. Since the overall latency of the iterative threshold decoding process is proportional to the memory length of the codes, therefore, when searching for the best (CSOC)-C-2-WS of a given J value, the memory length of the codes should be chosen to be as small as possible. In this paper, we present a code-searching technique based on heuristic computer searching algorithms which have yielded the best known (CSOC)-C-2-WS. The construction method for (CSOC)-C-2-WS has provided the best known r = 1/2 codes with the shortest memory length having J ≤ 30. Although not very complex to implement, the search method presented here is quite efficient especially in reducing very substantially the execution time required to determine the codes with the shortest spans. Furthermore, in addition to presenting the search results for the codes, error performances obtained by simulation are also provided.

关键词： convolutional code convolutional self-doubly orthogonal code ((CSOC)-C-2) span of the code systematic encoder threshold decoder

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Searching for Voltage Graph-Based LDPC Tailbiting codes With Large Girth

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IEEE TRANSACTIONS ON INFORMATION THEORY 2012年第4期58卷 2265-2279页

作者： Bocharova, Irina E. Hug, Florian Johannesson, Rolf Kudryashov, Boris D. Satyukov, Roman V. St Petersburg Univ Informat Technol Mech & Opt Dept Informat Syst St Petersburg Russia Lund Univ Dept Elect & Informat Technol Lund Sweden Google Switzerland Zurich Switzerland

The relation between parity-check matrices of quasi-cyclic (QC) low-density parity-check (LDPC) codes and biadjacency matrices of bipartite graphs supports searching for powerful LDPC block codes. Using the principle of tailbiting, compact representations of bipartite graphs based on convolutional codes can be found. Bounds on the girth and the minimum distance of LDPC block codes constructed in such a way are discussed. Algorithms for searching iteratively for LDPC block codes with large girth and for determining their minimum distance are presented. Constructions based on all-one matrices, Steiner Triple Systems, and QC block codes are introduced. Finally, new QC regular LDPC block codes with girth up to 24 are given.

关键词： Biadjacency matrix convolutional code girth low-density parity-check (LDPC) code minimum distance tailbiting Tanner graph

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A Method for Blind Identification of a Scrambler Based on Matrix Analysis

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IEEE COMMUNICATIONS LETTERS 2018年第11期22卷 2198-2201页

作者： Han, Shunan Zhang, Min Natl Univ Def Technol Coll Elect Engn Hefei 230031 Anhui Peoples R China

Existing methods for identifying a scrambler placed after a convolutional encoder require prior knowledge about the encoding type and a dual word of the convolutional code. To overcome these limitations, we propose here a method for blind identification of a scrambler based on matrix analysis. The rank behaviors of self-synchronously and synchronously scrambled convolutional code bit matrices are first analyzed theoretically. Based on their rank deficient characteristics, preliminary identification of the encoding type of a received sequence can then take place. After this, by using the bases in the null space of the received bit matrix, the feedback polynomial of the scrambler can be reconstructed. Furthermore, according to the rank behavior of the descrambled sequence, the type of the scrambler can be determined. This method can thus arrive at the blind identification of a scrambler without any prior knowledge.

关键词： Scrambler convolutional code blind identification matrix analysis

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Analysis of PAM Mapping for convolutional-coded Physical-Layer Network Coding

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IEEE COMMUNICATIONS LETTERS 2022年第6期26卷 1254-1258页

作者： Chen, Pingping Xu, Fangjin Fang, Yi Chen, Feng Wang, Feng Fuzhou Univ Dept Elect Informat Fuzhou 350108 Fujian Peoples R China Guangdong Univ Technol Sch Informat Engn Guangzhou 510006 Peoples R China Quanzhou Normal Univ Sch Informat Engn Quanzhou 510006 Peoples R China

In this letter, we investigate iterative decoding for convolutional-coded physical-layer network coding operated with bit-interleaved coded modulation (BICM-PNC) over two-way relay channel (TWRC). The superimposed constellation at the relay from two users may not remain the same characteristic as the original modulation at the users. Thus, we first propose a design of mapping for PAM modulations at the users and enable the superimposed constellation of the maximum squared Euclidean weight (MSEW). Then, we analyze the PNC mappings by means of an extrinsic information transfer (EXIT) chart. The analysis and simulation results show that the proposed mapping can provide a good match to a given outer channel code. In particular, it achieves much better error performance than the conventional semi-Gray and binary-bit mappings at high SNR region for both 8-PAM and 16-PAM modulations.

关键词： Modulation Relays Iterative decoding Decoding convolutional codes Transfer functions Signal to noise ratio PAM modulation convolutional code physical-layer network coding

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On Multiple Slice Turbo codes

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ANNALS OF TELECOMMUNICATIONS 2005年第1-2期60卷 79-102页

作者： Gnaedig, D Boutillon, E Jézéquel, M Gaudet, VC Gulak, PG Technopole Brest Iroise TurboConcept F-29280 Plouzane France Univ Bretagne Sud LESTER F-56321 Lorient France PRACOM CNRS Unite 2658 ENST BretagneGET F-29285 Brest France Univ Alberta Dept ECE Edmonton AB T6G 2V4 Canada Univ Toronto Dept ECE Toronto ON M5S 3G4 Canada

The main problem with the hardware implementation of turbo codes is the lack of parallelism in the MAP-based decoding algorithm. This paper proposes to overcome this problem by using a new family of turbo codes called Multiple Slice Turbo codes. This family is based on two ideas: the encoding of each dimension with P independent tail-biting codes and a constrained interleaver structure that allows the parallel decoding of the P independent codewords in each dimension. The optimization of the interleaver is described. A high degree of parallelism is obtained with equivalent or better performance than the DVB-RCS turbo code. For very high throughput applications, the parallel architecture decreases both decoding latency and hardware complexity compared to the classical serial architecture, which requires memory duplication.

关键词： error correcting code turbo code decoding convolutional code parallelism interleaving recursivity A posteriori probability

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Optimizing the Parallel Tree-Search for Finding Shortest-Span Error-Correcting CDO codes

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IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS 2014年第11期25卷 2992-3001页

作者： Kowarzyk, Gilbert Belanger, Normand Haccoun, David Savaria, Yvon Ecole Polytech Montreal Montreal PQ Canada

Finding optimal/short-span convolutional Self-Doubly Orthogonal (CDO) codes and Simplified-CDO (S-CDO) codes for a specified order J is computationally very challenging. This paper describes several optimizations that were applied to an implicitly-exhaustive search algorithm in order to reduce the time required for finding these types of codes. The resulting high-performance parallel implementation provides an impressive speedup that is greater than 16 300 (CDO, J - 7) and 6300 (S-CDO, J - 8) over the reference implicitly-exhaustive search algorithm, and greater than 2000 (J - 17) over the fastest published CDO validation function used in high-performance pseudorandom search algorithms. These speedups are achieved through enhancements in the deterministic search-space reduction, and a vastly improved validation function that makes use of a novel data structure for enabling data-reuse and incremental computations. The resulting validation function speedup is greater than 60 000 (S-CDO, J = 17) and 190 000 (CDO, J = 17) when compared to its reference implementation. The combination of optimizations and load-balancing techniques allowed us to leverage hundreds of processor cores in order to complete an exhaustive search over a search space that is some 10(14) times larger than what was previously possible.

关键词： convolutional code self-doubly orthogonal code parallel tree-traversal data-reuse systematic encoder threshold decoder

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Cherry-Picking Reliable PUF Bits With Differential Sequence Coding

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IEEE TRANSACTIONS ON INFORMATION FORENSICS AND SECURITY 2016年第9期11卷 2065-2076页

作者： Hiller, Matthias Yu, Meng-Day (Mandel) Sigl, Georg Tech Univ Munich Chair Secur Informat Technol D-80333 Munich Germany Verayo Inc San Jose CA 95129 USA Katholieke Univ Leuven Comp Secur & Ind Cryptog Res Grp B-3001 Leuven Belgium MIT Comp Sci & Artificial Intelligence Lab 77 Massachusetts Ave Cambridge MA 02139 USA

Silicon physical unclonable functions (PUFs) produce a sequence of response bits from chip-unique manufacturing variations. Since the response bits are physically derived, there is noise present. To generate bit-exact cryptographic keys, error correction algorithms are used. The error correction is typically split into small processing blocks to reduce implementation complexity. The reliability of PUF responses varies from bit to bit, but there has been very little work so far that mathematically analyzes the effect of the block size on the reliability of PUF response sequences. We use the information theoretical concept of typicality to show that the probability of drawing an unreliable sequence decreases exponentially with the block size. We present differential sequence coding that scales efficiently across larger block sizes without having the super-linear increase in decoding complexity of prior approaches. It scans the entire PUF response sequentially and then only operates on one single, maximally reliable, block to generate the cryptographic key. Our sample FPGA implementation with a convolutional code is designed for a popular SRAM PUF scenario. It generates a 128-bit key for an average input bit error probability of 15% with an output bit error probability of 6.14 . 10(-9) and only uses 974 PUF bits and 1, 108 helper data bits. There are 36% less PUF bits and 71% less helper data bits than the best previous individual results in both criteria without increasing the implementation size of the key generation module noticeably.

关键词： Physical unclonable function (Puf) syndrome coding error correction differential sequence coding (Dsc) typicality convolutional code FPGA

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