436 research outputs found

    A Cascadable Pragmatic Block Decoding Algorithm Exploiting Channel Measurement Information

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    The complexity of algorithms to perform soft decision decoding on block codes has impeded their inclusion in practical systems. A well-known class of algorithms for decoding block codes utilizing channel measurement information along with the algebraic properties of the code are the Chase algorithms.1 In this paper a decoding method similar to Chase\u27s third algorithm is presented. However, in this method, a single test pattern or alternate codeword makes up one stage of the decoder. The method uses information from the previous decoding(s) to assist in generating a test pattern. This single stage ‘Second Chance Algorithm’ can then be extended to a ‘Third Chance Algorithm’ (and beyond) to enhance performance. The method does not invoke the hard decision decoder as often as the Chase algorithms

    Determinate-state convolutional codes

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    A determinate state convolutional code is formed from a conventional convolutional code by pruning away some of the possible state transitions in the decoding trellis. The type of staged power transfer used in determinate state convolutional codes proves to be an extremely efficient way of enhancing the performance of a concatenated coding system. The decoder complexity is analyzed along with free distances of these new codes and extensive simulation results is provided of their performance at the low signal to noise ratios where a real communication system would operate. Concise, practical examples are provided

    Peak-to-Mean Power Control in OFDM, Golay Complementary Sequences, and Reed–Muller Codes

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    We present a range of coding schemes for OFDM transmission using binary, quaternary, octary, and higher order modulation that give high code rates for moderate numbers of carriers. These schemes have tightly bounded peak-to-mean envelope power ratio (PMEPR) and simultaneously have good error correction capability. The key theoretical result is a previously unrecognized connection between Golay complementary sequences and second-order Reed–Muller codes over alphabets â„€2h. We obtain additional flexibility in trading off code rate, PMEPR, and error correction capability by partitioning the second-order Reed–Muller code into cosets such that codewords with large values of PMEPR are isolated. For all the proposed schemes we show that encoding is straightforward and give an efficient decoding algorithm involving multiple fast Hadamard transforms. Since the coding schemes are all based on the same formal generator matrix we can deal adaptively with varying channel constraints and evolving system requirements

    Performance of binary block codes at low signal-to-noise ratios

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    The performance of general binary block codes on an unquantized additive white Gaussian noise (AWGN) channel at low signal-to-noise ratios is considered. Expressions are derived for both the block error and the bit error probabilities near the point where the bit signal-to-noise ratio is zero. These expressions depend on the global geometric structure of the code, although the minimum distance still seems to play a crucial role. Examples of codes such as orthogonal codes, biorthogonal codes, the (24,12) extended Golay code, and the (15,6) expurgated BCH code are discussed. The asymptotic coding gain at low signal-to-noise ratios is also studied

    Decoding techniques and a modulation scheme for band-limited communications

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    Iterative decoding for error resilient wireless data transmission

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    Both turbo codes and LDPC codes form two new classes of codes that offer energy efficiencies close to theoretical limit predicted by Claude Shannon. The features of turbo codes include parallel code catenation, recursive convolutional encoders, punctured convolutional codes and an associated decoding algorithm. The features of LDPC codes include code construction, encoding algorithm, and an associated decoding algorithm. This dissertation specifically describes the process of encoding and decoding for both turbo and LDPC codes and demonstrates the performance comparison between theses two codes in terms of some performance factors. In addition, a more general discussion of iterative decoding is presented. One significant contribution of this dissertation is a study of some major performance factors that intensely contribute in the performance of both turbo codes and LDPC codes. These include Bit Error Rate, latency, code rate and computational resources. Simulation results show the performance of turbo codes and LDPC codes under different performance factors

    Sparse Graph Codes for Quantum Error-Correction

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    We present sparse graph codes appropriate for use in quantum error-correction. Quantum error-correcting codes based on sparse graphs are of interest for three reasons. First, the best codes currently known for classical channels are based on sparse graphs. Second, sparse graph codes keep the number of quantum interactions associated with the quantum error correction process small: a constant number per quantum bit, independent of the blocklength. Third, sparse graph codes often offer great flexibility with respect to blocklength and rate. We believe some of the codes we present are unsurpassed by previously published quantum error-correcting codes.Comment: Version 7.3e: 42 pages. Extended version, Feb 2004. A shortened version was resubmitted to IEEE Transactions on Information Theory Jan 20, 200

    Self-Dual Codes

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    Self-dual codes are important because many of the best codes known are of this type and they have a rich mathematical theory. Topics covered in this survey include codes over F_2, F_3, F_4, F_q, Z_4, Z_m, shadow codes, weight enumerators, Gleason-Pierce theorem, invariant theory, Gleason theorems, bounds, mass formulae, enumeration, extremal codes, open problems. There is a comprehensive bibliography.Comment: 136 page

    802.11 Payload Iterative decoding between multiple transmission attempts

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    Abstract. The institute of electrical and electronics engineers (IEEE) 802.11 standard specifies widely used technology for wireless local area networks (WLAN). Standard specifies high-performance physical and media access control (MAC) layers for a distributed network but lacks an effective hybrid automatic repeat request (HARQ). Currently, the standard specifies forward error correction (FEC), error detection (ED), and automatic repeat request (ARQ), but in case of decoding errors, the previously transmitted information is not used when decoding the retransmitted packet. This is called Type 1 HARQ. Type 1 HARQ uses received energy inefficiently, but the simple implementation makes it an attractive solution. Unfortunately, research applying more sophisticated HARQ schemes on top of IEEE 802.11 is limited. In this Master’s Thesis, a novel HARQ technology based on packet retransmissions that can be decoded in a turbo-like manner, keeping as much as possible compatibility with vanilla 802.11, is proposed. The proposed technology is simulated with both the IEEE 802.11 code and with the robust, efficient and smart communication in unpredictable environments (RESCUE) code. An additional interleaver is added before the convolutional encoder in the proposed technology, interleaving either the whole frame or only the payload to enable effective iterative decoding. For received frames, turbo-like iterations are done between initially transmitted packet copy and retransmissions. Results are compared against the non-iterative combining method maximizing signal-to-noise ratio (SNR), maximum ratio combining (MRC). The main design goal for this technology is to maintain compatibility with the 802.11 standard while allowing efficient HARQ. Other design goals are range extension, higher throughput, and better performance in terms of bit error rate (BER) and frame error rate (FER). This technology can be used for range extension at low SNR range and may provide up to 4 dB gain at medium SNR range compared to MRC. At high SNR, technology can reduce the penalty from retransmission allowing higher average modulation and coding scheme (MCS). However, these gains come with the cost of computational complexity from the iterative decoding. The main limiting factors of the proposed technology are decoding errors in the header and the scrambler area, and resource-hungry-processing. In simulations, perfect synchronization and packet detection is assumed, but in reality, especially at low SNR, packet detection and synchronization would be challenging. 802.11 pakettien iteratiivinen dekoodaus lĂ€hetysten vĂ€lillĂ€. TiivistelmĂ€. IEEE 802.11-standardi mÀÀrittelee yleisesti kĂ€ytetyn teknologian langattomille lĂ€hiverkoille. Standardissa mÀÀritellÀÀn tehokas fyysinen- ja verkkoliityntĂ€kerros hajautetuille verkoille, mutta siitĂ€ puuttuu tehokas yhdistetty automaattinen uudelleenlĂ€hetys. NykyisellÀÀn standardi mÀÀrittelee virheenkorjaavan koodin, virheellisen paketin tunnistuksen sekĂ€ automaattisen uudelleenlĂ€hetyksen, mutta aikaisemmin lĂ€hetetyn paketin informaatiota ei kĂ€ytetĂ€ hyvĂ€ksi uudelleenlĂ€hetystilanteessa. TĂ€mĂ€ menetelmĂ€ tunnetaan tyypin yksi yhdistettynĂ€ automaattisena uudelleenlĂ€hetyksenĂ€. Tyypin yksi yhdistetty automaattinen uudelleenlĂ€hetys kĂ€yttÀÀ vastaanotettua signaalia tehottomasti, mutta yksinkertaisuus tekee siitĂ€ houkuttelevan vaihtoehdon. Valitettavasti edistyneempien uudelleenlĂ€hetysvaihtoehtojen tutkimusta 802.11-standardiin on rajoitetusti. TĂ€ssĂ€ diplomityössĂ€ esitellÀÀn uusi yhdistetty uudelleenlĂ€hetysteknologia, joka pohjautuu pakettien uudelleenlĂ€hetykseen, sallien turbo-tyylisen dekoodaamisen sĂ€ilyttĂ€en mahdollisimman hyvĂ€n taaksepĂ€in yhteensopivuutta alkuperĂ€isen 802.11-standardin kanssa. TĂ€mĂ€ teknologia on simuloitu kĂ€yttĂ€en sekĂ€ 802.11- ettĂ€ nk. RESCUE-virheenkorjauskoodia. Teknologiassa uusi lomittaja on lisĂ€tty konvoluutio-enkoodaajan eteen, sallien tehokkaan iteratiivisen dekoodaamisen, lomittaen joko koko paketin tai ainoastaan hyötykuorman. Vastaanotetuille paketeille tehdÀÀn turbo-tyyppinen iteraatio alkuperĂ€isen vastaanotetun kopion ja uudelleenlĂ€hetyksien vĂ€lillĂ€. Tuloksia vertaillaan eiiteratiiviseen yhdistĂ€mismenetelmÀÀn, maksimisuhdeyhdistelyyn, joka maksimoi yhdistetyn signaali-kohinasuhteen. TĂ€rkeimpĂ€nĂ€ suunnittelutavoitteena tĂ€ssĂ€ työssĂ€ on tehokas uudelleenlĂ€hetysmenetelmĂ€, joka yllĂ€pitÀÀ taaksepĂ€in yhteensopivuutta IEEE 802.11-standardin kanssa. Muita tavoitteita ovat kantaman lisĂ€ys, nopeampi yhteys ja matalampi bitti- ja pakettivirhesuhde. KehitettyĂ€ teknologiaa voidaan kĂ€yttÀÀ kantaman lisĂ€ykseen matalan signaalikohinasuhteen vallitessa ja se on jopa 4 dB parempi kohtuullisella signaalikohinasuhteella kuin maksimisuhdeyhdistely. Korkealla signaali-kohinasuhteella teknologiaa voidaan kĂ€yttÀÀ pienentĂ€mÀÀn hĂ€viötĂ€ epĂ€onnistuneesta paketinlĂ€hetyksestĂ€ ja tĂ€ten sallien korkeamman modulaatio-koodiasteen kĂ€yttĂ€misen. Valitettavasti nĂ€mĂ€ parannukset tulevat kasvaneen laskennallisen monimutkaisuuden kustannuksella, johtuen iteratiivisesta dekoodaamisesta. Isoimmat rajoittavat tekijĂ€t teknologian kĂ€ytössĂ€ ovat dekoodausvirheet otsikossa ja datamuokkaimen siemenessĂ€. TĂ€mĂ€n lisĂ€ksi kĂ€yttöÀ rajoittaa resurssisyöppö prosessointi. Simulaatioissa oletetaan tĂ€ydellinen synkronisointi, mutta todellisuudessa, erityisesti matalalla signaali-kohinasuhteella, paketin tunnistus ja synkronointi voivat olla haasteellisia
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