110 research outputs found
EXIT charts for system design and analysis
Near-capacity performance may be achieved with the aid of iterative decoding, where extrinsic soft information is exchanged between the constituent decoders in order to improve the attainable system performance. Extrinsic information Transfer (EXIT) charts constitute a powerful semi-analytical tool used for analysing and designing iteratively decoded systems. In this tutorial, we commence by providing a rudimentary overview of the iterative decoding principle and the concept of soft information exchange. We then elaborate on the concept of EXIT charts using three iteratively decoded prototype systems as design examples. We conclude by illustrating further applications of EXIT charts, including near-capacity designs, the concept of irregular codes and the design of modulation schemes
Coding theorems for turbo code ensembles
This paper is devoted to a Shannon-theoretic study of turbo codes. We prove that ensembles of parallel and serial turbo codes are "good" in the following sense. For a turbo code ensemble defined by a fixed set of component codes (subject only to mild necessary restrictions), there exists a positive number Îł0 such that for any binary-input memoryless channel whose Bhattacharyya noise parameter is less than Îł0, the average maximum-likelihood (ML) decoder block error probability approaches zero, at least as fast as n -ÎČ, where ÎČ is the "interleaver gain" exponent defined by Benedetto et al. in 1996
Self-concatenated code design and its application in power-efficient cooperative communications
In this tutorial, we have focused on the design of binary self-concatenated coding schemes with the help of EXtrinsic Information Transfer (EXIT) charts and Union bound analysis. The design methodology of future iteratively decoded self-concatenated aided cooperative communication schemes is presented. In doing so, we will identify the most important milestones in the area of channel coding, concatenated coding schemes and cooperative communication systems till date and suggest future research directions
Trapping Set Enumerators for Repeat Multiple Accumulate Code Ensembles
The serial concatenation of a repetition code with two or more accumulators
has the advantage of a simple encoder structure. Furthermore, the resulting
ensemble is asymptotically good and exhibits minimum distance growing linearly
with block length. However, in practice these codes cannot be decoded by a
maximum likelihood decoder, and iterative decoding schemes must be employed.
For low-density parity-check codes, the notion of trapping sets has been
introduced to estimate the performance of these codes under iterative message
passing decoding. In this paper, we present a closed form finite length
ensemble trapping set enumerator for repeat multiple accumulate codes by
creating a trellis representation of trapping sets. We also obtain the
asymptotic expressions when the block length tends to infinity and evaluate
them numerically.Comment: 5 pages, to appear in proc. IEEE ISIT, June 200
Good Concatenated Code Ensembles for the Binary Erasure Channel
In this work, we give good concatenated code ensembles for the binary erasure
channel (BEC). In particular, we consider repeat multiple-accumulate (RMA) code
ensembles formed by the serial concatenation of a repetition code with multiple
accumulators, and the hybrid concatenated code (HCC) ensembles recently
introduced by Koller et al. (5th Int. Symp. on Turbo Codes & Rel. Topics,
Lausanne, Switzerland) consisting of an outer multiple parallel concatenated
code serially concatenated with an inner accumulator. We introduce stopping
sets for iterative constituent code oriented decoding using maximum a
posteriori erasure correction in the constituent codes. We then analyze the
asymptotic stopping set distribution for RMA and HCC ensembles and show that
their stopping distance hmin, defined as the size of the smallest nonempty
stopping set, asymptotically grows linearly with the block length. Thus, these
code ensembles are good for the BEC. It is shown that for RMA code ensembles,
contrary to the asymptotic minimum distance dmin, whose growth rate coefficient
increases with the number of accumulate codes, the hmin growth rate coefficient
diminishes with the number of accumulators. We also consider random puncturing
of RMA code ensembles and show that for sufficiently high code rates, the
asymptotic hmin does not grow linearly with the block length, contrary to the
asymptotic dmin, whose growth rate coefficient approaches the Gilbert-Varshamov
bound as the rate increases. Finally, we give iterative decoding thresholds for
the different code ensembles to compare the convergence properties.Comment: To appear in IEEE Journal on Selected Areas in Communications,
special issue on Capacity Approaching Code
Analysis and Design of Tuned Turbo Codes
It has been widely observed that there exists a fundamental trade-off between
the minimum (Hamming) distance properties and the iterative decoding
convergence behavior of turbo-like codes. While capacity achieving code
ensembles typically are asymptotically bad in the sense that their minimum
distance does not grow linearly with block length, and they therefore exhibit
an error floor at moderate-to-high signal to noise ratios, asymptotically good
codes usually converge further away from channel capacity. In this paper, we
introduce the concept of tuned turbo codes, a family of asymptotically good
hybrid concatenated code ensembles, where asymptotic minimum distance growth
rates, convergence thresholds, and code rates can be traded-off using two
tuning parameters, {\lambda} and {\mu}. By decreasing {\lambda}, the asymptotic
minimum distance growth rate is reduced in exchange for improved iterative
decoding convergence behavior, while increasing {\lambda} raises the asymptotic
minimum distance growth rate at the expense of worse convergence behavior, and
thus the code performance can be tuned to fit the desired application. By
decreasing {\mu}, a similar tuning behavior can be achieved for higher rate
code ensembles.Comment: Accepted for publication in IEEE Transactions on Information Theor
Iteratively Decoded Irregular Variable Length Coding and Sphere-Packing Modulation-Aided Differential Space-Time Spreading
In this paper we consider serially concatenated and iteratively decoded Irregular Variable Length Coding (IrVLC) combined with precoded Differential Space-Time Spreading (DSTS) aided multidimensional Sphere Packing (SP) modulation designed for near-capacity joint source and channel coding. The IrVLC scheme comprises a number of component Variable Length Coding (VLC) codebooks having different coding rates for the sake of encoding particular fractions of the input source symbol stream. The relative length of these source-stream fractions can be chosen with the aid of EXtrinsic Information Transfer (EXIT) charts in order to shape the EXIT curve of the IrVLC codec, so that an open EXIT chart tunnel may be created even at low Eb/N0 values that are close to the capacity bound of the channel. These schemes are shown to be capable of operating within 0.9 dB of the DSTS-SP channelâs capacity bound using an average interleaver length of 113, 100 bits and an effective bandwidth efficiency of 1 bit/s/Hz, assuming ideal Nyquist filtering. By contrast, the equivalent-rate regular VLC-based benchmarker scheme was found to be capable of operating at 1.4 dB from the capacity bound, which is about 1.56 times the corresponding discrepancy of the proposed IrVLC-aided scheme
802.11 Payload Iterative decoding between multiple transmission attempts
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 Masterâs 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 lÀhetysten vÀlillÀ. TiivistelmÀ. IEEE 802.11-standardi mÀÀrittelee yleisesti kÀytetyn teknologian langattomille lÀhiverkoille. Standardissa mÀÀritellÀÀn tehokas fyysinen- ja verkkoliityntÀkerros hajautetuille verkoille, mutta siitÀ puuttuu tehokas yhdistetty automaattinen uudelleenlÀhetys. NykyisellÀÀn standardi mÀÀrittelee virheenkorjaavan koodin, virheellisen paketin tunnistuksen sekÀ automaattisen uudelleenlÀhetyksen, mutta aikaisemmin lÀhetetyn paketin informaatiota ei kÀytetÀ hyvÀksi uudelleenlÀhetystilanteessa. TÀmÀ menetelmÀ tunnetaan tyypin yksi yhdistettynÀ automaattisena uudelleenlÀhetyksenÀ. Tyypin yksi yhdistetty automaattinen uudelleenlÀhetys kÀyttÀÀ vastaanotettua signaalia tehottomasti, mutta yksinkertaisuus tekee siitÀ houkuttelevan vaihtoehdon. Valitettavasti edistyneempien uudelleenlÀhetysvaihtoehtojen tutkimusta 802.11-standardiin on rajoitetusti.
TÀssÀ diplomityössÀ esitellÀÀn uusi yhdistetty uudelleenlÀhetysteknologia, joka pohjautuu pakettien uudelleenlÀhetykseen, sallien turbo-tyylisen dekoodaamisen sÀilyttÀen mahdollisimman hyvÀn taaksepÀin yhteensopivuutta alkuperÀisen 802.11-standardin kanssa. TÀmÀ teknologia on simuloitu kÀyttÀen sekÀ 802.11- ettÀ nk. RESCUE-virheenkorjauskoodia. Teknologiassa uusi lomittaja on lisÀtty konvoluutio-enkoodaajan eteen, sallien tehokkaan iteratiivisen dekoodaamisen, lomittaen joko koko paketin tai ainoastaan hyötykuorman. Vastaanotetuille paketeille tehdÀÀn turbo-tyyppinen iteraatio alkuperÀisen vastaanotetun kopion ja uudelleenlÀhetyksien vÀlillÀ. Tuloksia vertaillaan eiiteratiiviseen yhdistÀmismenetelmÀÀn, maksimisuhdeyhdistelyyn, joka maksimoi yhdistetyn signaali-kohinasuhteen. TÀrkeimpÀnÀ suunnittelutavoitteena tÀssÀ työssÀ on tehokas uudelleenlÀhetysmenetelmÀ, joka yllÀpitÀÀ taaksepÀin yhteensopivuutta IEEE 802.11-standardin kanssa. Muita tavoitteita ovat kantaman lisÀys, nopeampi yhteys ja matalampi bitti- ja pakettivirhesuhde.
KehitettyÀ teknologiaa voidaan kÀyttÀÀ kantaman lisÀykseen matalan signaalikohinasuhteen vallitessa ja se on jopa 4 dB parempi kohtuullisella signaalikohinasuhteella kuin maksimisuhdeyhdistely. Korkealla signaali-kohinasuhteella teknologiaa voidaan kÀyttÀÀ pienentÀmÀÀn hÀviötÀ epÀonnistuneesta paketinlÀhetyksestÀ ja tÀten sallien korkeamman modulaatio-koodiasteen kÀyttÀmisen. Valitettavasti nÀmÀ parannukset tulevat kasvaneen laskennallisen monimutkaisuuden kustannuksella, johtuen iteratiivisesta dekoodaamisesta. Isoimmat rajoittavat tekijÀt teknologian kÀytössÀ ovat dekoodausvirheet otsikossa ja datamuokkaimen siemenessÀ. TÀmÀn lisÀksi kÀyttöÀ rajoittaa resurssisyöppö prosessointi. Simulaatioissa oletetaan tÀydellinen synkronisointi, mutta todellisuudessa, erityisesti matalalla signaali-kohinasuhteella, paketin tunnistus ja synkronointi voivat olla haasteellisia
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