A unary error correction code for the near-capacity joint source and channel coding of symbol values from an infinite set

A novel Joint Source and Channel Code (JSCC) is proposed, which we refer to as the Unary Error Correction (UEC) code. Unlike existing JSCCs, our UEC facilitates the practical encoding of symbol values that are selected from a set having an infinite cardinality. Conventionally, these symbols are conveyed using Separate Source and Channel Codes (SSCCs), but we demonstrate that the residual redundancy that is retained following source coding results in a capacity loss, which is found to have a value of 1.11 dB in a particular practical scenario. By contrast, the proposed UEC code can eliminate this capacity loss, or reduce it to an infinitesimally small value. Furthermore, the UEC code has only a moderate complexity, facilitating its employment in practical low-complexity applications

Viterbi algorithm in continuous-phase frequency shift keying

The Viterbi algorithm, an application of dynamic programming, is widely used for estimation and detection problems in digital communications and signal processing. It is used to detect signals in communication channels with memory, and to decode sequential error-control codes that are used to enhance the performance of digital communication systems. The Viterbi algorithm is also used in speech and character recognition tasks where the speech signals or characters are modeled by hidden Markov models. This project explains the basics of the Viterbi algorithm as applied to systems in digital communication systems, and speech and character recognition. It also focuses on the operations and the practical memory requirements to implement the Viterbi algorithm in real-time. A forward error correction technique known as convolutional coding with Viterbi decoding was explored. In this project, the basic Viterbi decoder behavior model was built and simulated. The convolutional encoder, BPSK and AWGN channel were implemented in MATLAB code. The BER was tested to evaluate the decoding performance. The theory of Viterbi Algorithm is introduced based on convolutional coding. The application of Viterbi Algorithm in the Continuous-Phase Frequency Shift Keying (CPFSK) is presented. Analysis for the performance is made and compared with the conventional coherent estimator. The main issue of this thesis is to implement the RTL level model of Viterbi decoder. The RTL Viterbi decoder model includes the Branch Metric block, the Add-Compare-Select block, the trace-back block, the decoding block and next state block. With all done, we further understand about the Viterbi decoding algorithm

Design Of Fountain Codes With Error Control

This thesis is focused on providing unequal error protection (uep) to two disjoint sources which are communicating to a comdestination via a comrelay by using distributed lt codes over a binary erasure channel (bec), and designing fountain codes with error control property by integrating lt codes with turbo codes over a binary input additive white gaussian noise (bi-awgn) channel. A simple yet efficient technique for decomposing the rsd into two entirely different degree distributions is developed and presented in this thesis. These two distributions are used to encode data symbols at the sources and the encoded symbols from the sources are selectively xored at the relay based on a suitable relay operation before the combined codeword is transmitted to the destination. By doing so, it is shown that the uep can be provided to these sources. The performance of lt codes over the awgn channel is well studied and presented in this thesis which indicates that these codes have weak error correction ability over the channel. But, errors introduced into individual symbols during the transmission of information over noisy channels need correction by some error correcting codes. Since it is found that lt codes alone are weak at correcting those errors, lt codes are integrated with turbo codes which are good error correcting codes. Therefore, the source data (symbols) are at first turbo encoded and then lt encoded and transmitted over the awgn channel. When the corrupted encoded symbols are received at receiver, lt decoding is conducted folloby turbo decoding. The overall performance of the integrated system is studied and presented in this thesis, which suggests that the errors left after lt decoding can be corrected to some extent by turbo decoder

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 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 lähetysten välillä. Tiivistelmä. IEEE 802.11-standardi määrittelee yleisesti käytetyn teknologian langattomille lähiverkoille. Standardissa määritellään tehokas fyysinen- ja verkkoliityntäkerros hajautetuille verkoille, mutta siitä puuttuu tehokas yhdistetty automaattinen uudelleenlähetys. Nykyisellään standardi määrittelee virheenkorjaavan koodin, virheellisen paketin tunnistuksen sekä automaattisen uudelleenlähetyksen, mutta aikaisemmin lähetetyn paketin informaatiota ei käytetä hyväksi uudelleenlähetystilanteessa. Tämä menetelmä tunnetaan tyypin yksi yhdistettynä automaattisena uudelleenlähetyksenä. Tyypin yksi yhdistetty automaattinen uudelleenlähetys käyttää vastaanotettua signaalia tehottomasti, mutta yksinkertaisuus tekee siitä houkuttelevan vaihtoehdon. Valitettavasti edistyneempien uudelleenlähetysvaihtoehtojen tutkimusta 802.11-standardiin on rajoitetusti. Tässä diplomityössä esitellään uusi yhdistetty uudelleenlähetysteknologia, joka pohjautuu pakettien uudelleenlähetykseen, sallien turbo-tyylisen dekoodaamisen säilyttäen mahdollisimman hyvän taaksepäin yhteensopivuutta alkuperäisen 802.11-standardin kanssa. Tämä teknologia on simuloitu käyttäen sekä 802.11- että nk. RESCUE-virheenkorjauskoodia. Teknologiassa uusi lomittaja on lisätty konvoluutio-enkoodaajan eteen, sallien tehokkaan iteratiivisen dekoodaamisen, lomittaen joko koko paketin tai ainoastaan hyötykuorman. Vastaanotetuille paketeille tehdään turbo-tyyppinen iteraatio alkuperäisen vastaanotetun kopion ja uudelleenlähetyksien välillä. Tuloksia vertaillaan eiiteratiiviseen yhdistämismenetelmään, maksimisuhdeyhdistelyyn, joka maksimoi yhdistetyn signaali-kohinasuhteen. Tärkeimpänä suunnittelutavoitteena tässä työssä on tehokas uudelleenlähetysmenetelmä, joka ylläpitää taaksepäin yhteensopivuutta IEEE 802.11-standardin kanssa. Muita tavoitteita ovat kantaman lisäys, nopeampi yhteys ja matalampi bitti- ja pakettivirhesuhde. Kehitettyä teknologiaa voidaan käyttää kantaman lisäykseen matalan signaalikohinasuhteen vallitessa ja se on jopa 4 dB parempi kohtuullisella signaalikohinasuhteella kuin maksimisuhdeyhdistely. Korkealla signaali-kohinasuhteella teknologiaa voidaan käyttää pienentämään häviötä epäonnistuneesta paketinlähetyksestä ja täten sallien korkeamman modulaatio-koodiasteen käyttämisen. Valitettavasti nämä parannukset tulevat kasvaneen laskennallisen monimutkaisuuden kustannuksella, johtuen iteratiivisesta dekoodaamisesta. Isoimmat rajoittavat tekijät teknologian käytössä ovat dekoodausvirheet otsikossa ja datamuokkaimen siemenessä. Tämän lisäksi käyttöä rajoittaa resurssisyöppö prosessointi. Simulaatioissa oletetaan täydellinen synkronisointi, mutta todellisuudessa, erityisesti matalalla signaali-kohinasuhteella, paketin tunnistus ja synkronointi voivat olla haasteellisia

Irregular Variable Length Coding

In this thesis, we introduce Irregular Variable Length Coding (IrVLC) and investigate its applications, characteristics and performance in the context of digital multimedia broadcast telecommunications. During IrVLC encoding, the multimedia signal is represented using a sequence of concatenated binary codewords. These are selected from a codebook, comprising a number of codewords, which, in turn, comprise various numbers of bits. However, during IrVLC encoding, the multimedia signal is decomposed into particular fractions, each of which is represented using a different codebook. This is in contrast to regular Variable Length Coding (VLC), in which the entire multimedia signal is encoded using the same codebook. The application of IrVLCs to joint source and channel coding is investigated in the context of a video transmission scheme. Our novel video codec represents the video signal using tessellations of Variable-Dimension Vector Quantisation (VDVQ) tiles. These are selected from a codebook, comprising a number of tiles having various dimensions. The selected tessellation of VDVQ tiles is signalled using a corresponding sequence of concatenated codewords from a Variable Length Error Correction (VLEC) codebook. This VLEC codebook represents a specific joint source and channel coding case of VLCs, which facilitates both compression and error correction. However, during video encoding, only particular combinations of the VDVQ tiles will perfectly tessellate, owing to their various dimensions. As a result, only particular sub-sets of the VDVQ codebook and, hence, of the VLEC codebook may be employed to convey particular fractions of the video signal. Therefore, our novel video codec can be said to employ IrVLCs. The employment of IrVLCs to facilitate Unequal Error Protection (UEP) is also demonstrated. This may be applied when various fractions of the source signal have different error sensitivities, as is typical in audio, speech, image and video signals, for example. Here, different VLEC codebooks having appropriately selected error correction capabilities may be employed to encode the particular fractions of the source signal. This approach may be expected to yield a higher reconstruction quality than equal protection in cases where the various fractions of the source signal have different error sensitivities. Finally, this thesis investigates the application of IrVLCs to near-capacity operation using EXtrinsic Information Transfer (EXIT) chart analysis. Here, a number of component VLEC codebooks having different inverted EXIT functions are employed to encode particular fractions of the source symbol frame. We show that the composite inverted IrVLC EXIT function may be obtained as a weighted average of the inverted component VLC EXIT functions. Additionally, EXIT chart matching is employed to shape the inverted IrVLC EXIT function to match the EXIT function of a serially concatenated inner channel code, creating a narrow but still open EXIT chart tunnel. In this way, iterative decoding convergence to an infinitesimally low probability of error is facilitated at near-capacity channel SNRs

Bit flipping decoding for binary product codes

Error control coding has been used to mitigate the impact of noise on the wireless channel. Today, wireless communication systems have in their design Forward Error Correction (FEC) techniques to help reduce the amount of retransmitted data. When designing a coding scheme, three challenges need to be addressed, the error correcting capability of the code, the decoding complexity of the code and the delay introduced by the coding scheme. While it is easy to design coding schemes with a large error correcting capability, it is a challenge finding decoding algorithms for these coding schemes. Generally increasing the length of a block code increases its error correcting capability and its decoding complexity. Product codes have been identified as a means to increase the block length of simpler codes, yet keep their decoding complexity low. Bit flipping decoding has been identified as simple to implement decoding algorithm. Research has generally been focused on improving bit flipping decoding for Low Density Parity Check codes. In this study we develop a new decoding algorithm based on syndrome checking and bit flipping to use for binary product codes, to address the major challenge of coding systems, i.e., developing codes with a large error correcting capability yet have a low decoding complexity. Simulated results show that the proposed decoding algorithm outperforms the conventional decoding algorithm proposed by P. Elias in BER and more significantly in WER performance. The algorithm offers comparable complexity to the conventional algorithm in the Rayleigh fading channel

Iterative decoding and detection for physical layer network coding

PhD ThesisWireless networks comprising multiple relays are very common and it is important that all users are able to exchange messages via relays in the shortest possible time. A promising technique to achieve this is physical layer network coding (PNC), where the time taken to exchange messages between users is achieved by exploiting the interference at the relay due to the multiple incoming signals from the users. At the relay, the interference is demapped to a binary sequence representing the exclusive-OR of both users’ messages. The time to exchange messages is reduced because the relay broadcasts the network coded message to both users, who can then acquire the desired message by applying the exclusive-OR of their original message with the network coded message. However, although PNC can increase throughput it is at the expense of performance degradation due to errors resulting from the demapping of the interference to bits. A number of papers in the literature have investigated PNC with an iterative channel coding scheme in order to improve performance. However, in this thesis the performance of PNC is investigated for end-to-end (E2E) the three most common iterative coding schemes: turbo codes, low-density parity-check (LDPC) codes and trellis bit-interleaved coded modulation with iterative decoding (BICM-ID). It is well known that in most scenarios turbo and LDPC codes perform similarly and can achieve near-Shannon limit performance, whereas BICM-ID does not perform quite as well but has a lower complexity. However, the results in this thesis show that on a two-way relay channel (TWRC) employing PNC, LDPC codes do not perform well and BICM-ID actually outperforms them while also performing comparably with turbo codes. Also presented in this thesis is an extrinsic information transfer (ExIT) chart analysis of the iterative decoders for each coding scheme, which is used to explain this surprising result. Another problem arising from the use of PNC is the transfer of reliable information from the received signal at the relay to the destination nodes. The demapping of the interference to binary bits means that reliability information about the received signal is lost and this results in a significant degradation in performance when applying soft-decision decoding at the destination nodes. This thesis proposes the use of traditional angle modulation (frequency modulation (FM) and phase modulation (PM)) when broadcasting from the relay, where the real and imaginary parts of the complex received symbols at the relay modulate the frequency or phase of a carrier signal, while maintaining a constant envelope. This is important since the complex received values at the relay are more likely to be centred around zero and it undesirable to transmit long sequences of low values due to potential synchronisation problems at the destination nodes. Furthermore, the complex received values, obtained after angle demodulation, are used to derive more reliable log-likelihood ratios (LLRs) of the received symbols at the destination nodes and consequently improve the performance of the iterative decoders for each coding scheme compared with conventionally coded PNC. This thesis makes several important contributions: investigating the performance of different iterative channel coding schemes combined with PNC, presenting an analysis of the behaviour of different iterative decoding algorithms when PNC is employed using ExIT charts, and proposing the use of angle modulation at the relay to transfer reliable information to the destination nodes to improve the performance of the iterative decoding algorithms. The results from this thesis will also be useful for future research projects in the areas of PNC that are currently being addressed, such as synchronisation techniques and receiver design.Iraqi Ministry of Higher Education and Scientific Research

On Coding and Detection Techniques for Two-Dimensional Magnetic Recording

Edited version embargoed until 15.04.2020 Full version: Access restricted permanently due to 3rd party copyright restrictions. Restriction set on 15/04/2019 by AS, Doctoral CollegeThe areal density growth of magnetic recording systems is fast approaching the superparamagnetic limit for conventional magnetic disks. This is due to the increasing demand for high data storage capacity. Two-dimensional Magnetic Recording (TDMR) is a new technology aimed at increasing the areal density of magnetic recording systems beyond the limit of current disk technology using conventional disk media. However, it relies on advanced coding and signal processing techniques to achieve areal density gains. Current state of the art signal processing for TDMR channel employed iterative decoding with Low Density Parity Check (LDPC) codes, coupled with 2D equalisers and full 2D Maximum Likelihood (ML) detectors. The shortcoming of these algorithms is their computation complexity especially with regards to the ML detectors which is exponential with respect to the number of bits involved. Therefore, robust low-complexity coding, equalisation and detection algorithms are crucial for successful future deployment of the TDMR scheme. This present work is aimed at finding efficient and low-complexity coding, equalisation, detection and decoding techniques for improving the performance of TDMR channel and magnetic recording channel in general. A forward error correction (FEC) scheme of two concatenated single parity bit systems along track separated by an interleaver has been presented for channel with perpendicular magnetic recording (PMR) media. Joint detection decoding algorithm using constrained MAP detector for simultaneous detection and decoding of data with single parity bit system has been proposed. It is shown that using the proposed FEC scheme with the constrained MAP detector/decoder can achieve a gain of up to 3dB over un-coded MAP decoder for 1D interference channel. A further gain of 1.5 dB was achieved by concatenating two interleavers with extra parity bit when data density along track is high. The use of single bit parity code as a run length limited code as well as an error correction code is demonstrated to simplify detection complexity and improve system performance. A low-complexity 2D detection technique for TDMR system with Shingled Magnetic Recording Media (SMR) was also proposed. The technique used the concatenation of 2D MAP detector along track with regular MAP detector across tracks to reduce the complexity order of using full 2D detection from exponential to linear. It is shown that using this technique can improve track density with limited complexity. Two methods of FEC for TDMR channel using two single parity bit systems have been discussed. One using two concatenated single parity bits along track only, separated by a Dithered Relative Prime (DRP) interleaver and the other use the single parity bits in both directions without the DRP interleaver. Consequent to the FEC coding on the channel, a 2D multi-track MAP joint detector decoder has been proposed for simultaneous detection and decoding of the coded single parity bit data. A gain of up to 5dB was achieved using the FEC scheme with the 2D multi-track MAP joint detector decoder over un-coded 2D multi-track MAP detector in TDMR channel. In a situation with high density in both directions, it is shown that FEC coding using two concatenated single parity bits along track separated by DRP interleaver performed better than when the single parity bits are used in both directions without the DRP interleaver.9mobile Nigeri

Performance of turbo multi-user detectors in space-time coded DS-CDMA systems

Includes bibliographical references (leaves 118-123).In this thesis we address the problem of improving the uplink capacity and the performance of a DS-CDMA system by combining MUD and turbo decoding. These two are combined following the turbo principle. Depending on the concatenation scheme used, we divide these receivers into the Partitioned Approach (PA) and the Iterative Approach (IA) receivers. To enable the iterative exchange of information, these receivers employ a Parallel Interference Cancellation (PIC) detector as the first receiver stage