Efficient LLR Calculation for Non-Binary Modulations over Fading Channels

Log-likelihood ratio (LLR) computation for non-binary modulations over fading channels is complicated. A measure of LLR accuracy on asymmetric binary channels is introduced to facilitate good LLR approximations for non-binary modulations. Considering piecewise linear LLR approximations, we prove convexity of optimizing the coefficients according to this measure. For the optimized approximate LLRs, we report negligible performance losses compared to true LLRs.Comment: Submitted to IEEE Transactions on Communication

Optimized Bit Mappings for Spatially Coupled LDPC Codes over Parallel Binary Erasure Channels

In many practical communication systems, one binary encoder/decoder pair is used to communicate over a set of parallel channels. Examples of this setup include multi-carrier transmission, rate-compatible puncturing of turbo-like codes, and bit-interleaved coded modulation (BICM). A bit mapper is commonly employed to determine how the coded bits are allocated to the channels. In this paper, we study spatially coupled low-density parity check codes over parallel channels and optimize the bit mapper using BICM as the driving example. For simplicity, the parallel bit channels that arise in BICM are replaced by independent binary erasure channels (BECs). For two parallel BECs modeled according to a 4-PAM constellation labeled by the binary reflected Gray code, the optimization results show that the decoding threshold can be improved over a uniform random bit mapper, or, alternatively, the spatial chain length of the code can be reduced for a given gap to capacity. It is also shown that for rate-loss free, circular (tail-biting) ensembles, a decoding wave effect can be initiated using only an optimized bit mapper

LDPC code-based bandwidth efficient coding schemes for wireless communications

This dissertation deals with the design of bandwidth-efficient coding schemes with Low-Density Parity-Check (LDPC) for reliable wireless communications. Code design for wireless channels roughly falls into three categories: (1) when channel state information (CSI) is known only to the receiver (2) more practical case of partial CSI at the receiver when the channel has to be estimated (3) when CSI is known to the receiver as well as the transmitter. We consider coding schemes for all the above categories. For the first scenario, we describe a bandwidth efficient scheme which uses highorder constellations such as QAM over both AWGN as well as fading channels. We propose a simple design with LDPC codes which combines the good properties of Multi-level Coding (MLC) and bit-interleaved coded-modulation (BICM) schemes. Through simulations, we show that the proposed scheme performs better than MLC for short-medium lengths on AWGN and block-fading channels. For the first case, we also characterize the rate-diversity tradeoff of MIMO-OFDM and SISO-OFDM systems. We design optimal coding schemes which achieve this tradeoff when transmission is from a constrained constellation. Through simulations, we show that with a sub-optimal iterative decoder, the performance of this coding scheme is very close to the optimal limit for MIMO (flat quasi-static fading), MIMO-OFDM and SISO OFDM systems. For the second case, we design non-systematic Irregular Repeat Accumulate (IRA) codes, which are a special class of LDPC codes, for Inter-Symbol Interference (ISI) fading channels when CSI is estimated at the receiver. We use Orthogonal Frequency Division Multiplexing (OFDM) to convert the ISI fading channel into parallel flat fading subchannels. We use a simple receiver structure that performs iterative channel estimation and decoding and use non-systematic IRA codes that are optimized for this receiver. This combination is shown to perform very close to a receiver with perfect CSI and is also shown to be robust to change in the number of channel taps and Doppler. For the third case, we look at bandwidth efficient schemes for fading channels that perform close to capacity when the channel state information is known at the transmitter as well as the receiver. Schemes that achieve capacity with a Gaussian codebook for the above system are already known but not for constrained constellations. We derive the near-optimum scheme to achieve capacity with constrained constellations and then propose coding schemes which perform close to capacity. Through linear transformations, a MIMO system can be converted into non-interfering parallel subchannels and we further extend the proposed coding schemes to the MIMO case too

Performance Prediction of Nonbinary Forward Error Correction in Optical Transmission Experiments

In this paper, we compare different metrics to predict the error rate of optical systems based on nonbinary forward error correction (FEC). It is shown that the correct metric to predict the performance of coded modulation based on nonbinary FEC is the mutual information. The accuracy of the prediction is verified in a detailed example with multiple constellation formats, FEC overheads in both simulations and optical transmission experiments over a recirculating loop. It is shown that the employed FEC codes must be universal if performance prediction based on thresholds is used. A tutorial introduction into the computation of the threshold from optical transmission measurements is also given.Comment: submitted to IEEE/OSA Journal of Lightwave Technolog

Bandwidth-efficient communication systems based on finite-length low density parity check codes

Low density parity check (LDPC) codes are linear block codes constructed by pseudo-random parity check matrices. These codes are powerful in terms of error performance and, especially, have low decoding complexity. While infinite-length LDPC codes approach the capacity of communication channels, finite-length LDPC codes also perform well, and simultaneously meet the delay requirement of many communication applications such as voice and backbone transmissions. Therefore, finite-length LDPC codes are attractive to employ in low-latency communication systems. This thesis mainly focuses on the bandwidth-efficient communication systems using finite-length LDPC codes. Such bandwidth-efficient systems are realized by mapping a group of LDPC coded bits to a symbol of a high-order signal constellation. Depending on the systems' infrastructure and knowledge of the channel state information (CSI), the signal constellations in different coded modulation systems can be two-dimensional multilevel/multiphase constellations or multi-dimensional space-time constellations. In the first part of the thesis, two basic bandwidth-efficient coded modulation systems, namely LDPC coded modulation and multilevel LDPC coded modulation, are investigated for both additive white Gaussian noise (AWGN) and frequency-flat Rayleigh fading channels. The bounds on the bit error rate (BER) performance are derived for these systems based on the maximum likelihood (ML) criterion. The derivation of these bounds relies on the union bounding and combinatoric techniques. In particular, for the LDPC coded modulation, the ML bound is computed from the Hamming distance spectrum of the LDPC code and the Euclidian distance profile of the two-dimensional constellation. For the multilevel LDPC coded modulation, the bound of each decoding stage is obtained for a generalized multilevel coded modulation, where more than one coded bit is considered for level. For both systems, the bounds are confirmed by the simulation results of ML decoding and/or the performance of the ordered-statistic decoding (OSD) and the sum-product decoding. It is demonstrated that these bounds can be efficiently used to evaluate the error performance and select appropriate parameters (such as the code rate, constellation and mapping) for the two communication systems.The second part of the thesis studies bandwidth-efficient LDPC coded systems that employ multiple transmit and multiple receive antennas, i.e., multiple-input multiple-output (MIMO) systems. Two scenarios of CSI availability considered are: (i) the CSI is unknown at both the transmitter and the receiver; (ii) the CSI is known at both the transmitter and the receiver. For the first scenario, LDPC coded unitary space-time modulation systems are most suitable and the ML performance bound is derived for these non-coherent systems. To derive the bound, the summation of chordal distances is obtained and used instead of the Euclidean distances. For the second case of CSI, adaptive LDPC coded MIMO modulation systems are studied, where three adaptive schemes with antenna beamforming and/or antenna selection are investigated and compared in terms of the bandwidth efficiency. For uncoded discrete-rate adaptive modulation, the computation of the bandwidth efficiency shows that the scheme with antenna selection at the transmitter and antenna combining at the receiver performs the best when the number of antennas is small. For adaptive LDPC coded MIMO modulation systems, an achievable threshold of the bandwidth efficiency is also computed from the ML bound of LDPC coded modulation derived in the first part

LDPC-coded modulation for transmission over AWGN and flat rayleigh fading channels

La modulation codée est une technique de transmission efficace en largeur de bande qui intègre le codage de canal et la modulation en une seule entité et ce, afin d'améliorer les performances tout en conservant la même efficacité spectrale comparé à la modulation non codée. Les codes de parité à faible densité (low-density parity-check codes, LDPC) sont les codes correcteurs d'erreurs les plus puissants et approchent la limite de Shannon, tout en ayant une complexité de décodage relativement faible. L'idée de combiner les codes LDPC et la modulation efficace en largeur de bande a donc été considérée par de nombreux chercheurs. Dans ce mémoire, nous étudions une méthode de modulation codée à la fois puissante et efficace en largeur de bande, ayant d'excellentes performances de taux d'erreur binaire et une complexité d'implantation faible. Ceci est réalisé en utilisant un encodeur rapide, un décoder de faible complexité et aucun entrelaceur. Les performances du système proposé pour des transmissions sur un canal additif gaussien blanc et un canal à évanouissements plats de Rayleigh sont évaluées au moyen de simulations. Les résultats numériques montrent que la méthode de modulation codée utilisant la modulation d'amplitude en quadrature à M niveaux (M-QAM) peut atteindre d'excellentes performances pour toute une gamme d'efficacité spectrale. Une autre contribution de ce mémoire est une méthode simple pour réaliser une modulation codée adaptative avec les codes LDPC pour la transmission sur des canaux à évanouissements plats et lents de Rayleigh. Dans cette méthode, six combinaisons de paires encodeur modulateur sont employées pour une adaptation trame par trame. L'efficacité spectrale moyenne varie entre 0.5 et 5 bits/s/Hz lors de la transmission. Les résultats de simulation montrent que la modulation codée adaptative avec les codes LDPC offre une meilleure efficacité spectrale tout en maintenant une performance d'erreur acceptable