Logarithmic Maximum A Posteriori Research Articles

Turbo Decoder Design based on an LUT-Normalized Log-MAP Algorithm.

Turbo codes have been widely used in wireless communication systems due to their good error correction performance. Under time division long term evolution (TD-LTE) of the 3rd generation partnership project (3GPP) wireless communication standard, a Log maximum a posteriori (Log-MAP) decoding algorithm with high complexity is usually approximated as a lookup-table Log-MAP (LUT-Log-MAP) algorithm and Max-Log-MAP algorithm, but these two algorithms have high complexity and high bit error rate, respectively. In this paper, we propose a normalized Log-MAP (Nor-Log-MAP) decoding algorithm in which the function max* is approximated by using a fixed normalized factor multiplied by the max function. Combining a Nor-Log-MAP algorithm with a LUT-Log-MAP algorithm creates a new kind of LUT-Nor-Log-MAP algorithm. Compared with the LUT-Log-MAP algorithm, the decoding performance of the LUT-Nor-Log-MAP algorithm is close to that of the LUT-Log-MAP algorithm. Based on the decoding method of the Nor-Log-MAP algorithm, we also put forward a normalization functional unit (NFU) for a soft-input soft-output (SISO) decoder computing unit. The simulation results show that the LUT-Nor-Log-MAP algorithm can save about 2.1% of logic resources compared with the LUT-Log-MAP algorithm. Compared with the Max-Log-MAP algorithm, the LUT-Nor-Log-MAP algorithm shows a gain of 0.25~0.5 dB in decoding performance. Using the Cyclone IV platform, the designed Turbo decoder can achieve a throughput of 36 Mbit/s under a maximum clock frequency of 44 MHz.

Performance enhancement of MC-CDMA system through novel sensitive bit algorithm aided turbo multi user detection.

Multi carrier code division multiple access (MC-CDMA) system is a promising multi carrier modulation (MCM) technique for high data rate wireless communication over frequency selective fading channels. MC-CDMA system is a combination of code division multiple access (CDMA) and orthogonal frequency division multiplexing (OFDM). The OFDM parts reduce multipath fading and inter symbol interference (ISI) and the CDMA part increases spectrum utilization. Advantages of this technique are its robustness in case of multipath propagation and improve security with the minimize ISI. Nevertheless, due to the loss of orthogonality at the receiver in a mobile environment, the multiple access interference (MAI) appears. The MAI is one of the factors that degrade the bit error rate (BER) performance of MC-CDMA system. The multiuser detection (MUD) and turbo coding are the two dominant techniques for enhancing the performance of the MC-CDMA systems in terms of BER as a solution of overcome to MAI effects. In this paper a low complexity iterative soft sensitive bits algorithm (SBA) aided logarithmic-Maximum a-Posteriori algorithm (Log MAP) based turbo MUD is proposed. Simulation results show that the proposed method provides better BER performance with low complexity decoding, by mitigating the detrimental effects of MAI.

Two Novel Decoding Algorithms for Turbo Codes Based on Taylor Series in 3GPP LTE System

This paper proposes two novel methods to simply Logarithmic Maximum a posteriori (Log-MAP) algorithm for turbo codes in the Third Generation Partnership Project Long Term Evolution (3GPP LTE). Firstly, we exploit a new function to replace the logarithmic term in the Jacobian logarithmic function based on Taylor series, which has the best approximated accuracy compared with the existing methods. With this method, we get algorithm I. Secondly, to further simplify the complexity, we propose a new piece-wise ladder function to approximate the logarithmic term according to algorithm I. In this way, we obtain algorithm II. Simulation results show that the performance of the algorithm I is most close to the optimal algorithm. Algorithm II owns the complexity which is similar to the MAX-Log-MAP algorithm, meanwhile it can offer 0.37-0.4db performance gains than MAX-Log-MAP algorithm. DOI : http://dx.doi.org/10.11591/telkomnika.v12i5.2547

A Novel Decoding Algorithm for BICM-ID Embedded Turbo Codes

Bit-interleaved coded modulation iterative decoding (BICM-ID) embedded turbo code is widely used in wireless communication because of its excellent performance. This paper proposes an improved logarithmic maximum a posteriori (Log-MAP) algorithm for BICM-ID embedded turbo codes. It can yield excellent bit error rate (BER) performance with much lower complexity. The proposed algorithm exploits a linear interpolation and Least Squares approximation function to replace the logarithmic correction in the Jacobian logarithmic function, which avoids complicated logarithm look-up table operations in Log-MAP algorithm. Simulation results show that the novel algorithm can offer almost equivalent performance to the optimal algorithm with much less computation. Compared with the improved MAX-Log-MAP algorithm proposed by Talakoub, the proposed algorithm can reduce about 36% of computational complexity, meanwhile it achieves 0.1db-0.16db performance gains. In addition, it obtains 0.35-0.4db gains than MAX-Log-MAP algorithm.

Simplified Log-MAP Algorithm for Very Low-Complexity Turbo Decoder Hardware Architectures

Motivated by the importance of hardware implementation in practical turbo decoders, a simplified, yet effective, <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex></formula> -input <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\max^{\ast}$</tex> </formula> approximation algorithm is proposed with the aim being its efficient implementation for very low-complexity turbo decoder hardware architectures. The simplification is obtained using an appropriate digital circuit for finding the first two maximum values in a set of <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$n$</tex></formula> data that embeds the computation of a correction term. Various implementation results show that the proposed architecture is simpler by 30%, on average, than the constant logarithmic-maximum a posteriori (Log-MAP) one, in terms of chip area with the same delay. This comes at the expense of very small performance degradation, in the order of 0.1 dB for up to moderate bit error rates, e.g., <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$10^{-5}$</tex></formula> , assuming binary turbo codes. However, when applying scaling to the extrinsic information, the proposed algorithm achieves almost identical Log-MAP turbo code performance for both binary and double-binary turbo codes, without increasing noticeably the implementation complexity.

Efficient Power Allocation in Turbo Decoded OFDM Systems Using Logarithmic Maximum A-Posteriori Algorithm and Soft Output Viterbi Algorithm Under Various Fading Environments

Orthogonal frequency division multiplexing (OFDM) is a multicarrier modulation technique which is gaining wide popularity in Wireless cellular networks as it is used to mitigate the multipath effects and to achieve high data rate. The Coded Orthogonal Frequency Division Multiplex (COFDM) technique is an extension of the conventional OFDM systems as they provide reliable reception of signals affected by strong distortions. The increase spectral efficiency in turn increases power. Therefore power optimization has to be considered, when coding is incorporated into the existing system. In this paper, the conventional Viterbi decoder is used along with soft coding technique which provides better convergence property. These results are compared to the Soft Output Viterbi Algorithm (SOVA) and Logarithmic Maximum A-posteriori Decoder (Log-Map) which give better performance than conventional Viterbi algorithm. The power optimization is done in all the cases and the advantages of multicarrier modulation are thus reassured without much channel information feedback from receiver to transmitter.

Low Power Design of near Shannon Limit Coding: Turbo Codes

In this paper secure channel coding schemes based on Turbo Codes are suggested and implemented. The design of encoder using Recursive Systematic Code (RSC) with puncturing techniques is presented. Component decoders are implemented by Log-Maximum-a-Posteriori (Log-MAP) algorithm and thereafter implementation of overall turbo decoder is illustrated in detail. Finally we have investigated low power design technique of the turbo decoder design with variable iteration techniques.

Soft Output Decoding Algorithm for Turbo Codes Implementation in Mobile Wi-Max Environment

In the area of wireless communication system, researchers are concentrating on powerful forward error correction (FEC) coding techniques. A literature survey has shown that in the field of mobile Wi-Max environment Turbo code provides a coding gain close to Shannon limit. Since the performance of turbo codes depend on iterative decoding algorithms. Among various soft outputs decoding algorithms, Maximum A Posteriori (MAP) algorithm is used, which works on the principle of symbol estimation of the received signal. This paper presents logarithmic version of MAP decoding algorithm (Log-MAP). The author has taken efforts to modify the available Log MAP decoding algorithm in order to reduce the computational complexity. The results are presented for this new developed Max-Log-MAP decoding algorithm. Bit Error Rate (BER) performance and computational complexity of these algorithms are compared with reference to the standard defined by IEEE802.16e for mobile Wi-Max system.

Reduced-Complexity RBF-Assisted TEQ Using Extended FCM Algorithm for Dispersive Rayleigh-Fading Channels

In this paper, we propose a reduced-complexity radial basis function (RBF)-assisted decision-feedback equalizer (DFE)-based turbo equalization (TEQ) scheme using a novel extended fuzzy c-means (FCM) algorithm, which not only is comparable in performance to the Jacobian RBF DFE-based TEQ but also is low-complexity. Previous TEQ research has shown that the Jacobian RBF DFE TEQ considerably reduces the computational complexity with similar performance, when compared to the logarithmic maximum a posteriori (Log-MAP) TEQ. In this study, the proposed reduced-complexity RBF DFE TEQ further greatly reduces the computational complexity and is capable of attaining a similar performance in contrast to the Jacobian RBF DFE TEQ in the context of both binary phaseshift keying (BPSK) modulation and 4 quadrature amplitude modulation (QAM). With this proposal, the materialization of the RBF-assisted TEQ scheme becomes more feasible.

Low‐complexity fuzzy filter‐assisted turbo equalization for dispersive Rayleigh‐fading channels

AbstractTurbo equalisation (TEQ) is an iterative detection and decoding technique that has been shown to be successful in mitigating the effects of intersymbol interference (ISI) introduced by partial response modems and by dispersive channels. In this paper, we propose a fuzzy filter‐assisted decision‐feedback equaliser (DFE)‐based TEQ scheme that not only is comparable in performance to the Jacobian radial basis function (RBF) DFE‐based TEQ but also is low‐complexity. The per iteration computation of both the fuzzy filter DFE TEQ using product inference and maximum defuzzification and the fuzzy filter DFE TEQ using minimum inference and maximum defuzzification is much lower than that of the Jacobian RBF DFE TEQ for binary phase‐shift keying (BPSK) modulation, 4 quadrature amplitude modulation (QAM), and 16 QAM. Notably, the computational complexity of the Jacobian RBF DFE TEQ is exponentially related to the feedforward order, but the fuzzy filter DFE TEQ using minimum inference and maximum defuzzification is independent of that. Previous TEQ research has shown that the Jacobian RBF DFE TEQ considerably reduces the computational complexity compared to the logarithmic maximum a posteriori (Log‐MAP) TEQ with similar performance. In this present study, the proposed fuzzy filter DFE TEQ further reduces the computational complexity with slight performance degradation in contrast to the Jacobian RBF DFE TEQ. With this, the materialisation of the TEQ scheme becomes more feasible. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Complexity Reduction in SISO Decoding of Block Codes

SISO decoding for block codes can be carried out based on a trellis representation of the code. However, the complexity entailed by such decoding is most often prohibitive and thus prevents practical implementation. This paper examines a new decoding scheme based on the soft-output Viterbi algorithm (SOVA) applied to a sectionalized trellis for linear block codes. The computational complexities of the new SOVA decoder and of the conventional SOVA decoder, based on a bit-level trellis, are theoretically analyzed and derived for different linear block codes. These results are used to obtain optimum sectionalizations of a trellis for SOVA. For comparisons, the optimum sectionalizations for Maximum A Posteriori (MAP) and Maximum Logarithm MAP (Max-Log-MAP) algorithms, and their corresponding computational complexities are included. The results confirm that the new SOVA decoder is the most computationally efficient SISO decoder, in comparisons to MAP and Max-Log-MAP algorithms. The simulation results of the bit error rate (BER) performance, assuming binary phase -- shift keying (BPSK) and additive white Gaussian noise (AWGN) channel, demonstrate that the performance of the new decoding scheme is not degraded. The BER performance of iterative SOVA decoding of serially concatenated block codes shows no difference in the quality of the soft outputs of the new decoding scheme and of the conventional SOVA.