Erasure-Correction-Enhanced Iterative Decoding for LDPC-RS Product Codes

Low-density parity-check(LDPC)codes are widely used due to their significant errorcorrection capability and linear decoding complexity.However,it is not sufficient for LDPC codes to satisfy the ultra low bit error rate(BER)requirement of next-generation ultra-high-speed communications due to the error floor phenomenon.According to the residual error characteristics of LDPC codes,we consider using the high rate Reed-Solomon(RS)codes as the outer codes to construct LDPC-RS product codes to eliminate the error floor and propose the hybrid error-erasure-correction decoding algorithm for the outer code to exploit erasure-correction capability effectively.Furthermore,the overall performance of product codes is improved using iteration between outer and inner codes.Simulation results validate that BER of the product code with the proposed hybrid algorithm is lower than that of the product code with no erasure correction.Compared with other product codes using LDPC codes,the proposed LDPC-RS product code with the same code rate has much better performance and smaller rate loss attributed to the maximum distance separable(MDS)property and significant erasure-correction capability of RS codes.

An Iterative Decoding Scheme for Davey-MacKay Construction

In the Davey-MacKay(DM) construction,the inner decoder treats unknown transmitted bits as random independent substitution errors. It limits the synchronization capability of the inner decoder, and thus weakens the error-correcting capability of the DM construction.In order to improve the performance of the DM construction, an iterative decoding scheme is proposed, which iteratively utilizes the more accurate estimates of transmitted codewords. In the proposed scheme, the estimated average bit error rates and the estimated low-density parity-check(LDPC) codewords from the outer decoder are fed back into the inner decoder to update the synchronization process. Simulation results show that the proposed iterative decoding scheme significantly outperforms the traditional DM construction.

JOINT ITERATIVE DECODING FOR SIMPLE-ENCODING SYSTEMATIC IRREGULAR-LDPC-BASED CODED COOPERATION IN NON-IDEAL RELAY CHANNEL

In this paper, a new kind of simple-encoding irregular systematic LDPC codes suitable for one-relay coded cooperation is designed, where the proposed joint iterative decoding is effectively performed in the destination which is in accordance with the corresponding joint Tanner graph characterizing two different component LDPC codes used by the source and relay in ideal and non-ideal relay cooperations. The theoretical analysis and simulations show that the coded cooperation scheme obviously outperforms the coded non-cooperation one under the same code rate and decoding complex. The significant performance improvement can be virtually credited to the additional mutual exchange of the extrinsic information resulted by the LDPC code employed by the source and its counterpart used by the relay in both ideal and non-ideal cooperations.

Jointly-check iterative decoding algorithm for quantum sparse graph codes

For quantum sparse graph codes with stabilizer formalism, the unavoidable girth-four cycles in their Tanner graphs greatly degrade the iterative decoding performance with standard belief-propagation （BP） algorithm. In this paper, we present a jointly-check iterative algorithm suitable for decoding quantum sparse graph codes efficiently. Numerical simulations show that this modified method outperforms standard BP algorithm with an obvious performance improvement.

Iterative Decoding of Parallel Concatenated Block Codes and Coset Based MAP Decoding Algorithm for F24 Code

A multi dimensional concatenation scheme for block codes is introduced, in which information symbols are interleaved and re encoded for more than once. It provides a convenient platform to design high performance codes with flexible interleaver size. Coset based MAP soft in/soft out decoding algorithms are presented for the F24 code. Simulation results show that the proposed coding scheme can achieve high coding gain with flexible interleaver length and very low decoding complexity.

CHANNEL ESTIMATION FOR ITERATIVE DECODING OVER FADING CHANNELS

A method of coherent detection and channel estimation for punctured convolutional coded binary Quadrature Amplitude Modulation (QAM) signals transmitted over a frequency-flat Rayleigh fading channels used for a digital radio broadcasting transmission is presented. Some known symbols are inserted in the encoded data stream to enhance the channel estimation process.The pilot symbols are used to replace the existing parity symbols so no bandwidth expansion is required. An iterative algorithm that uses decoding information as well as the information contained in the known symbols is used to improve the channel parameter estimate. The scheme complexity grows exponentially with the channel estimation filter length. The performance of the system is compared for a normalized fading rate with both perfect coherent detection (corresponding to a perfect knowledge of the fading process and noise variance) and differential detection of Differential Amplitude Phase Shift Keying (DAPSK). The tradeoff between simplicity of implementation and bit-error-rate performance of different techniques is also compared.

Joint Iterative Decoding for Network-Coding-Based Multisource LDPC-Coded Cooperative MIMO

A network-coding-based multisource LDPC-coded cooperative MIMO scheme is proposed,where multiple sources transmit their messages to the destination with the assistance from a single relay.The relay cooperates with multiple sources simultaneously via network-coding.It avoids the issues of imperfect frequency/timing synchronization and large transmission delay which may be introduced by frequency-division multiple access(FDMA)/code-division multiple access(CDMA)and time-division multiple access(TDMA)manners.The proposed joint″Min-Sum″iterative decoding is effectively carried out in the destination.Such a decoding algorithm agrees with the introduced equivalent joint Tanner graph which can be used to fully characterize LDPC codes employed by the sources and relay.Theoretical analysis and numerical simulation show that the proposed scheme with joint iterative decoding can achieve significant cooperation diversity gain.Furthermore,for the relay,compared with the cascade scheme,the proposed scheme has much lower complexity of LDPC-encoding and is easier to be implemented in the hardware with similar bit error rate(BER)performance.

New Applications of EXIT Chart for Iterative Decoding Systems

Applications on iterative control and multiple input multiple output (MIMO) system were developed. Two new charts derived from extrinsic information transfer (EXIT) chart were employed as the designing tools, which are called as output mutual information chart with defined iterative degree (DID) chart and near optimum output mutual information (NOMI) chart respectively. Different from the EXIT chart, they can show the iterative performance on the whole signal-to-noise ratio range with one single curve, whereas computation complexity is greatly reduced compared with conventional bit error ratio (BER) performance curve. The iterative control was implemented according to a near-optimum iterative degree vector determined by NOMI chart, the reasonability of uncertain parameters was analyzed in one MIMO system. The concepts were illustrated based on bit-interleaved coded modulation with iterative decoding (BICM-ID).

Design and Implementation of a Novel Algorithm for Iterative Decoding of Product Codes

A novel product code iterative decoding algorithm and its high speed implementation scheme are proposed in this paper. Based on partial combination of selected columns of check matrix, the reduced-complexity syndrome decoding method is proposed to decode sub-codes of product code and deliver soft output information. So iterative decoding of product codes is possible. The fast sorting algorithm and a look-up method are proposed for high speed implementation of this algorithm. Compared to the conventional weighing iterative algorithm, the proposed algorithm has lower complexity while offering better performance, which is demonstrated by simulations and implementation analysis. The implementation scheme and verilog HDL simulation show that it is feasible to achieve high speed decoding with the proposed algorithm.

A NEW LABELING SEARCH ALGORITHM FOR BIT-INTERLEAVED CODED MODULATION WITH ITERATIVE DECODING

Bit-Interleaved Coded Modulation with Iterative Decoding (BICM-ID) is a bandwidth ef- ficient transmission, where the bit error rate is reduced through the iterative information exchange between the inner demapper and the outer decoder. The choice of the symbol mapping is the crucial design parameter. This paper indicates that the Harmonic Mean of the Minimum Squared Euclidean (HMMSE) distance is the best criterion for the mapping design. Based on the design criterion of the HMMSE distance, a new search algorithm to find the optimized labeling maps for BICM-ID system is proposed. Numerical results and performance comparison show that the new labeling search method has a low complexity and outperforms other labeling schemes using other design criterion in BICM-ID system, therefore it is an optimized labeling method.

Low complexity iterative differential decoding algorithm for multiband UWB communication systems

Due to not requiring channel state information （CSI） at both the transmitter and the receiver, noncoherent ultra-wideband （UWB） incurs a performance penalty of approximately 3 dB in the required signal to noise ratio （SNR） compared to the coherent case. To overcome the gap, an effective differential encoding and decoding scheme for multiband UWB systems is proposed. The proposed scheme employs the parallel concatenation of two recursive differential unitary space-frequency encoders at the transmitter. At the receiver, two component decoders iteratively decode information bits by interchanging soft metric values between each other. To reduce the computation complexity, a decoding algorithm which only uses transition probability to calculate the log likelihood ratios （LLRs） for the decoded bits is given. Simulation results show that the proposed scheme can dramatically outperform the conventional differential and even coherent detection at high SNR with a few iterations.

Early stopping for the iterative decoding for Q-LDPC

Q-ary low-density parity-check （Q-LDPC） codes have a better performance than those of the binary low-density parity-check （B-LDPC） codes, at short and medium block lengths, but the decoder of Q-LDPC has more complexity. In this article, a new stop criterion is proposed. By analyzing the changes of the maximum posteriori probability of the variable node, the criterion decides whether the iteration of the decoder must be stopped. The simulation results show that the stop criterion can effectively reduce the computation complexity of the Q-LDPC decoder with negligible performance loss.

Accelerating BP-Based Iterative Low-Density Parity-Check Decoding by Modified Vertical and Horizontal Processes

Two modified BP algorithms related to vertical and horizontal processes are proposed to accelerate iterative low-density parity- check （LDPC） decoding over an additive white Gaussian noise （AWGN） channel, where the newly updated extrinsic information is immediately used in the current decoding round. Theoretical analysis and simulation results demonstrate that both the modified approaches provide significant performance improvements over the traditional BP algorithm with almost no additional decoding complexity. The proposed algorithm with modified horizontal process offers even better performance than another algorithm with the modified horizontal process. The two modified BP algorithms are very promising in practical communications since both can achieve an excellent trade-off between the performance and decoding complexity.

Code Design and Shuffled Iterative Decoding of a Quasi-Cyclic LDPC Coded OFDM System

In multipath environments, the error rate performance of orthogonal frequency division multiplexing （OFDM） is severely degraded by the deep fading subcarriers. Powerful error-correcting codes must be used with OFDM. This paper presents a quasi-cyclic low-density parity-check （LDPC） coded OFDM system, in which the redundant bits of each codeword are mapped to a higher-order modulation constellation. The op- timal degree distribution was calculated using density evolution. The corresponding quasi-cyclic LDPC code was then constructed using circulant permutation matrices. Group shuffled message passing scheduling was used in the iterative decoding. Simulation results show that the system achieves better error rate performance and faster decoding convergence than conventional approaches on both additive white Gaussian noise （AWGN） and Rayleigh fading channels.

Iterative Demodulation and Decoding Scheme with 16 QAM

Iterative demodulation and decoding scheme is analyzed and modulation labeling is considered to be one of the crucial factors to this scheme. By analyzing the existent mapping design criterion, four aspects are found as the key techniques for choosing a label mapping. Based on this discovery, a novel mapping design criteflon is proposed and two label mappings are searched according to it. Simulation results show that the performance of BICM-ID using the novel mappings is better than the former ones. The extrinsic information transfer （EXIT） chart is introduced and it is used to evaluate the proposed mapping design criteria.

Realtime robust speech communication based on iterative joint source-channel decoding and demodulation algorithm for MELP vocoder

Realtime speech communications require high efficient compression algorithms to encode speech signals. As the compressed speech parameters are highly sensitive to transmission errors, robust source and channel decoding and demodulation schemes are both important and of practical use. In this paper, an it- erative joint souree-channel decoding and demodulation algorithm is proposed for mixed excited linear pre- diction （MELP） vocoder by both exploiting the residual redundancy and passing soft information through- out the receiver while introducing systematic global iteration process to further enhance the performance. Being fully compatible with existing transmitter structure, the proposed algorithm does not introduce addi- tional bandwidth expansion and transmission delay. Simulations show substantial error correcting perfor- mance and synthesized speech quality improvement over conventional separate designed systems in delay and bandwidth constraint channels by using the joint source-channel decoding and demodulation （JSCCM） algorithm.

AMP Dual-Turbo Iterative Detection and Decoding for LDPC Coded Multibeam MSC Uplink

The uplink of mobile satellite communication(MSC) system with hundreds of spot beams is essentially a multiple-input multiple-output(MIMO) channel. Dual-turbo iterative detection and decoding as a kind of MIMO receiver, which exchanges soft extrinsic information between a soft-in soft-out(SISO) detector and an SISO decoder in an iterative fashion, is an efficient method to reduce the uplink inter-beam-interference(IBI),and so the receiving bit error rate(BER).We propose to replace the linear SISO detector of traditional dual-turbo iterative detection and decoding with the AMP detector for the low-density parity-check(LDPC) coded multibeam MSC uplink. This improvement can reduce the computational complexity and achieve much lower BER.

Iterative Detection and Decoding Algorithm in Dual Polarized Land Mobile Satellite MIMO Systems

An iterative detection and decoding algorithm with outer code decision feedback is proposed for the dual polarized( DP) land mobile satellite( LMS) MIMO systems using concatenated codes. A feedback structure is added after the outer decoder in the proposed algorithm. The feedback information is exploited to control the detecting list in the MIMO detector and reduce the number of symbols which have to be processed at each iteration. As a result,the computational complexity is reduced. Meanwhile,the successfully decoded outer code words are used to calculate the more reliable initial information for the inner decoder and the system performance can be improved by this step. The simulation results show that the proposed algorithm can reduce the computational complexity compared to the traditional iterative detection and decoding algorithm and achieve better performance.

Convergence Analysis of Iterative Threshold Decoding Process

Today the error correcting codes are present in all the telecom standards, in particular the low density parity check (LDPC) codes. The choice of a good code for a given network is essentially linked to the decoding performance obtained by the bit error rate (BER) curves. This approach requires a significant simulation time proportional to the length of the code, to overcome this problem Exit chart was introduced, as a fast technique to predict the performance of a particular class of codes called Turbo codes. In this paper, we success to apply Exit chart to analyze convergence behavior of iterative threshold decoding of one step majority logic decodable (OSMLD) codes. The iterative decoding process uses a soft-input soft-output threshold decoding algorithm as component decoder. Simulation results for iterative decoding of simple and concatenated codes transmitted over a Gaussian channel have shown that the thresholds obtained are a good indicator of the Bit Error Rate (BER) curves.

VARIABLE NON-UNIFORM QUANTIZED BELIEF PROPAGATION ALGORITHM FOR LDPC DECODING

Non-uniform quantization for messages in Low-Density Parity-Check(LDPC)decoding canreduce implementation complexity and mitigate performance loss.But the distribution of messagesvaries in the iterative decoding.This letter proposes a variable non-uniform quantized Belief Propaga-tion(BP)algorithm.The BP decoding is analyzed by density evolution with Gaussian approximation.Since the probability density of messages can be well approximated by Gaussian distribution,by theunbiased estimation of variance,the distribution of messages can be tracked during the iteration.Thusthe non-uniform quantization scheme can be optimized to minimize the distortion.Simulation resultsshow that the variable non-uniform quantization scheme can achieve better error rate performance andfaster decoding convergence than the conventional non-uniform quantization and uniform quantizationschemes.