On multilevel codes and iterative multistage decoding

This paper develops an approach to iterative multistage decoding of multilevel codes. This involves passing reliability information to previous and subsequent decoders instead of only hard decisions to subsequent decoders. The paper also develops an adaptive version of the suboptimal soft output decoding algorithm of Picart and Pyndiah (1996). This adaptive algorithm provides a gain of approximately 0.24 dB at a bit error rate (BER) of 10^-5 after four iterations and approximately 0.43 dB after ten iterations over the algorithm of Picart et al. If the adaptive algorithm is used in conjunction with iterative multistage decoding then a gain of approximately 0.62 dB is obtained at a BER of 10^-5 after four iterations and approximately 0.9 dB after ten iterations over the algorithm of Picart et al     

On the iterative decoding of multilevel codes

Iterative decoding of multilevel coded modulation is discussed. Despite its asymptotic optimality with proper design, the error correcting capability of multilevel codes may not be fully exploited for finite block length with conventional multistage decoding. This fact stems from the suboptimality of multistage decoding giving rise to increased error multiplicity at lower index stages and the associated error propagation to higher stages. Such problems can be overcome in many situations by introducing iterative decoding which often significantly compensates the suboptimality of a staged decoder. The class of multilevel codes achieving practically important bit-error performance near the Shannon limit becomes far wider with iterative decoding     

Shuffled iterative decoding

Shuffled versions of iterative decoding of low-density parity-check codes and turbo codes are presented. The proposed schemes have about the same computational complexity as the standard versions, and converge faster. Simulations show that the new schedules offer better performance/complexity tradeoffs, especially when the maximum number of iterations has to remain small.     

Improved iterative joint detection and decoding of coded V-BLAST systems

Soft iterative detection and decoding techniques have been shown to achieve near-capacity performance in multiple antenna systems. In most cases, obtaining optimal soft information in a joint detection and decoding algorithm by marginalizing over the entire observation space is prohibitively complex. In this paper, an improved scheme adaptable to various list-type detectors providing superior performance is proposed.     

Rate optimization for IDMA systems with iterative joint multi-user decoding

In this letter, we develop a rate allocation scheme for interleave-division multiple-access (IDMA) systems with iterative decoding. We use a fully-analytical approach to predict the performance of the scheme. Then, we propose a modified linear programming method to find the best rate profile for the scheme. Numerical results show that with just repetition coding and optimal rate allocation, the performance of the scheme is only about 5 dB away from the capacity for a wide range of SNR, provided that the number of users is sufficiently large. Compared with power allocation schemes for IDMA, the proposed rate allocation scheme achieves a similar performance at a moderate spectral efficiency and the requirement of sophisticated power amplifiers can be relaxed.     

A modified medium access control algorithm for systems with iterative decoding

Efficient transmission methods for fading radio channels often require an iterative decoder. This is for example the case for systems using turbo codes. Receiver decoder iterations could potentially lead to a latency problem which impacts the performance of the medium access control protocol. In this paper, we present modifications based on the carrier sense multiple access with collision avoidance (CSMA/CA) medium access control (MAC) protocol to accommodate the increased latency in the iterative processing. One area of applications is wireless local area networks (WLANs) with high data rate. The simulation results performed in the IEEE 802.11a WLAN environment by replacing the 802:11a's convolutional coding with turbo coding demonstrate that the proposed algorithm provides a throughput gain over the conventional method.     

Signal-space characterization of iterative decoding

By tracing the flow of computations in the iterative decoders for low-density parity-check codes, we formulate a signal-space view for a finite number of iterations in a finite-length code. On a Gaussian channel, maximum a posteriori (MAP) codeword decoding (or “maximum-likelihood decoding”) decodes to the codeword signal that is closest to the channel output in Euclidean distance. In contrast, we show that iterative decoding decodes to the “pseudosignal” that has highest correlation with the channel output. The set of pseudosignals corresponds to “pseudocodewords”, only a vanishingly small number of which correspond to codewords. We show that some pseudocodewords cause decoding errors, but that there are also pseudocodewords that frequently correct the deleterious effects of other pseudocodewords     

Multiuser SCCPM with iterative decoding

The recent technique of serially concatenated continuous phase modulation (SCCPM) is extended to a multiuser system with a carrier frequency offset between the users. Simulation results for up to five users with an iterative decoder show that the performance loss is small considering the substantial spectral overlap. Consequently, power/bandwidth efficiencies which are better than for SCCPM are achievable     

Low-density parity check codes and iterative decoding for long-haul optical communication systems

A forward-error correction (FEC) scheme based on low-density parity check (LDPC) codes and iterative decoding using belief propagation in code graphs is presented in this paper. We show that LDPC codes provide a significant system performance improvement with respect to the state-of-the-art FEC schemes employed in optical communications systems. We present a class of structured codes based on mutually orthogonal Latin rectangles. Such codes have high rates and can lend themselves to very low-complexity encoder/decoder implementations. The system performance is further improved by a code design that eliminates short cycles in a graph employed in iterative decoding.     

SFBC-OFDM系统中联合迭代信道估计与空频解码算法

提出了一种基于SFBC-OFDM系统的联合迭代信道估计与空频解码算法。首先为提高初始信道估计器的性能,提出了一种基于时频变换(TFT)的信道估计算法;其次提出了利用信道估计值与解码符号进行联合迭代信道估计与空频解码算法。分析与仿真结果显示,在准静态、快时变以及相关信道条件下,新的联合迭代信道估计与空频解码算法都有效地提高了系统性能。     

On general linear block code decoding using the sum-product iterative decoder

The sum-product iterative decoder, conventionally used for low-density parity-check (LDPC) codes, hold promise as a decoder for general linear block code decoding. However, the promise is only partly fulfilled because, as we show experimentally, the decoder performance degrades rapidly as a function of parity check matrix weight. Even in the case of decoder failure, however, we demonstrate that there is information present in the decoder output probabilities that can still help with the decoding problem.     

LDPC调制系统中迭代解调解码信息的线性优化

在中短码长低密度奇偶校验（LDPC）码编码的比特交织编码调制系统（BICM）中,由二分图短圈导致的置信传播（BP）解码器输出外附信息之间的相关性是降低迭代解调/解码性能的主要原因,因此有必要对解码器输出外附对数似然比（LLR）信息进行优化。针对该问题,提出了一种简单有效的LLR线性优化算法。该算法首先基于匹配LLR值应满足的连续性条件,并结合BP解码器输出外附LLR信息的统计特性,对解码器输出LLR信息的条件概率密度函数（PDF）的计算进行简化,推导出了乘性优化因子,据此对解码器输出外附信息进行线性优化。仿真结果表明,与未优化方案相比,对于(504,252) LDPC 码编码的BICM系统,所提优化算法可获得0.6~0.8 dB 的信噪比增益;和推广互信息（GMI）优化方法相比,两者的误码性能接近,所提算法仅差0.1 dB,且具有更小的运算复杂度。     

Noncoherent iterative (turbo) decoding

Previously, noncoherent sequence detection schemes for coded linear and continuous phase modulations have been proposed, which deliver hard decisions by means of a Viterbi algorithm. The current trend in digital transmission systems toward iterative decoding algorithms motivates an extension of these schemes. In this paper, we propose two noncoherent soft-output decoding algorithms. The first solution has a structure similar to that of the well-known algorithm by Bahl et al. (1974), whereas the second is based on noncoherent sequence detection and a reduced-state soft-output Viterbi algorithm. Applications to the combined detection and decoding of differential or convolutional codes are considered. Further applications to noncoherent iterative decoding of turbo codes and serially concatenated interleaved codes are also considered. The proposed noncoherent detection schemes exhibit moderate performance loss with respect to corresponding coherent schemes and are very robust to phase and frequency instabilities     

Bit-interleaved coded modulation with iterative decoding

A simple iterative decoding technique using hard-decision feedback is presented for bit-interleaved coded modulation (BICM). With an 8-state, rate-2/3 convolutional code, and 8-PSK modulation, the improvement over the conventional BICM scheme exceeds 1 dB for a fully-interleaved Rayleigh flat-fading channel and exceeds 1.5 dB for a channel with additive white Gaussian noise. This robust performance makes BICM with iterative decoding suitable for both types of channels     

New stopping criteria for iterative decoding of LDPC codes in H‐ARQ systems

Under severely unreliable channel, decoding of error‐correcting codes frequently fails, which requires a lot of computational complexity, especially, in the iterative decoding algorithm. In hybrid automatic repeat request systems, most of computation power is wasted on failed decoding if a codeword is retransmitted many times. Therefore, early stopping of iterative decoding needs to be adopted. In this paper, we propose a new stopping algorithm of iterative belief propagation decoding for low‐density parity‐check codes, which is effective on both high and low signal‐to‐noise ratio ranges and scalable to variable code rate and length. The proposed stopping algorithm combines several good stopping criteria. Each criterion is extremely simple and will not be a burden to the overall system. With the proposed stopping algorithm, it is shown via numerical analysis that the decoding complexity of hybrid automatic repeat request system with adaptive modulation and coding scheme can be fairly reduced. Copyright © 2012 John Wiley & Sons, Ltd.     

Distance based adaptive scaling in suboptimal iterative decoding

This article develops an alternative adaptive iterative Chase (1972) based decoding algorithm for block turbo/product codes. The decoder considers only a small subset of codewords, so that estimates of the extrinsic information are required in some cases. This article develops such an estimate based on code distance properties     

Bit-interleaved space-time coded modulation with iterative decoding

Bit-interleaved space-time coded modulation (BI-STC), which combines serial concatenation of bit-interleaved coded modulation (BICM) with space-time block codes, can effectively exploit the available diversity in space and time under various fading conditions. In this letter, we propose to use iterative decoding to further improve the performance of BI-STC by exploiting the concatenating structure of the codes. The decoding metric is therefore modified to fit for the iterative process, and the derived error bounds suggest that set-partition labeling instead of gray labeling should be used when considering iterative decoding.