In this research, low complexity turbo equalization algorithms are examined as an alternatives to the optimal, but, much more complex, Bahl-Cocke-Jelinek-Raviv (BCJR) algorithm. First, the soft-in soft-out (SISO) decision feedback equalizer (DFE) algorithm with the extrinsic information mapping methods that directly take into account the error propagation effects of DFE is presented. We also utilize a pair of DFE operating in opposite directions in turbo equalization setting to remove the effect of intersymbol interference (ISI) at the receiver with new extrinsic information combining strategy that explores error correlation between the two sets of DFE outputs. When this method is combined with the proposed DFE extrinsic information formulation, the resulting "bidirectional" turbo-DFE achieves excellent performance-complexity tradeoffs compared to the turbo equalization based on the BCJR algorithm. Furthermore, a self-iterating soft equalizer (SISE) consisting of a few relatively weak equalizers is shown to provide robust performance in severe ISI channels. Constituent suboptimal equalizers are allowed to exchange soft information based on the method that are designed to suppress significant correlation among their soft outputs. The resulting SISE works well as a stand-alone equalizer or as the equalizer component of a turbo equalization system. The performance advantages of the proposed algorithms are validated with bit-error-rate (BER) simulations and extrinsic information transfer (EXIT) chart analysis.;In the thesis, provable lower bounds are also presented for the information rate of any finite ISI channels. Let us consider I( X;X + S + N) where X is the symbol drawn independently and uniformly from a fixed, finite-size alphabet, S a discretevalued random variable (RV) and N a Gaussian RV. Especially, when S represents the precursor ISI after the infinite-length unbiased minimum mean-squared error (MMSE) DFE is applied at the channel output, the mutual information I( X;X + S + N) serves as a tight lower bound for the symmetric information rate (SIR) as well as capacity of the ISI channel corrupted by Gaussian noise. The new lower bounds are obtained by first introducing a "mismatched" mutual information function that can be proved as a lower bound to I(X; X + S + N) and then further lower-bounding this function with expressions that can be computed via a few single-dimensional integrations with a small computational load. The new bounds provide a similar level of tightness as the well-known conjectured lower bound by Shamai and Laroia for a wide variety of ISI channels of practical interest.
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机译：在这项研究中，对低复杂度涡轮均衡算法进行了研究，以替代最优的，但更为复杂的Bahl-Cocke-Jelinek-Raviv（BCJR）算法。首先，提出了一种采用外在信息映射方法的软入软出（SISO）决策反馈均衡器（DFE）算法，该算法直接考虑了DFE的误差传播效应。我们还利用一对在涡轮均衡设置中在相反方向上运行的DFE，通过探索两个DFE输出之间的误差相关性的新的外部信息组合策略，消除了接收机处的符号间干扰（ISI）的影响。当此方法与提出的DFE外在信息表示法相结合时，与基于BCJR算法的Turbo均衡相比，所得的“双向” turbo-DFE可以实现出色的性能-复杂性折衷。此外，显示了由几个相对较弱的均衡器组成的自迭代软均衡器（SISE）在严重的ISI信道中提供了强大的性能。组成次优均衡器允许基于旨在抑制软输出之间显着相关性的方法交换软信息。所得的SISE可以作为独立均衡器或Turbo均衡系统的均衡器组件很好地工作。通过误码率（BER）仿真和外在信息传递（EXIT）图分析验证了所提算法的性能优势。本文还针对任意有限ISI信道的信息率提出了可证明的下界。让我们考虑I（X; X + S + N），其中X是从固定的有限大小的字母表中独立且一致地绘制的符号，S是离散值随机变量（RV），N是高斯RV。特别是，当在通道输出上应用无限长的无偏最小均方误差（MMSE）DFE之后，S表示前体ISI时，互信息I（X; X + S + N）充当对称信息速率（SIR）以及被高斯噪声破坏的ISI信道的容量。通过首先引入一个“不匹配的”互信息函数来获得新的下界，该函数可被证明是I（X; X + S + N）的下界，然后将该函数进一步下界到可以通过以下公式计算的表达式少量的单维积分，计算量很小。对于许多具有实际意义的ISI渠道，新界限提供的紧密度与Shamai和Laroia众所周知的推测下限相似。
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