A Study of Concatenated Codes and Coded Modulation Systems

我们将在我们最新发明的基础上，研究一类一般的级联码和编码调制。我们的级联方案比传统的级联编码更一般，因为编码器可以是具有记忆的信道(例如，部分响应信道、具有符号间干扰和/或多径延迟的信道、具有突发噪声的信道)，或者具有某种约束或记忆的调制器(例如，连续相位调制(CPM)、网格编码调制(Tcm))。我们还可以连接两个以上的编码器。在我们提出的系统中，“模糊区域检测器(AZD)”起着至关重要的作用。AZD引入了广义的“擦除”符号，被发现是利用软判决输出的最有效的方法。正如Turbo码中所做的那样，我们还利用了“排列”和“迭代译码”。但与Turbo码和乘积码等其他已知方案不同的是，我们的系统所需的置换大小不需要这么大。我们的方法不同于现有技术的主要优势是其极其简单的解码算法。因此，该解码器易于实现，并且保持最小的解码延迟。我们系统的性能，以残留误差/擦除来衡量，是非常好的。例如，对于采用汉明码和部分响应信道G(D)=1+D的系统，我们的初步结果表明，我们的译码算法在几次迭代内收敛，并且即使当超过50%的AZD输出被标记为“擦除”时，也能产生几乎无差错的输出。在这项拟议的研究中，我们打算执行以下研究任务：1.对特定应用实例(例如，部分响应信道、具有CPM的无线信道)的模拟2.确定良好的排列和有效的解码器(例如，模糊区域的最佳选择)3.对所提出的码和编码调制方案的性能分析(例如，解码错误概率的界和近似)4.使用更一般的级联拓扑(例如，并串级联)构造强大的码，以及相应的解码过程。我们还期望在本研究中获得的见解将有助于更好地理解Turbo码，反之亦然。

We will investigate a general class of concatenated codes and coded-modulation, by building upon our recent invention. Our concatenated scheme is more general than the conventional concatenated codes in that a "coder" can be a channel with memory (e.g., a partial-response channel, a channel with intersymbol interference and/or multipath delays, a channel with burst noise), or a modulator with some constraint or memory (e.g., continuous phase modulation (CPM), trellis-coded modulation (TCM)). We can also concatenate more than two coders. In our proposed system an "ambiguity zone detector (AZD)" plays a critical role. The AZD introduces generalized "erasure" symbols, and is found to be a most efficient way of exploiting soft-decision outputs. We also make use of a "permutation" and "iterative decoding", as has been done in Turbo codes. But unlike the Turbo codes and such other known schemes as product codes, the permutation size required for our system needs not be so large. The main advantage that differentiates our approach from prior arts is its extremely simple decoding algorithm. Hence, the decoder is easily implementable and the decoding delay is kept minimal. The performance of our system, measured in terms of residual errors/erasures, is extremely good. For example, our initial result obtained for a system which adopts a Hamming code and a partial-response channel G(D)=1+D demonstrates that our decoding algorithm converges within several iterations, and produces nearly error-free outputs even when more than 50% of the AZD outputs are labeled "erasures". In this proposed study we intend to perform the following research tasks: 1. Simulation of specific application examples (e.g., partial-response channels, wireless channels with CPM) 2. Determination of good permutations and effective decoders (e.g., optimal selections of the ambiguity zones) 3. Performance analysis of the proposed codes, and coded modulation schemes (e.g., bounds and approximation for t he decoding error probability) 4. Construction of powerful codes, using a more general concatenation topology (e.g. a parallel-serial concatenation), and the corresponding decoding procedures. We also expect that insights to be gained in the present study should lead to a better understanding of the Turbo codes, and vice versa.