A Study of Concatenated Codes and Coded Modulation Systems

我们将以我们最近的发明为基础，研究一类一般的串联码和编码调制。我们的串联方案比传统的串联码更通用，因为“编码器”可以是具有存储器的信道（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），或者具有某些约束或存储器的调制器（例如，连续相位调制（CPM），栅格编码调制（TCM））。我们也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）”起着关键作用。AZD引入了广义的“擦除”符号，并被发现是利用软决策输出的最有效方法。我们还使用了“置换”和“迭代解码”，就像在Turbo代码中所做的那样。但与Turbo代码和其他已知的方案如产品代码不同，我们的系统所需的排列大小不需要那么大。将我们的方法与现有技术区分开来的主要优势是其极其简单的解码算法。因此，解码器很容易实现，并且解码延迟保持最小。我们的系统的性能，以残余误差/擦除量来衡量，是非常好的。例如，对于采用汉明码和部分响应通道G(D)=1+D的系统，我们获得的初始结果表明，我们的解码算法在几次迭代内收敛，并且即使超过50%的AZD输出被标记为“擦除”，也能产生几乎无错误的输出。在本研究中，我们打算完成以下研究任务：1。具体应用实例的仿真（例如，部分响应信道，带CPM的无线信道）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）对所提出的编码和编码调制方案的性能分析（例如，解码错误概率的边界和近似）。构造强大的代码，使用更一般的连接拓扑（如并行-串行连接），以及相应的解码过程。我们还期望在本研究中获得的见解应该导致对Turbo代码的更好理解，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.