Code Capacity and Code Design

本研究将通过检查每个编码和译码步骤导致的容量损失来分析在加性高斯信道(AWGN)和各种衰落信道上操作的级联编码系统和调制方案的性能。然后，这些信息将被用于指导新编码系统的设计。这项研究中描述的技术允许单独评估编码和解码器，从而识别发生容量损失的位置。了解这种容量损失对于通信系统的整体设计是重要的，例如，对于评估产生超出最大似然估计的信息的内部解码器的好处。首先，发展了一种计算正交码和AWGN信道隔离的综合容量的通用技术。然后，已经开发了正交码、AWGN信道和各种内部解码器的综合容量，包括估计1的逐比特概率的解码器，如在Turbo码中。这些例子中的计算表明，最大似然解码器引入了很大的容量损失。这种容量损失中的一部分可以通过仅使用稍微复杂的内部解码器来恢复，例如用于输出两个最可能频率的M进制频移键控的检测器，并且ML估计正确的概率比仅输出最可能频率的检测器给出的降级要小得多。本项目将这些结果推广到其他编码和其他通道。实际有用的结果应该是用于高斯信道的接近球形填充界限的短码，以及用于衰落信道的改进的传统和并行级联码。实验研究将包括在工作中。

This research will analyze the performance of concatenated coding systems and modulation schemes operating over the additive Gaussian channel (AWGN) and various fading channels by examining the loss of capacity resulting from each of the encoding and decoding steps. This information will then be used to guide the design of new coding systems. The techniques described in this research allow the separate evaluation of codes and decoders and thus the identification of where loss of capacity occurs. Knowledge of this capacity loss is important for the overall design of a communications system, e.g. for evaluating the benefits of inner decoders that produce information beyond the maximum likelihood estimate. First a general technique for calculating the composite capacity of an orthogonal code and the AWGN channel in isolation has been developed. Then the composite capacities of an orthogonal code, the AWGN channel, and various inner decoders including the decoder estimating the bit-by-bit probability of a one, as in turbo codes, has been developed. The calculations in these examples show that the maximum likelihood decoder introduces a large loss in capacity. Some of this capacity loss can be regained by using only slightly more complex inner decoders, e.g. a detector for M-ary frequency-shift-keying that outputs the two most likely frequencies and the probability that the ML estimate is correct gives substantially less degradation than one which only outputs the most likely frequency. This project extends these results to other codes and other channels. Practically useful results should be short codes that come close to the sphere packing bound for the Gaussian channel and improved conventional and parallel concatenated codes for fading channels. Experimental studies will be included in the work.