RIA: Bandwidth and Energy Efficient Communication Via Ring Encoded Continuous Phase Modulation

本课题研究了通过信道编码来降低多进制连续相位调制(CPM)方案的误码率的问题。通常涉及外部二进制卷积编码器的技术是不自然的，并且它只利用了编码增益的一部分。该方案基于一种新的解决方案，其目的是在相同的译码复杂度下获得更大的编码增益。该方法借助于显式地使用它们馈送的CPM方案的状态信息的M元卷积信道编码器(CE)。使用这种方法的能力在于CPM的模型，该模型由表示为连续相位编码器(CPE)的线性时序电路和紧随其后的无记忆调制器(MM)组成。由于CPE是M进制的，所以可以反馈它的存储单元的内容并在CE中显式地使用它，CE也是M进制的，并且在模M的整数环上是线性的。因此，CE有它自己的存储单元和那些与CPE共享的存储单元。这种共生增加了CE的约束长度，而不增加状态的总体数量。在不增加译码复杂度的情况下，获得了比通常的码更强大的码。此外，这种解决方案并不局限于输入字母表大小为2的幂的CPM方案。对环码的研究本身就很有意义。最近的各种结果清楚地表明，环码和群码对于非二进制调制方案是非常重要的。

This project considers the problem of decreasing the probability of error of M-ary continuous-phase modulation (CPM) schemes by means of channel coding. It is argued that the usual technique involving an external binary convolutional encoder is unnatural, and it exploits only part of the coding gain. This project is based on a new solution, which aims to obtain a larger coding gain for the same decoding complexity. The method is by means of M-ary convolutional channel encoders (CE) that explicitly use the state information of the CPM scheme that they feed. The ability to use this method lies in the model for CPM, which consists of a linear sequential circuit denoted continuous-phase encoder (CPE) followed by a memoryless modulator (MM). Since the CPE is M-ary, one can feed-back the content of its memory units and use it explicitly in the CE which is also M-ary and linear over the ring of integers modulo M. Thus the CE has its own memory units and those shared with the CPE. This symbiosis increases the constraint length of the CE without increasing the overall number of states. Codes that are more powerful than the usual ones are obtained without increasing the decoding complexity. Moreover, this solution is not constrained to CPM schemes whose input alphabet's size M is a power of 2. The research on ring codes is of interest in its own. Various recent results are a clear indication that ring and group codes are of great importance for nonbinary modulation schemes.