Rate-adaptive MacKay-Neal (MN) codes based on protographs are analyzed. The code construction employs an outer distribution matcher (DM) to adapt the rate of the scheme. The DM is coupled with an inner protograph-based low-density parity-check (LDPC) code. The performance achievable by the resulting code structure, that is nonlinear, is studied by means of an equivalent communication model that reduces the problem to the analysis of the inner (linear) LDPC code with transmission that takes place in parallel over the communication channel, and over a suitably defined binary symmetric channel. A density evolution analysis of protograph MN code ensembles is outlined, and it is complemented by an error floor analysis that relies on the derivation of the average input-output weight distribution of the inner LDPC code ensemble. Conditions on the shape of the normalized logarithmic asymptotic input-output weight distribution are defined, which allow discarding code ensembles with bad error floor properties during the code design phase. Examples of code designs are provided, showing how the use of a single LDPC code ensemble allows operating within 1 dB from the Shannon limit over a wide range of code rates, where the code rate is selected by tuning the DM parameters. By enabling rate flexibility with a constant blocklength, and with a fixed LDPC code as inner code, the construction provides an appealing solution for very high-throughput wireless (optical) links that employ binary-input modulations.

翻译：本文分析了基于原型的速率自适应MacKay-Neal（MN）码。该码构造采用外部分布匹配器（DM）以实现方案的速率自适应。DM与基于原型的内部低密度奇偶校验（LDPC）码相耦合。通过建立等效通信模型，将问题简化为分析在通信信道和适当定义的二进制对称信道上并行传输的内部（线性）LDPC码，从而研究了由此产生的非线性码结构的可达性能。本文概述了原型MN码集合的密度进化分析，并辅以基于内部LDPC码集合平均输入-输出重量分布推导的错误平层分析。定义了归一化对数渐近输入-输出重量分布形状的条件，这些条件允许在码设计阶段排除具有不良错误平层特性的码集合。文中提供了码设计实例，展示了使用单一LDPC码集合可在广泛码率范围内实现距香农极限1 dB以内的性能，其中码率通过调整DM参数进行选择。该构造通过恒定分组长度和固定LDPC码作为内部码实现速率灵活性，为采用二进制输入调制方式的超高吞吐量无线（光）链路提供了一种极具吸引力的解决方案。