We investigate weakly constrained codes, in which specific patterns occur with prescribed frequencies rather than being strictly forbidden as in conventional constrained coding. We propose a capacity-achieving construction of a weakly constrained codebook based on Eulerian cycles. We then obtain, via expurgation, weakly constrained codes with linear minimum distance and positive rate, and analyze the rates achievable. Finally, we propose a practical concatenated code construction that supports polynomial-time encoding and decoding.

翻译：我们研究了弱约束码，其中特定模式以规定的频率出现，而非像传统约束编码中那样被严格禁止。我们提出了一种基于欧拉环路的容量可达的弱约束码本构造方法。接着，通过删余方法，我们获得了具有线性最小距离和正速率的弱约束码，并分析了其可达速率。最后，我们提出了一种实用的级联码构造方案，支持多项式时间编码与解码。