We derive Singleton-type bounds on the free distance and column distances of trellis codes. Our results show that, at a given time instant, the maximum attainable column distance of trellis codes can exceed that of convolutional codes. Moreover, using expander graphs, we construct trellis codes over constant-size alphabets that achieve a rate-distance trade-off arbitrarily close to that of convolutional codes with a maximum distance profile. By comparison, all known constructions of convolutional codes with a maximum distance profile require working over alphabets whose size grows at least exponentially with the number of output symbols per time instant.

翻译：我们推导了网格码的自由距离与列距离的Singleton型界。结果表明，在给定时刻，网格码可达到的最大列距离能够超越卷积码。此外，利用扩展图，我们构造了在恒定大小字母表上的网格码，其速率-距离权衡可任意逼近具有最大距离特性的卷积码。相比之下，所有已知的具有最大距离特性的卷积码构造均要求字母表大小随每时刻输出符号数至少呈指数增长。