标题： 关于人类语言编码最优性类及其与zipf定律的起源 显示英文标题

标题： On the class of coding optimality of human languages and the origins of Zipf's law

摘要： 我们在此提出了一类新的编码系统的最优性。该类别的成员线性偏离了最优编码，因此表现出齐夫定律，即频率等级的幂律分布。在该类别内，齐夫定律、规模-排名定律和规模-概率定律形成了一种类似群组的结构。我们识别出属于该类别的自然语言。所有与齐夫定律足够一致的语言都可能是该类别的潜在成员。相比之下，其他物种中的通信系统由于表现出指数分布而非幂律分布，因而不可能成为该类别的一员，但海豚和座头鲸可能是个例外。我们对频率与排名在双对数尺度下的图表提供了新的见解。对于任何系统，在该尺度上呈现一条直线表明非奇异编码和唯一可解编码下最优码长的差异由一个线性函数表示，其斜率即为齐夫定律的指数。对于受压缩且受限于唯一可解编码的系统，这样的直线可能表明该系统接近最优编码。我们的研究结果为齐夫定律源于压缩的假设提供了支持。 显示英文摘要

摘要： Here we present a new class of optimality for coding systems. Members of that class are displaced linearly from optimal coding and thus exhibit Zipf's law, namely a power-law distribution of frequency ranks. Within that class, Zipf's law, the size-rank law and the size-probability law form a group-like structure. We identify human languages that are members of the class. All languages showing sufficient agreement with Zipf's law are potential members of the class. In contrast, there are communication systems in other species that cannot be members of that class for exhibiting an exponential distribution instead but dolphins and humpback whales might. We provide a new insight into plots of frequency versus rank in double logarithmic scale. For any system, a straight line in that scale indicates that the lengths of optimal codes under non-singular coding and under uniquely decodable encoding are displaced by a linear function whose slope is the exponent of Zipf's law. For systems under compression and constrained to be uniquely decodable, such a straight line may indicate that the system is coding close to optimality. Our findings provide support for the hypothesis that Zipf's law originates from compression.