The probability shaping coding circuit (1) includes an mth
lookup table (11) for layer x+1 that converts an mth transmission bit sequence of layer x+1, which is composed of an mth transmission information bit sequence of layer x+1, which is a part of an information bit sequence to be communicated, and an mth transmission address bit sequence of layer x+1, into an mth transmission shaping bit sequence of layer x+1, where x, m, and n[x] are natural numbers (m=1, 2, . . . , n[x]), and a layer The communication
system includes an mth distribution circuit (12) of x, a (2m-1)th
lookup table (14) of layer x that generates a (2m-1)th transmission shaping bit sequence of layer x from the (2m-1)th
source address bit sequence of layer x and the (2m-1)th transmission information bit sequence of layer x, which is a part of the information bit sequence of the communication target, and a 2mth
lookup table (15) of layer x that generates a 2mth transmission shaping bit sequence of layer x from the 2mth
source address bit sequence of layer x and the 2mth transmission information bit sequence of layer x, which is a part of the information bit sequence of the communication target. The lookup tables are arranged hierarchically in a
tree structure, and each
source address bit sequence obtained by the m-th distribution circuit (12) of layer x corresponds to designation information specifying a combination of
signal points in a
signal space managed by each of the plurality of lookup tables of layer x, and each transmission shaping bit sequence generated by the (2m-1)-th lookup table (14) of layer x and the 2m-th lookup table (15) of layer x corresponds to designation information specifying a combination of
signal points in a signal space managed by each of the plurality of lookup tables of the immediately lower hierarchical level, or signal point information indicating a signal point arrangement in the signal space.