Feedback codes with uniformly bounded codeword lengths and zero-error capacities

A certain class of variable-length codes with feedback whose codeword lengths are uniformly upper bounded is considered. For this class of variable-length codes, it is shown that the zero-error capacity region for the, single-user and multiuser channels with feedback can be extended up to the ordinary average-error capacity under some conditions, if variable-length codes (semiblock codes) are used in place of fixed-length codes. This condition is different from that of M.V. Burnashev (1976) for variable-length codes with feedback but without any uniform bound on the codeword lengths. It is also shown that the capacity region for variable-length feedback codes coincides with that for fixed-length feedback codes.