Forward error correction (FEC) codes combined with high order modulator formats, i.e. coded modulation (CM), are essential in optical communication networks to achieve highly efficient and reliable communication. The task of providing additional error control in the design of CM systems with high-performance requirements remains urgent. As an additional control of CM systems, we propose to use indivisible error detection codes based on the position number system. In this work, we evaluated the indivisible code using the averaged probability method (APM) for the binary symmetric channel (BSC), which has the simplicity, versatility and reliability of the estimate, which is close to reality. The APM allows evaluation and compares indivisible codes according to the parameters of correct transmission, detectable and undetectable errors. Indivisible codes allow end-to-end (E2E) control of the transmission and processing of information in digital systems and design devices with a regular structure and high speed. This paper research a fractal decoder device for additional error control, implemented in a field-programmable gate array (FPGA) software with FEC for short-reach optical interconnects with multilevel pulse amplitude (PAM-M) modulated with Gray code mapping. Indivisible codes with natural redundancy re-choir far below hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We have achieved a reduction in hardware costs for a fractal decoder by using the fractal property of the indivisible code from 10 to 30% for different n while receiving the reciprocal of the golden ratio.