A new scientific article is published in MDPI Entropy, with the contribution from the RTU ComTech, Institute of Telecommunications, KTH Royal Institute (Applied Physics Department), RISE Research Institutes of Sweden, and Sumy State University (Department of Electronics and Computer Technology). The article proposes to use indivisible error detection codes based on a positional number system as additional control of coded modulation (CM) systems.
Why is it relevant?
Forward error correction (FEC) codes combined with high-order modulator formats, i.e., coded modulation (CM), is 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 a positional number system.
In this work, we evaluated the indivisible code using the average 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 for evaluation and compares indivisible codes according to parameters of correct transmission, and detectable and undetectable errors. Indivisible codes allow for the 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 study researched 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 require far fewer hardware costs to develop and implement encoding and decoding devices with a sufficiently high error detection efficiency. We 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.
What has been demonstrated and what results have been achieved?
In this paper, we investigate a fractal decoder, which was implemented in FPGA using Intel Quartus Prime software. The device was investigated for a 56 and 35 Gbaud PAM- M (M = 4, 8) modulation with Gray code mapping using wavelength division multiplexed (WDM) optical interconnect model with a standard single-mode fibre (SSMF) and erbiumdoped fibre amplifier (EDFA).
We investigate the combination of an indivisible natural redundancy error detection code with an artificial redundancy FEC based on the interleaved BCH + LDPC and RS + LDPC FEC. We also evaluate the indivisible error detecting code using the average probability method (APM), which demonstrated that the simplicity, versatility, and reliability of estimation are close to reality. This shows that it is possible to reduce the saving hardware costs of the fractal decoder by using the fractal property of indivisible code. An increase in the savings in hardware costs occurs with an increase in the code length of the indivisible code, which is limited to the reciprocal of the golden ratio. With fractal decoding, the signal delays twice as much as the standard method of constructing line Fibonacci decoders.
The work is open access on MDPI entropy, click on this DOI link to read the full paper.
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