Investigation of the energy and spectral efficiency of systems based on convolutional codes with soft decoding

A priority in the development of modern telecommunication systems is the enhancement of energy efficiency, which ensures reliable data transmission at minimal power expenditure. Nevertheless, the pursuit of maximum energy efficiency often conflicts with the need for high-rate information transfer within a limited bandwidth – that is, with the requirement for high spectral efficiency. The solution to this contradiction lies in the joint application of channel coding and multi-level modulation schemes, which serves as the key approach to achieving the necessary balance in modern communication systems. This work presents a detailed performance analysis of systems that combine convolutional coding with higher-order modulation schemes, specifically Quadrature Phase Shift Keying (QPSK) and Quadrature Amplitude Modulation (QAM). A central focus of this investigation is the evaluation of system performance when utilizing soft-decision decoding for the convolutional codes.The primary objective is to investigate the reliability of digital information transmission over an Additive White Gaussian Noise channel, as well as to quantitatively evaluate the impact of different modulation types and code rates on system performance. To achieve the stated objective, a hybrid methodology was utilized, integrating theoretical analysis based on coding theory with numerical simulations performed in MATLAB. One of the most significant results obtained in this study is the demonstration that the application of soft-decision decoding provides a coding gain of 2 to 4 dB compared to the hard-decision decoding method under identical bandwidth conditions. The results of the in-depth analysis presented in the article make it possible to increase the coding gain, as well as to determine the trade-off between energy and spectral efficiency in practical communication systems.

1. Sklar B. Digital Communications. Fundamentals and Applications. Moscow: Izdatel'skii dom "Vil'yams"; 2003. 1104 p. (In Russ.).

2. Proakis J.G. Digital Communications. Moscow: Radio i svyaz'; 2000. 800 p. (In Russ.).

3. Paramonov A.A., Chu V.V. Noise Immunity of QAM-OFDM Signal Reception Using Soft-Decision Demodulation in the Presence of Narrowband Interference. Russian Technological Journal. 2024;12(5):17–32. https://doi.org/10.32362/2500-316X-2024-12-5-17-32

4. Perişoară L.A., Stoian R. The Decision Reliability of MAP, Log-MAP, Max-Log-MAP and SOVA Algorithms for Turbo Codes. International Journal of Communications. 2008;2(1):65–74.

5. Cao X., Liu Yi, Hu D. Simplified LLR Algorithm for M‐QAM Demodulation. The Journal of Engineering. 2019;2019(21):7370–7375. https://doi.org/10.1049/joe.2019.0634

6. Berlekamp E.R. Algebraic Coding Theory. Moscow: Mir; 1971. 479 p. (In Russ.).

7. Katta K. Design of Convolutional Encoder and Viterbi Decoder Using MATLAB. International Journal for Research in Emerging Science and Technology. 2014;1(7):10–15.

8. Mosleh M.F., Abid F.A. Log-Likelihood Ratio to Improve Hard Decision Viterbi Algorithm. Engineering and Technology Journal. 2013;31(9):1779–1790. https://doi.org/10.30684/etj.2013.82189

9. Shennon K.E. Raboty po teorii informatsii i kibernetike. Moscow: Izd. inostr. literatury; 1963. 829 p. (In Russ.).

10. Makarov S.B., Tsikin I.A. Peredacha diskretnykh soobshchenii po radiokanalam s ogranichennoi polosoi propuskaniya. Moscow: Radio i svyaz'; 1988. 304 p. (In Russ.).