Noise Immunity of Communication and Broadcasting Systems with Multi-Stage Different-Type Coding and Multi-Position Modulation

The article presents analytical models for calculating and a methodology for studying the noise immunity, energy, and information efficiency of systems with sequential composite coding based on long-length convolutional codes in combination with binary block Bose – Chaudhuri – Hocquenghem codes, and convolutional and nonbinary Reed-Solomon codes. The calculation models allow for detailed studies of the properties of composite code structures with multi-position modulation types and decoding using the Viterbi algorithm with a soft decision for convolutional and Bose – Chaudhuri – Hocquenghem codes and a hard decision for Reed – Solomon codes. Unlike known approaches, this methodology does not require knowledge of the spectral weighting coefficients of the codes used, does not limit the choice of code locations within the code structure, and does not involve the use of complex computer modeling procedures in the calculations. The studies are performed in a closed-loop manner based on the specified parameters of the codes in the composite structure and the requirements for ensuring reliable reception. It is shown that the noise immunity of systems with two-stage sequential coding based on convolutional codes with a design length of K = 13 in combination with simple convolutional codes, such as Bose – Chaudhuri – Hocquenghem or Reed – Solomon codes, is comparable to the noise immunity of the best turbo code models with iterative parallel MAP decoding. Furthermore, the disadvantages of turbo codes caused by the use of high-dimensional interleavers are eliminated.

1. Berrou C., Glavieux A. (1996) Near Optimum Error Correcting Coding and Decoding. IEEE Transactions on Communications. 44 (10), 1261–1271.

2. Zolotarev V. V., Ovechkin G. V. (2004) Noisy-Correcting Coding. Methods and Algorithms. Moscow, Hotline – Telecom Publ. (in Russian).

3. Shloma A. M., Bakulin M. G., Kreindelin V. B., Shumov A. P. (2008) New Algorithms for Signal Generation and Processing in Mobile Communication Systems. Moscow, Hotline – Telecom Publ. (in Russian).

4. Lipkovich E. B., Rabtsevich V. V. (2023) A Method for Calculating of the Efficiency of Communication Systems with Multiple Modulation Types and Multi-Stage Composite Coding. Doklady BGUIR. 21 (6), 45–52. http://dx.doi.org/10.35596/1729-7648-2023-21-6-45-52 (in Russian).

5. Morelos-Zaragoza R. (2005) The Art of Error Correcting Coding. Methods, Algorithms, Application. Moscow, Technosphere Publ. (in Russian).

6. Lipkovich E. B., Belenkevich N. I., Zorka M. I. (2025) Methodology for Calculation the Energy Efficiency of Communication and Broadcasting Systems with Noise-Immune Block Coding and Multi-Position Modulation. Doklady BGUIR. 23 (5), 45–52. http://dx.doi.org/10.35596/1729-7648-2025-23-5-45-52 (in Russian).