Performance Analysis of Algebraic Cascaded Convolutional Codes

Аuthors

Volkov A. S.

National Research University of Electronic Technology, 1, sq. Shokina, Moscow, Zelenograd, 124498, Russia

e-mail: leshvol@mail.ru

Abstract

This paper is dedicated to the design of a cascaded code based on non-binary algebraic convolutional codes. The relevance of the research is driven by the widespread use of error-correcting coding in modern wireless communication systems, the benefits of using a cascaded coding scheme, and the properties of non-binary algebraic convolutional codes.
The goal of this work is the theoretical estimation and simulation of the noise immunity of an algebraic convolutional code and a cascaded code with non-binary algebraic convolutional codes at the outer and inner stages, constructed based on Reed-Solomon codes over extended Galois fields. An estimation of the error probability in an AWGN channel using BPSK and 16-PSK modulation is provided.
The proposed approach makes it possible to design codes based on algebraic methods with high error-correction capabilities and estimate their theoretically achievable noise immunity. Due to the large codeword lengths, the classical binomial approach to calculating the error probability was replaced by a more accurate integral method using the incomplete beta function. The simulation accounted for the influence of interleaving between the coding stages. The results showed that using a real interleaver with finite depth (exemplified by a depth of 1000 bits) leads to a degradation in noise immunity compared to the ideal case due to burst error propagation. 
Thus, the possibility of applying algebraic methods from block code theory to estimate the noise immunity of cascaded convolutional structures is demonstrated. The simulation confirmed the correctness of the proposed methodology and revealed the dependence of the code's efficiency on the interleaver parameters. 
The research revealed that the algebraic decoder does not account for the frame redundancy and specific properties of the algebraic convolutional code. Consequently, to eliminate this shortcoming of the algebraic decoder and to incorporate the code's properties, it is necessary to synthesize a decoding method that combines the algebraic approach with the maximum likelihood method.

Keywords:

convolutional codes, decoding of convolutional codes, cascaded convolutional codes, algebraic convolutional codes, noise immunity calculation

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