MODELS OF CONCATENATE CODE STRUCTURES

Abstract

In the era of the active development of digital data transmission systems - space, satel-lite, and mobile - ensuring reliable transmission has become especially pressing. The wire-less channels used in all of these systems are susceptible to various types of interference, which often results in errors in received data. However, in many practical applications, only a minimal error rate in the processed digital data is acceptable. The theory of error-correcting coding makes a significant contribution in overcoming this problem. Within this framework, numerous codes and decoding methods have been developed, differing in pa-rameters such as energy gain, introduced redundancy, implementation complexity, and oth-ers.

Cascade codes, first proposed by Forni in 1966, remain one of the fundamental ap-proaches in error-correcting coding theory. Over the past fifteen years, this field has under-gone significant changes driven by the development of new applications: distributed data storage systems, quantum computing, 5G wireless standards, and the Internet of Things. Concatenated coding is a powerful method for constructing long codes with good error-correcting properties by sequentially applying two or more simpler codes. The basic idea is that an outer code encodes the original data, and then each code word symbol of the outer code is further encoded by an inner code. This hierarchical approach, in some designs, achieves performance close to the theoretical Shannon limit while maintaining acceptable computational complexity.

This article systematizes the main coding methods in concatenated design models, ana-lyzes modern decoding algorithms, and discusses practical implementations of concatenat-ed codes in various fields. Particular attention is paid to a comparative analysis of concate-nated codes with other families of error-correcting codes, including turbo codes, LDPC codes, polar codes, and others.