Characteristics of Coding and Modulation Systems from the Standpoint of Concatenated Codes

The article considers several modulation and coding systems (MCS) for a memoryless Gaussian channel. The asymptotic dependences (with respect to dimension) of the code transmission rate on the Euclidean distance normalized with respect to the average energy and on the signal-to-noise ratio are investigated. For many systems, an explicit expression is obtained for the exponent of incorrect decoding, and “rate/energy” exchange relations for specific lengths and error probabilities. Some considerations regarding the complexity of realization of decoders in the systems under consideration are given.