A Building Block Approach for Designing Multilevel Coding Schemes

A novel building block (BB) design approach is presented for systematically constructing multilevel codes (MLCs) under the balanced distances rule (BDR). In contrast to the traditional method of starting from an overall signal constellation and then using a mapping policy, the BB approach starts by designing a BB constellation for the first level of the MLC and then uses two copies of this BB to construct a second level constellation. This process is continued to the highest level by constructing the next level constellation using multiple copies of the current level constellation as a BB. Compared to the traditional method of construction of MLCs according to the BDR, the BB approach provides additional flexibility in selecting component codes and is able to exactly balance the distances of all levels. Compared with MLCs constructed using the traditional BDR approach, MLCs constructed using the BB approach have the same decoding complexity and perform better in the error floor region, which is typically the operating region for MLCs constructed with convolutional component codes.