k-bit grouping moment balancing templates for spectral shaping codes

We investigate moment balancing templates for spectral shaping codes, e.g., dc-free codes, high-order spectral-null codes and spectral nulls code. A new approach by adding k grouped bits at determinate indices of the code word is found to balance the moment of the code word. Moment balanced code words preserve the spectral-null properties and can guarantee to correct one insertion or deletion error. The redundancy, which is a constant factor greater than that of the universal template for uncoded sequence, can be kept small. The new approach also involves the application of the optimized moment balancing template and the non-binary enumeration of balancing moment values.