Simplified Composite Coding for Index Coding

Simplification methods are introduced for composite coding, which is an existing layered random coding technique for the index coding problem. As the problem size grows, the original number of composite indices grows exponentially and the number of possible decoding configurations (decoding sets) grows super exponentially, leading to considerably high computational complexity. The proposed simplifications address both issues and do not affect the performance (tightness) of the coding scheme. Removing composite indices is achieved by pairwise comparison of any two indices and removing one if its corresponding rate can be transferred without loss to the other in the expressions of the achievable rate region. Decoding configurations are reduced by establishing a baseline or natural decoding configuration, where no smaller decoding configuration can provide a strictly larger rate region. A heuristic method is also proposed for reducing the number of composite indices even further, but possibly with some performance loss. Numerical results demonstrate good performance with substantial reduction in complexity. To achieve the capacity region for all 9608 non-isomorphic index coding problems with n = 5, a single natural decoding configuration per problem and less than 3 out of 2
⁵
-1=31 composite indices are sufficient, on average. In only 31 problems, 7 to at most 10 composite indices are used.