Existence and construction of block interleavers

For an (N/sub 1/, N/sub 2/) interleaver of block size L, we prove that L/spl ges/N/sub 1/N/sub 2/. Conversely, we prove that whenever L/spl ges/N/sub 1/N/sub 2/, an (N/sub 1/, N/sub 2/) interleaver of block size L exists. Explicit algebraic constructions are provided. It is also proven that rectangular interleavers are not optimal.