Permutation decoding of systematic codes

A symmetry of a systematic code is a permutation of bit positions in each code word (the same permutation is applied to all code words) which preserves the code as a whole. Permutation decoding makes use of these symmetries to build up a decoding algorithm for the code. It is difficult to find an appropriate set of symmetries for a code picked at random. For cyclic codes the problem is somewhat easier, and for some special cyclic codes it is solved completely in this paper. For these codes, at least, it is evident that permutation decoding is easy to implement and inexpensive compared with other decoding schemes. Permutation decoding as a n eans of error control is evaluated for the binary symmetric channel and for the switched telephone network as represented by experimental data. It is found to be extremely effective on the binary symmetric channel and of very doubtful value on the present telephone network.