Redundant data transmission and nonlinear codes

Abstract

In their paper the authors investigate redundant data transmission protected by arbitrary (not necessarily linear) codes. They generalize results known so far for linear codes, in particular for cyclic redundancy checks (CRCs). They use the concept of the Generalized Erasure Channel (GEC) to determine the probability of undetected error for some binary symmetric and non-symmetric channels protected by appropriate encoding procedures. In detail, they investigate communication via different Binary Symmetric Channels (BSCs), Generalized Erasure Channels and Symmetrized Binary Non Symmetric Channels (BNSCs). Simple upper bounds are given, relating the new formulas to that one of the BSC, and the channel capacities are calculated. Finally the results in connection with an inequality for proper codes are applied to multi channel coloured transmission via laser beams propagating through Polymer Optical Fiber (POF).