Concatenated Constrained Coding: A New Approach to Efficient Constant-Weight Codes

The design of low-complexity and efficient constrained codes has been a major research item for many years. This paper reports on a versatile method named concatenated constrained codes for designing efficient fixed-length constrained codes with small complexity. A concatenated constrained code comprises two (or more) cooperating constrained codes of low complexity enabling long constrained codes that are not practically feasible with prior art methods. We apply the concatenated coding approach to two case studies, namely the design of constant-weight and low-weight codes. In a binary constant-weight code, each codeword has the same number, w, of 1's, where w is called the weight of a codeword. We specifically focus on the trading between coder complexity and redundancy.