DC-free binary convolutional coding

A novel DC-free binary convolutional coding scheme is presented. The proposed scheme achieves the DC-free and error correcting capability simultaneously. The scheme has a simple cascaded structure of the RDS(running digital sum) control encoder and the conventional convolutional encoder. A given sequence becomes DC-free if and only if the absolute RDS value of the sequence is bounded by a constant for any time instant. The RDS control encoder generates a sequence which gives the convolutional coded sequence with a bounded RDS value. The structure allows us to exploit efficient soft decision decoding which attains additional coding gains compared with hard decision decoding over an additive white Gaussian noise(AWGN) channel. Bounds on the RDS value are explicitly established for the proposed scheme. By using the bounds, we have performed computer searches for finding good RDS control encoders. The proposed scheme provides wide varieties of reasonable tradeoffs between the coding gain, the RDS constraint, and decoding complexity. For example, a 64-state DC-free coding scheme with the overall rate 6/16 and the minimum free distance 10 has been obtained. This scheme satisfies a bounded RDS constraint(from −18 to +18) and it yields a considerably high asymptotic coding gain(over an AWGN channel) of 5.7 dB. Keywords— DC-free coding, Convolutional code, Additive encoding.