Multi-Stage Threshold Decoding for Self-Orthogonal Convolutional Codes

This paper describes a least complex, high speed decoding method named multi-stage threshold decoding (MTD-DR). Each stage of MTD-DR is formed by the traditional threshold decoder with a special shift register, called difference register (DR). After flipping each information bit, DR helps to shorten the Hamming and the Euclidian distance between a received word and the decoded codeword for hard and soft decoding, respectively. However, the MTD-DR with self-orthogonal convolutional codes (SOCCs), type 1 in this paper, makes an unavoidable error group, which depends on the tap connection patterns in the encoder, and limits the error performance. This paper introduces a class of SOCCs type 2 which can breakdown that error group, as a result, MTD-DR gives better error performance. For a shorter code (code length =4200), hard and soft decoding MTD-DR achieves 4.7dB and 6.5dB coding gain over the additive white Gaussian noise (AWGN) channel at the bit error rate (BER) 10-5, respectively. In addition, hard and soft decoding MTD-DR for a longer code (code length =80000) give 5.3dB and 7.1dB coding gain under the same condition, respectively. The hard and the soft decoding MTD-DR experiences error flooring at high Eb/N0 region. For improving overall error performance of MTD-DR, this paper proposes parity check codes concatenation with soft decoding MTD-DR as well.