This paper presents an improved version of multi-stage threshold decoding with a difference register (MTD-DR) for self-orthogonal convolutional codes (SOCCs). An approximate lower bound on the bit error rate (BER) with the maximum likelihood (ML) decoding is also given. MTD-DR is shown to achieve an approximate lower bound of ML decoding performance at the higher Eb/N0. The code with larger minimum Hamming distance reduces the BER in error floor, but the BER in waterfall shifts to the higher Eb/N0. This paper gives a decoding scheme that improves the BER in both directions, waterfall and error floor. In the waterfall region, a 2-step decoding (2SD) improves the coding gain of 0.40 dB for shorter codes (code length 4200) and of 0.55 dB for longer codes (code length 80000) compared to the conventional MTD-DR. The 2-step decoding that serially concatenates the parity check (PC) decoding improves the BER in the error floor region. This paper gives an effective use of PC decoding, that further makes the BER 1/8 times compared to the ordinary use of PC decoding in the error floor region. Therefore, the 2SD with effective use of parity check decoding improves the BER in the waterfall and the error floor regions simultaneously.

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 4.7 dB and 6.5 dB 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 5.3 dB and 7.1 dB 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.