Simple computation method of soft value, that is used in iterative soft decision decoding, is proposed. For the product code composed of BCH(63, 57) and that composed of BCH(63, 45), computation time with the proposed method is 1/15-1/6 as that with a method based on the Chase algorithm. Bit error rate (BER) performance with the proposed method is within 0.8 [dB] inferior to that with the method based on the Chase algorithm at BER=10-5.

In high-speed digital land mobile radio communication, communication quality is degraded by frequency selective fading that has intersymbol interference. It causes increase of bit error rate (BER). To decrease BER in the channel, this paper proposes a system with combined multilevel coding and adaptive equalization using interleaving. By using interleaving, the proposed system obtains time diversity effect. Furthermore the system realizes a type of decision feedback adaptive equalizer where signal after multilevel decoder is fed back. These features of the system cause decrease of BER. The proposed system is compared with a similar system with a feedback signal before multilevel decoder. The average bit error rate of the proposed system is less than 1/100 with that of the compared system at average Eb/No = 22 [dB] in a case of fading channel with one intersymbol interference.

This paper proposes methods to improve soft-input and soft-output decoding performance of BCH codes by sum-product algorithm (SPA). A method to remove cycles of length four (RmFC) in the Tanner graph has been proposed. However, the RmFC can not realize good decoding performance for BCH codes which have more than one error correcting capability. To overcome this problem, this paper proposes two methods. One is to use a parity check matrix of the echelon canonical form as the starting check matrix of RmFC. The other is to use a parity check matrix that is concatenation (ConC) of multiple parity check matrices. For BCH(31,11,11) code, SPA with ConC realizes Eb/No 3.7 dB better at bit error rate 10-5 than the original SPA, and 3.1 dB better than the SPA with only RmFC.