A soft decision decoding of product BCH and Reed-Müller codes

Orthogonal Frequency Division Multiplexing (OFDM) is a very attractive modulation scheme for data transmission in multipath channels. But the high Peak-to-MEan Power Ratio (PMEPR) of the modulated signal is a major drawback and makes the use of some circuits very tricky : for instance, power amplifiers at the emission side could have nonlinear characteristics and a high PMEPR could exhibits intermodulation noise and distortions. A very recent theory based on Reed-Müller codes controls the PMEPR and exploits the correction capacity of the code to correct error propagation : the PMEPR is reduced to a level of 3 dB and the distance of the code is the quarter of the codeword (in this specific application of Reed-Müller and OFDM). But the correction capacity is limited and have to be balanced with the code rate. This paper first presents a product coding scheme based on BCH and Reed-Müller codes to improve error correction and to keep the PMEPR propriety of the modulated signal. Next, we present a soft decision decoding based on Chase’s algorithm associated to Reed-Müller codes. Then, we analyse the BER performances of both hard and soft decoding associated to the product coding scheme modelling AWGN and nonlinear TWTA power amplifiers. With this soft decision decoding, we obtain a 1.5 dB coding gain compared to hard decoding when using product codes and about 5 dB coding gain compared to an uncoded system, at BER=10. Balanced with the global code rate, BCH(255,231,7) with Reed-Müller codes have higher coding gain compared to other product codes. Nonlinear distortions degrade BER performances and the coding gain is still about 2 dB at BER=10. The applications concerns high data rate and broadband transmissions using OFDM where power efficiency is a major challenge. Key-Words OFDM, peak-factor, coding, Reed-Müller codes, soft decoding, nonlinear amplifiers.