In this paper we are concerned with the provision of broadband wireless access to mobile users via high altitude platform (HAP) system, which is characterized by a challenging propagation environment in the allocated frequency bands, requiring the development of efficient radio interface. The latter has to offer the ability to adapt to rapid channel variations, for which the low propagation delay is the essential enabling characteristic. Assuming the forward link based on the DVB-S2 standard, adapted for the operation over HAPs, we focus in this paper on the design and performance evaluation of an adaptive coding and modulation (ACM) scheme, which is used to maximize the link reliability and/or throughput. The scheme considers a subset of transmission modes (MODCODs) defined in the standard and exploits two parameters in making the MODCOD switching decisions, the estimated signal-to-noise ratio (SNR) and the estimated bit error rate (BER), which take effect on different time scales. For the SNR estimation SNORE algorithm was adopted, while for the BER estimation we propose a new algorithm exploiting the properties of LDPC decoder and compare its performance to the traditional approach based on cyclic-redundancy check (CRC) computation. The performance evaluation results are provided in terms of suitable internal parameters of the algorithm and as the trade-off analysis between BER and spectral efficiency.