Modified Min-Sum Algorithm for LDPC Decoders in UWB Communications

Several variations of the sum-product algorithm (SPA) have been proposed for the decoding of the low density parity check (LDPC) codes. Among these, the log domain belief propagation algorithm (log-BPA or simply BPA) is widely adopted in most of the proposed LDPC decoder architectures. The check node unit (CNU), which computes the check-to-variable (C2V) messages, is computationally the most complex part of the decoder employing the belief propagation algorithm. The BPA can be approximated using a sub-optimal min-sum algorithm; however, it suffers from the performance loss. The min-sum algorithm can be easily implemented with comparators and multiplexers, thereby reducing the area and the power consumption of the decoder, critical for the high data-rate applications such as ultra wide-band (UWB) communications system. Due to the performance degradation, the decoder needs to perform more decoding iterations to reach the desired performance. This, in turn, increases the decoder latency and reduces the decoder throughput. One approach to improve the decoder throughput is to layout more parallel CNUs inside a decoder, but this offsets the advantage of the min-sum implementation. On the other hand, the performance of the min-sum algorithm can be improved by scaling the node-to-check messages and it is possible to find optimal scaling factor for a given channel. In this paper, we propose an improvement to the min-sum algorithm based on the analysis of the error term in the min-sum algorithm. The proposed algorithm achieves the performance similar to the scaled min-sum (SMS) approach with optimal scaling, in the additive white Gaussian noise (AWGN) channel. We also show min-sum utilized with different fading channels and LDPC codes without any further adjustments. Thus, the proposed MMS algorithm provides flexibility in real applications, which need to support multiple code rates, block sizes and have to operate in unknown fading channels. The performance of the proposed a- - lgorithm is evaluated for the MB-OFDM UWB systems with short distance indoor channel models. To meet the speed requirement of the of the UWB systems, a bit-level pipelined comparator is developed, which significantly reduces the latency of the critical path in the comparison circuit