Reed-Solomon (RS) codes have been widely adopted in many modern communication systems. This paper describes a new method for error detection in the syndrome calculator block of RS decoders. The main feature of this method is to prove that it is possible to compute only a few syndrome coefficients — less than half — to detect whether the codeword is correct. The theoretical estimate of the probability that the new algorithm failed is shown to depend on the number of syndrome coefficients computed. The algorithm is tested using the RS(204,188) code with the first four coefficients. With a bit error rate of 1×10^-4, this method reduces the power consumption by 6% compared to the basic RS(204,188) decoder. The error detection algorithm for the syndrome calculator block does not require modification of the basic hardware implementation of the syndrome coefficients computation. The algorithm significantly reduces the computation complexity of the syndrome calculator block, thus lowering the power needed.

This paper presents a theoretical comparison of a single carrier system and a multi-carrier system through an analysis of the achievable rate under frequency selective fading with channel state information at the receiver. A scheme was designed to compare the achievable rates of a single carrier system and an Orthogonal Frequency Division Multiplexing (OFDM) system. A thorough theoretical analysis of the two-path channel was conducted, and simulations were also used to analyze practical stochastic channels. Analysis and simulation results show that the achievable rates of the two approaches are comparable when the channel is flat fading. However, when the channel is frequency selective fading, the single carrier system outperforms the OFDM system. The achievable rate of the OFDM system is about 10% lower than that of the single carrier system at higher SNRs.

A transform method was used to model a discrete time multi-tap direct sampling mixer. The method transforms the mixed filtering and down-sampling stages to separate cascade filtering and sampling stages to determine the unfolded frequency response which shows the anti-aliasing ability of the mixer. The transformation can also be applied to other mixed signal and multi-rate receiver systems to analyze their unfolded frequency responses. The transformed system architecture was used to calculate the unfolded frequency response of the multi-tap direct sampling mixer and compared with the mixer model without noise in the advanced design system 2005A environment to further evaluate the frequency response. The simulations show that the –3 dB bandwidth is 3.0 MHz and the voltage gain is attenuated by 1.5 dB within a 1-MHz baseband bandwidth.

Many communication systems use the cyclic redundancy code (CRC) technique for protecting key data fields from transmission errors by enabling both single-bit error correction and multi-bit error detection. The look-up table design is very important for the error-correction implementation. This paper presents a CRC look-up table optimization method for single-bit error correction. The optimization method minimizes the address length of the pre-designed look-up table while satisfying certain restrictions. The circuit implementation is also presented to show the feasibility of the method in the application specific integrated circuit design. An application of the optimization method in the generic framing procedure protocol is implemented using field programmable gate arrays. The result shows that the memory address length has been minimized, while keeping a very simple circuit implementation.