An adaptive interpolated FIR (IFIR) echo canceller was recently proposed for xDSL applications. This canceller consists of an FIR filter, an IFIR filter, and a tap-weight overlapping and nulling scheme. The FIR filter is used to cancel the short and rapidly changing head echo while the IFIR filter is used to cancel the long and slowly decaying tail echo. This echo canceller, which inherits the stable characteristics of the conventional FIR filter, requires low computational complexity. It is well known that the interpolation filter for an IFIR filter has great influence on the interpolated result. In this paper, a least-squares method is proposed to obtain optimal interpolation filters such that the performance of the IFIR echo canceller can be further improved. Simulations with a wide variety of loop topologies show that the optimal IFIR echo canceller can effectively cancel the echo up to 73.0 dB (for an SHDSL system). About 57% complexity reduction can be achieved compared to a conventional FIR filter.

A stopping criterion is an indispensable function to reduce unnecessary power consumption and decoding delay in turbo decoding. Until now, a common design philosophy in previous works has involved using the entire block of information from the MAP decoder and its input/output information to calculate the stopping index. It is an intuitive method but suffers from heavy memory requirements and high calculation complexity. In this paper, a low-complexity stopping criterion is proposed that avoids the aforementioned disadvantages. A general abstraction model is utilized to analyze the design bottleneck of stopping criteria. Instead of using an entire block of information, a compact representation derived from the internal information of the MAP decoder at a single time instant is used as a low-complexity stopping index. Theoretical explanation is provided to justify the feasibility of the proposed criterion. Simulation results show that the proposed criterion can reduce the complexity of stopping criterion dramatically while continuing to achieve the same level of performance as previous works.