Finite Precision Analysis for Space-Time Decoding

Low complexity optimal (or nearly optimal) decoders for space-time codes have recently been under intensive investigation. For example, recent works by Sirianunpiboon and others show that the Silver code and the Golden code can be decoded optimally (or nearly optimally) with quadratic decoding complexity. Fast decodability makes them very attractive in practice. In implementing these decoders, floating-point to fixed-point conversion (FFC) needs to be carefully undertaken to minimize hardware cost while retaining decoding performance. The process of quantization for fixed-point representations is often ignored by research community and lacks investigation, and so FFC is often conducted heuristically based on simulations. This paper studies the effects of quantization to space-time coded systems from an information theoretic perspective. It shows the analytical relationship between quantization error and decoding performance deterioration. This paper also proposes a general finite precision implementation methodology including two FFC criteria for space-time coded systems within an integer optimization framework. As a particular example, this paper examines the finite precision implementation of the quadratic optimal decoding algorithm of the Silver code. However, our methodology and techniques can be applied to general space-time codes.