Improved Coding-Theoretic and Subspace-Based Decoding Algorithms for a Wider Class of DCT and DST Codes

The decoding of a class of discrete cosine transform (DCT) and discrete sine transform (DST) codes that are maximum distance separable codes (MDS) is considered in this paper. These class of codes are considered for error correction over real fields. All the existing algebraic decoding algorithms are capable of decoding only a subclass of these codes [which can be characterized into the Bose-Chaudhuri-Hocquenghem (BCH) form], and fails to decode the remaining even though they are MDS. In this paper, we propose a new generic algorithm along the lines of coding theoretic and subspace methods to decode the entire class of MDS DCT and DST codes. The proposed subspace approaches are similar to popular ESPRIT and MUSIC algorithms. The proposed algorithms also perform significantly better than the existing algorithms on the BCH-like subclass. A perturbation analysis is also presented to study the effect of various parameters on the error localization due to the quantization noise. Simulation results are presented to demonstrate the capability of proposed algorithms to decode the entire class and to perform significantly better on the BCH-like subclass than the existing algorithm under the influence of quantization noise.