SUMMARYIn this paper an algebraic trellis vector quantization (ATVQ) that introduces algebraic codebooks into trellis coded vector quantization (TCVQ) structure is presented. Low encoding complexity and minimum memory storage requirements are achieved using the proposed approach. It exploits advantages of both the TCVQ and the algebraic codebooks to know the delayed decision, the codebook widening, the low computational complexity and the no storage of codebook. This novel vector quantization scheme is used to encode the wideband speech line spectral frequencies (LSF) parameters. Experimental results on wideband speech have shown that ATVQ yields the same performance as the traditional split vector quantization (SVQ) and the TCVQ in terms of spectral distortion (SD). It can achieve a transparent quality at 47 bits/frame with a considerable reduction of memory storage and computation complexity when compared to SVQ and TCVQ.
Since their rediscovery in the early 1990s, low-density parity-check (LDPC) codes have become the most popular error-correcting codes owing to their excellent performance. An LDPC code is a linear block code that has a sparse parity-check matrix. Cycles in this matrix, particularly short cycles, degrade the performance of such a code. Hence, several methods for counting short cycles in LDPC codes have been proposed, such as Fan?s method to detect 4-cycles, 6- cycles, 8-cycles, and 10-cycles. Unfortunately, this method fails to count all 6- cycles, i.e., ignores numerous 6-cycles, in some given parity-check matrices. In this paper, an improvement of this algorithm is presented that detects all 6-cycles in LDPC codes, as well as in general bipartite graphs. Simulations confirm that the improved method offers the exact number of 6-cycles, and it succeeds in detecting those ignored by Fan?s method.
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