We study a new synchronization algorithm based on low-density parity check codes. The algorithm was developed for scenarios with redundant information in 2010, [1]. We describe a revised version of the algorithm and, for the first time, we discuss the fundamentals about the coding and decoding theory. The results of this analysis define the scope and restrictions of the algorithm. We show that the algorithm is capable of recovering synchronization even in scenarios without redundant information. The algorithm has the characteristic of using not only cyclically permutable codes like the related proposals. Nevertheless special attention must be paid to short codes. Finally, an accurate approximation of the bound is introduced by using maximum likelihood decoding.

A new method for decoding low-density lattice codes is given, wherein the belief-propagation decoder messages are single Gaussian functions. Since the message can be represented by two numbers, a mean and a variance, the complexity of this decoder is lower than previous decoders, which either quantized the mixture, or used a mixture of Gaussians. The computational complexity at the check node is also lower. The performance of various code designs, under single-Gaussian decoding, is evaluated by noise thresholds. In particular, the proposed decoding algorithm has noise threshold within 0.1 dB of the quantized-message decoder, which is considerably more complex.

For decoding low-density parity-check (LDPC) codes on discrete memoryless channels, a method to quantize messages and to find message-passing decoding functions for the variable and check nodes is developed. These are used to obtain noise thresholds by density evolution. The message-passing decoding alphabet is restricted to be discrete with a fixed maximum alphabet size. Discrete quantization is required to obtain this fixed alphabet size; a greedy algorithm which uses the mutual information between the code bit and message is presented. It is argued that using this message-passing decoding framework is more efficient for approaching channel capacity than simply quantizing the belief-propagation algorithm. This method is evaluated using regular LDPC codes on the binary symmetric channel. Using a maximum alphabet size of 16 (4 bits), noise thresholds close to those of belief propagation are obtained.

Vector quantization of the BCJR and Viterbi algorithms' state metrics for detection of finite-state channels is considered. An estimate is given for the gain associated with vector quantization, over conventional implementations. This is expressed using the volume of the recurrent region, and the maximum state metric difference, which are both intrinsic properties of the channel detector. One application of this gain is the complexity evaluation of a previously proposed lookup-table BCJR implementation. The BCJR algorithm is of interest in turbo equalization used for communication over intersymbol-interference and finite-state Markov channels

For the class of rate k/(k+1) convolutional codes, Yamada et al. (1983) proposed an efficient maximum-likelihood decoding algorithm called the YHM algorithm. In order to reduce the complexity of the YHM algorithm, this paper presents two techniques for simplifying the trellis diagram used in the YHM algorithm. We further observe that the proposed techniques effectively reduce the complexity of the YHM algorithm for two classes /spl Xi/ and /spl Xi//sub f/ (which is a subclass of /spl Xi/) of rate k/(k+1) convolutional codes. The construction of codes in these classes is also discussed. It is shown that /spl Xi/ codes with d/sub free/=3,4 can be obtained by simple construction. A code search algorithm for /spl Xi/ codes with d/sub free//spl ges/5 is also introduced. Computer searches are performed to construct good /spl Xi/ and /spl Xi//sub f/ codes. For specified decoding complexities, a number of these new codes give better error performance than previously reported codes.

The authors give a tabulation of the numbers of codewords in new binary codes with the asymmetric/unidirectional error-correcting capabilities of 3, 4, 5, 6 for lengths 14, 15, . . . , 23. The new codes have greater sizes than the known codes for 14>