This paper introduces a hybrid aggregated packet (or fragment) procedure with selective retransmission, based on low power integer codes. The protection at aggregated level is performed using two checksums. In a case of detected error, intermediary results of coding procedure — two auxiliary checksums per packet — are used as incremental redundancy. Auxiliary syndromes at the receiver then determine further action — either error correction at packet level and correction verification at the aggregated level, or selective retransmission. Energy saving is achieved by the low power coding procedure. The performance analyses include retransmission, redundancy, delay and residual packet error rate.

In this paper we present a statistical analysis of the search for a set of predefined sequences in non-equiprobable data streams, both random and framed, and derive a number of corresponding statistical parameters. Most importantly, we derive the probability of occurrence of some sequence from the set at any given position, from which all other statistical quantities of interest can be obtained. The presented analysis is based on descriptors called cross-bifices, which express similarities among sequences in the set. Based on the obtained results, we examine the problem of frame synchronization in synchronous transmission and derive parameters that could be used for the evaluation of the properties of frame-synchronization sequences. We introduce a survival probability of the search in a frame and a list-miss probability for the list synchronizer, which give exact bounds on the probability of correct frame synchronization when hard-correlation is used as a sequence detection metric.

In this paper, we propose a simple and efficient two-stage list synchronizer for frame synchronization of low-density parity-check (LDPC) coded data transmitted over the additive white Gaussian noise (AWGN) channel. The proposed method uses both synchronization sequence and code constraints for frame synchronization. In the first stage, a list of the most likely frame starting positions is made using synchro-sequence, while in the second stage the code constraints are used to select the most likely position from the list. We analytically relate the synchro- sequence length, the frame length and the list length in order to keep the synchronization frame error rate (FER) lower than the error-correcting FER of the LDPC code, and we investigate the trade-off between the sequence length and the list length. We demonstrate that the proposed scheme outperforms both the frame synchronization methods based on synchro-sequence only and the recently proposed blind synchronization methods based on LDPC code constraints, the former in terms of the synchronization FER for the same sequence lengths and the latter in terms of complexity.

An analytical approach to a search process is a mathematical prerequisite for digital synchronization acquisition analysis and optimization. A search is performed for an arbitrary set of sequences within random but not equiprobable L-ary data. This paper derives in detail an expression for probability distribution function, from which other statistical parameters - expected value and variance - can be obtained. The probabilistic nature of (cross-) bifix indicators is shown and application examples are outlined, ranging beyond the usual telecommunication field

An analytical approach to a search process for a set of M fixed sequences in random data covers the problems of a search for the sequences with errors, as well as of a search for the distributed sequences. It is of greater practical interest than the formerly analysed case of search for a single sequence. This paper derives statistical parameters (probability distribution function, expected value, variance) of this process, introducing a new term "cross-bifix". The derived formulae are applied to the case of search for distributed sequences with errors.

A theoretical analysis of the search process for a fixed sequence in a frame is performed. An exact formula for the maximum reframe time (time necessary to achieve the synchronization) is derived. The analysis is based upon the bifix structure of the inserted synchronization signal. The results are applied to STM-1 signals.

The frame-alignment monitoring schemes for STM-1 frame are analyzed, considering the boundaries recommended by ITU-T. The analysis, based upon the mean time evaluations and probability density function, includes synchronization procedures, synchronization pattern lengths, allowed number of bit errors per synchronization pattern and amount of redundancy that should be tested.

It is shown that the optimal frame synchronization markers for channels with memory, considering the widely used postdetection maintenance and the minimum average rule, are not the ones optimized for an AWGN channel. A method for obtaining the optimal marker using the channel state diagram and the corresponding trellis is presented.>