Codebook and marker sequence design for synchronization-correcting codes

We propose a construction based on synchronization and error-correcting block codes and a matched marker sequence. The block codes can correct insertion, deletion and substitution errors within each codeword. The marker sequence allows the decoder to maintain synchronization at codeword boundaries even at high error rates. An upper bound is given for the performance of these codes over a channel with random substitutions and synchronization errors. It is shown that the performance is largely dependent on the code's minimum Levenshtein distance. The performance of these codes is verified by simulation and compared to published results. In concatenation with a non-binary outer code we obtain a significant improvement in frame error rate at similar overall code rates

Quickest Sequence Phase Detection

A phase detection sequence is a length-$n$ cyclic sequence, such that the location of any length-$k$ contiguous subsequence can be determined from a noisy observation of that subsequence. In this paper, we derive bounds on the minimal possible $k$ in the limit of $n\to\infty$, and describe some sequence constructions. We further consider multiple phase detection sequences, where the location of any length-$k$ contiguous subsequence of each sequence can be determined simultaneously from a noisy mixture of those subsequences. We study the optimal trade-offs between the lengths of the sequences, and describe some sequence constructions. We compare these phase detection problems to their natural channel coding counterparts, and show a strict separation between the fundamental limits in the multiple sequence case. Both adversarial and probabilistic noise models are addressed.Comment: To appear in the IEEE Transactions on Information Theor

Combined permutation codes for synchronization

Abstract: A combined code is a code that combines two or more characteristics of other codes. A construction is presented in this paper of permutation codes that are self-synchronizing and able to correct a number of deletion errors per codeword, thus a combined permutation code. Synchronization errors, modelled as deletion(s) and/or insertion(s) of bits or symbols, can be catastrophic if not detected and corrected. Some classes of codes have been proposed that are synchronizable, i.e. they can be used to regain synchronization although the error leading to the loss of synchronization is not corrected. Typically, different classes of codes are needed to correct deletion and/or insertion errors after codeword boundaries have been detected. The codebooks presented in this paper consist of codewords divided into segments. By imposing restrictions on the segments, the codewords are synchronizable. One deletion error can be detected and corrected per segment

Insertion/deletion error correction using path pruned convolutional codes and extended prefix codes

Synchronization error correction has been under discussion since the early development of coding theory. In this research report a novel coding system based on the previous done work on path-pruned convolutional codes and extended prefix synchronization codes is presented. This new coding scheme is capable of correcting insertion, deletion and synchronization errors. A codebook has been constructed that contains synchronization patterns made up of a constraint part (maker sequence) and an unconstraint part based on the concept of extended prefix codes. One of these synchronization error patterns are padded in front of each frame. This process is done by mapping information bit to a corresponding bit sequence using a mapping table. The mapping table is constructed by using path-pruning process. An original rate convolutional code is first punctured using a desired puncturing matrix to make enough paths available at each state of the trellis. The desired paths are then pruned and matches to the extended prefix codebook constructed. The path pruning process consists of a feedback mapper attached in front of the original rate parent convolutional encoder with puncturing. The state of the convolutional encoder is fed back to the mapper which maps first information bit of the frame into a multi-bit sequence that is fed into the convolutional encoder with puncturing and thus produces one of the synchronization patterns contained within the codebook constructed. The remaining bits of the frame are encoded normally using convolutional encoding with a puncturing process only. This process is repeated periodically depending on the condition of the channel. Simulations were performed to evaluate the ability of new system to resynchronize and correct insertion/deletion and synchronization errors at the receiver, from which favorable results were obtained. Simulations were performed with different synchronization pattern (extended prefix code word) lengths, different constraint lengths of the parent encoder and using Reed-Solomon codes as outer code in concatenation with new coding system. A complete concatenated coding system is thus demonstrated and studied that resynchronizes and corrects insertion, deletion and substitution errors

Codes for Synchronization in Channels and Sources with Edits

Edit channels are a class of communication channels where the output of the channel is an edited version of the input. The edits are considered to be deletions and insertions. DNA-based data storage system is one of the motivations for this model. This thesis studies various problems related to edit channel and also edit synchronization problem. Varshamov-Tenengolts (VT) codes are first introduced. These codes can correct a single deletion or insertion and have a linear-time decoder. The problem of efficient encoding of the non-binary version of VT codes is addressed, where a simple linear-time encoding method to systematically map binary message sequences onto VT codewords is proposed. Another model that is studied is segmented edit channels, where we have the additional assumption that the channel input sequence is implicitly divided into segments such that at most one edit can occur within a segment. A code construction is proposed for this model based on subsets of VT codes chosen with pre-determined prefxes and/or sufxes. Also an upper bound is derived on the rate of any zero-error code for the segmented edit channel in terms of the segment length. This upper bound shows that the rate scaling of the proposed codes as the segment length increases is the same as that of the maximal code. Edit synchronization is another problem studied in this thesis. In this model, there are two remote nodes (encoder and decoder), each having a binary sequence. The sequence X, available at the encoder, is the updated sequence and differs from Y (available at the decoder) by a small number of edits. The goal is to construct a message M, to be sent via a one-way error-free link, such that the decoder can reconstruct X using M and Y. A coding scheme is devised for this one-way synchronization model. The scheme is based on multiple layers of VT codes combined with off-the-shelf linear error-correcting codes and uses a list decoder. Motivated by the sequence reconstruction problem from traces in DNA-based storage, the problem of designing codes for the deletion channel when multiple observations (or traces) are available to the decoder is considered. A simple binary and non-binary code is proposed that splits the codeword into blocks and employs a VT code in each block. The availability of multiple traces helps the decoder to identify deletion-free copies of a block, and to avoid mis-synchronization while decoding. The encoding complexity of the proposed scheme is linear in the codeword length; the decoding complexity is linear in the codeword length and quadratic in the number of deletions and the number of traces. The list decoding technique for the proposed code is also considered

Synchronization with permutation codes and Reed-Solomon codes

D.Ing. (Electrical And Electronic Engineering)We address the issue of synchronization, using sync-words (or markers), for encoded data. We focus on data that is encoded using permutation codes or Reed-Solomon codes. For each type of code (permutation code and Reed-Solomon code) we give a synchronization procedure or algorithm such that synchronization is improved compared to when the procedure is not employed. The gure of merit for judging the performance is probability of synchronization (acquisition). The word acquisition is used to indicate that a sync-word is acquired or found in the right place in a frame. A new synchronization procedure for permutation codes is presented. This procedure is about nding sync-words that can be used speci cally with permutation codes, such that acceptable synchronization performance is possible even under channels with frequency selective fading/jamming, such as the power line communication channel. Our new procedure is tested with permutation codes known as distance-preserving mappings (DPMs). DPMs were chosen because they have de ned encoding and decoding procedures. Another new procedure for avoiding symbols in Reed-Solomon codes is presented. We call the procedure symbol avoidance. The symbol avoidance procedure is then used to improve the synchronization performance of Reed-Solomon codes, where known binary sync-words are used for synchronization. We give performance comparison results, in terms of probability of synchronization, where we compare Reed-Solomon with and without symbol avoidance applied