Andreas Lenz

Technical University of Munich | TUM · Institute for Communications Engineering

Sequential decoding, commonly applied to substitution channels, is a sub-optimal alternative to Viterbi decoding with significantly reduced memory costs. This work describes and analyzes a sequential decoder for convolutional codes over channels prone to insertion, deletion, and substitution errors. Our decoder expands the code trellis by a new cha...

In conventional DNA synthesis machines, usually many strands are synthesized in parallel by iterating through a supersequence s and adding in each cycle the next nucleotide to a programmable subset of the strands. The length of s determines the number of the cycles, hence the time and the cost of the synthesis process. Recently, in order to reduce...

In this paper we study function-correcting codes , a new class of codes designed to protect the function evaluation of a message against errors. We show that FCCs are equivalent to irregular-distance codes , i.e., codes that obey some given distance requirement between each pair of codewords. Using these connections, we study irregular-distance...

We consider error-correcting coding for DNA-based storage. We model the DNA storage channel as a multi-draw IDS channel where the input data is chunked into $M$ short DNA strands, which are copied a random number of times, and the channel outputs a random selection of $N$ noisy DNA strands. The retrieved DNA strands are prone to insertion, deletion...

In this work, a sequential decoder for convolutional codes over channels that are vulnerable to insertion, deletion, and substitution errors, is described and analyzed. The decoder expands the code trellis by introducing a new channel state variable, called drift state, as proposed by Davey-MacKay. A suitable decoding metric on that trellis for seq...

Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a concatenated coding scheme with an outer nonbinary low-density parity-check code or a polar code and either a...

Motivated by recent advances in DNA-based data storage, we study a communication system, where information is conveyed over many sequences in parallel. In this system, the receiver cannot control the access to these sequences and can only draw from these sequences, unaware which sequence has been drawn. Further, the drawn sequences are susceptible...

Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a concatenated coding scheme with an outer nonbinary low-density parity-check code or a polar code and either a...

A new family of codes, called clustering-correcting codes , is presented in this paper. This family of codes is motivated by the special structure of the data that is stored in DNA-based storage systems. The data stored in these systems has the form of unordered sequences, also called strands , and every strand is synthesized thousands to milli...

Analytic combinatorics in several variables is a powerful tool for deriving the asymptotic behavior of combinatorial quantities by analyzing multivariate generating functions. We study information-theoretic questions about sequences in a discrete noiseless channel under cost and forbidden substring constraints. Our main contributions involve the re...

Motivated by applications in machine learning and archival data storage, we introduce function-correcting codes, a new class of codes designed to protect a function evaluation on the data against errors. We show that function-correcting codes are equivalent to irregular distance codes, i.e., codes that obey some given distance requirement between e...

In this paper, we study achievable rates of concatenated coding schemes over a deoxyribonucleic acid (DNA) storage channel. Our channel model incorporates the main features of DNA-based data storage. First, information is stored on many, short DNA strands. Second, the strands are stored in an unordered fashion inside the storage medium and each str...

A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most prior work on covering codes has focused on the Hamming metric, we consider the problem of designing covering co...

In this paper we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where a data set is represented by an unordered set of $M$ sequences, each of length $L$ . Errors within that model are a loss of whole sequences and point errors inside the sequences, such as insertions...

A covering code is a set of codewords with the property that the union of balls, suitably defined, around these codewords covers an entire space. Generally, the goal is to find the covering code with the minimum size codebook. While most prior work on covering codes has focused on the Hamming metric, we consider the problem of designing covering co...

A new family of codes, called clustering-correcting codes, is presented in this paper. This family of codes is motivated by the special structure of data that is stored in DNA-based storage systems. The data stored in these systems has the form of unordered sequences, also called strands, and every strand is synthesized thousands to millions of tim...

In this work, we propose constructions that correct duplications of multiple consecutive symbols. These errors are known as tandem duplications, where a sequence of symbols is repeated; respectively as palindromic duplications, where a sequence is repeated in reversed order. We compare the redundancies of these constructions with code size upper bo...

Device-specific physical characteristics provide the foundation for physical unclonable functions (PUFs), a hardware primitive for secure storage of cryptographic keys. Thus far, they have been implemented by either directly evaluating a binary output or by mapping symbols from a higher-order alphabet to a fixed-length bit sequence. However, when c...

Motivated by DNA-based data storage, we investigate a system where digital information is stored in an unordered set of several vectors over a finite alphabet. Each vector begins with a unique index that represents its position in the whole data set and does not contain data. This paper deals with the design of error-correcting codes for such index...

In this paper we study error-correcting codes for the storage of data in synthetic deoxyribonucleic acid (DNA). We investigate a storage model where a data set is represented by an unordered set of $M$ sequences, each of length $L$. Errors within that model are a loss of whole sequences and point errors inside the sequences, such as insertions, del...

In this paper, we study codes correcting $t$ duplications of $\ell$ consecutive symbols. These errors are known as tandem duplication errors, where a sequence of symbols is repeated and inserted directly after its original occurrence. Using sphere packing arguments, we derive non-asymptotic upper bounds on the cardinality of codes that correct such...

In this paper we study error-correcting codes for the storage of data in synthetic DNA. We investigate a storage model where a data set is represented by an unordered set of M sequences, each of length L. Errors within that model are losses of whole sequences and point errors inside the sequences, such as insertions, deletions and substitutions. We...

In this work, we propose constructions that correct duplications of multiple consecutive symbols. These errors are known as tandem duplications, where a sequence of symbols is repeated; respectively as palindromic duplications, where a sequence is repeated in reversed order. We compare the redundancies of these constructions with code size upper bo...

Device-specific physical characteristics provide the foundation for Physical Unclonable Functions (PUFs), a hardware primitive for secure storage of cryptographic keys. So far, they have been implemented by either directly evaluating a binary output or by mapping outputs from a higher-order alphabet to a fixed-length bit sequence. However, the latt...

In this work, the optimization of the analog transmit waveform for joint delay-Doppler estimation under sub-Nyquist conditions is considered. In particular, we derive an estimation theoretic design rule for the Fourier coefficients of the analog transmit signal when violating the sampling theorem at the receiver by using a wide analog pre-filtering...

In this work, we derive upper bounds on the cardinality of tandem and palindromic duplication correcting codes by deriving the generalized sphere packing bound for these error types. We first prove that an upper bound for tandem or palindromic deletions is also an upper bound for inserting the respective type of duplications. Therefore, we derive t...

In this article a framework is presented for the joint optimization of the analog transmit and receive filter with respect to a channel estimation problem. At the receiver, conventional signal processing systems restrict the bandwidth of the analog pre-filter $B$ to the rate of the analog-to-digital converter $f_s$ in order to comply with the well-...

In this work, the optimization of the analog transmit waveform for joint delay-Doppler estimation under sub-Nyquist conditions is considered. Based on the Bayesian Cram\'er-Rao lower bound (BCRLB), we derive an estimation theoretic design rule for the Fourier coefficients of the analog transmit signal when violating the sampling theorem at the rece...

The problem of optimum analog receive filtering for digital signal detection and parameter estimation is considered. Here the case of a signal source with bandwidth Bt and a receiver with fixed sampling rate fs is discussed under the assumption that 2Bt > fs. We investigate the impact of adjusting the receive bandwidth Br of the analog pre-filter,...