Synchronization Strings: Codes for Insertions and Deletions Approaching the Singleton Bound

We introduce synchronization strings , which provide a novel way to efficiently deal with synchronization errors , i.e., insertions and deletions. Synchronization errors are strictly more general and much harder to cope with than more commonly considered Hamming-type errors , i.e., symbol substitutions and erasures. For every ε > 0, synchronization strings allow us to index a sequence with an ε -O(1) -size alphabet, such that one can efficiently transform k synchronization errors into (1 + ε)k Hamming-type errors . This powerful new technique has many applications. In this article, we focus on designing insdel codes , i.e., error correcting block codes (ECCs) for insertion-deletion channels. While ECCs for both Hamming-type errors and synchronization errors have been intensely studied, the latter has largely resisted progress. As Mitzenmacher puts it in his 2009 survey [30]: “ Channels with synchronization errors...are simply not adequately understood by current theory. Given the near-complete knowledge, we have for channels with erasures and errors...our lack of understanding about channels with synchronization errors is truly remarkable. ” Indeed, it took until 1999 for the first insdel codes with constant rate, constant distance, and constant alphabet size to be constructed and only since 2016 are there constructions of constant rate insdel codes for asymptotically large noise rates. Even in the asymptotically large or small noise regimes, these codes are polynomially far from the optimal rate-distance tradeoff. This makes the understanding of insdel codes up to this work equivalent to what was known for regular ECCs after Forney introduced concatenated codes in his doctoral thesis 50 years ago. A straightforward application of our synchronization strings-based indexing method gives a simple black-box construction that transforms any ECC into an equally efficient insdel code with only a small increase in the alphabet size. This instantly transfers much of the highly developed understanding for regular ECCs into the realm of insdel codes. Most notably, for the complete noise spectrum, we obtain efficient “near-MDS” insdel codes, which get arbitrarily close to the optimal rate-distance tradeoff given by the Singleton bound. In particular, for any δ ∈ (0,1) and ε > 0, we give a family of insdel codes achieving a rate of 1 - δ - ε over a constant-size alphabet that efficiently corrects a δ fraction of insertions or deletions.

Machine learning for decoding linear block codes: case of multi-class logistic regression model

<p>Facing the challenge of enormous data sets variety, several machine learning-based algorithms for prediction (e.g, Support vector machine, multi layer perceptron and logistic regression) have been highly proposed and used over the last years in many fields. Error correcting codes (ECCs) are extensively used in practice to protect data against damaged data storage systems and against random errors due to noise effects. In this paper, we will use machine learning methods, especially multi-class logistic regression combined with the famous syndrome decoding algorithm. The main idea behind our decoding method which we call logistic regression decoder (LRDec) is to use the efficient multi-class logistic regression models to find errors from syndromes in linear codes such as bose, ray-chaudhuri and hocquenghem (BCH), and the quadratic residue (QR). Obtained results of the proposed decoder have a significant benefit in terms of bit error rate (BER) for random binary codes. The comparison of our decoder with many competitors proves its power. The proposed decoder has reached a success percentage of 100% for correctable errors in the studied codes.</p>

Adaptive Switching Hybrid Blast-STBC MIMO System

Fading in a wireless channel has negative effects on the performance of communication systems. Bell Laboratories layered space-time (BLAST) has been used to get a high data rate while space-time block codes (STBC) have been used to get a low bit error rate (BER) performance. Under deep faded channels, hybrid BLAST-STBC systems are considered as a trade-off between BLAST and STBC systems. By exploiting the benefits of both systems, a new method to represent a 4 × 4 multiple-input and multiple-output (MIMO) system is proposed and studied, in which the transmission process is carried out adaptively between both 4 × 4 VBLAST, Quasi-Orthogonal STBC (QOSTBC) and Hybrid systems according to the transmit links state. The proposed adaptive switching hybrid system (ASHS) reduces the total transmitted power, achieves the maximum throughput by obtaining the best BER. An adaptive switching transmission scheme using the strategy of measuring the transmit links fading is investigated as well. The simulated results are obtained in an environment of a 4 × 4 MIMO system using MATLAB platform where the total transmitting power is normalized to unity. The detections are done using the maximum likelihood (ML) receiver. The proposed ASHS system shows a lot of advantages such as maximum throughput is obtained in bad channel states, no additional transmit power is needed and no additional bandwidth is needed. Finally, under deep fading condition, the proposed ASHS transmission scheme obtains the best BER, reduces wasting the total transmitted power, achieves the maximum throughput and obtains the best BER.

Multi-Kernel Polar Codes versus Classical Designs with Different Rate-Matching Approaches

Polar codes, which have been proposed as a family of linear block codes, has garnered a lot of attention from the scientific community, owing to their low-complexity implementation and provably capacity-achieving capability. Thus, they have been proposed to be used for encoding information on the control channels in the upcoming 5G wireless networks. The basic approach introduced by Arikan in his landmark paper to polarize bit channels of equal capacities to those of unequal capacities can be used to design only codewords of length N=2n, which is a major limitation when codewords of different lengths are required for the underlying applications. In the predecessor paper, this aspect was partially addressed by using a 3×3 kernel circuit (used to generate codewords of length M=3m), along with downsizing techniques such as puncturing and shortening to asses the optimal design and resizing techniques based on the underlying system parameters. In this article, we extend this research to include the assessment of multi-kernel rate-matched polar codes for applicability over a much wider range of codeword lengths.