Showing papers on "Code word published in 2021"

On the Automorphism Group of Polar Codes

Abstract: The automorphism group of a code is the set of permutations of the codeword symbols that map the whole code onto itself. For polar codes, only a part of the automorphism group was known, namely the lower-triangular affine group (LTA), which is solely based upon the partial order of the code's synthetic channels. Depending on the design, however, polar codes can have a richer set of automorphisms. In this paper, we extend the LTA to a larger subgroup of the general affine group (GA), namely the block lower-triangular affine group (BLTA) and show that it is contained in the automorphism group of polar codes. Furthermore, we provide a low complexity algorithm for finding this group for a given information/frozen set and determining its size. Most importantly, we apply these findings in automorphism-based decoding of polar codes and report a comparable error-rate performance to that of successive cancellation list (SCL) decoding with significantly lower complexity.

Performance Limit and Coding Schemes for Resistive Random-Access Memory Channels

Abstract: Resistive random-access memory (ReRAM) is a promising candidate for the next generation non-volatile memory technology due to its simple read/write operations and high storage density However, its crossbar array structure causes a severe interference effect known as the “sneak path” In this paper, we propose channel coding techniques that can mitigate both the sneak-path interference and the channel noise The main challenge is that the sneak-path interference is data-dependent, and also correlated within a memory array, and hence the conventional error correction coding scheme will be inadequate In this work, we propose an across-array coding strategy that assigns a codeword to multiple independent memory arrays, and exploit a real-time channel estimation scheme to estimate the instantaneous status of the ReRAM channel Since the coded bits from different arrays experience independent channels, a “diversity” gain can be obtained during decoding, and when the codeword is adequately distributed over different memory arrays, the code actually performs as that over an uncorrelated channel By performing decoding based on the scheme of treating-interference-as-noise (TIN), the ReRAM channel over different memory arrays is equivalent to a block varying channel we defined, for which we propose both the capacity bounds and a coding scheme The proposed coding scheme consists of a serial concatenation of an optimized error correction code with a data shaper, which enables the ReRAM system to achieve a near capacity limit storage efficiency

A Deep Learning-Based Data Minimization Algorithm for Fast and Secure Transfer of Big Genomic Datasets

Abstract: In the age of Big Genomics Data, institutions such as the National Human Genome Research Institute (NHGRI) are challenged in their efforts to share volumes of data between researchers, a process that has been plagued by unreliable transfers and slow speeds. These occur due to throughput bottlenecks of traditional transfer technologies. Two factors that affect the efficiency of data transmission are the channel bandwidth and the amount of data. Increasing the bandwidth is one way to transmit data efficiently, but might not always be possible due to resource limitations. Another way to maximize channel utilization is by decreasing the bits needed for transmission of a dataset. Traditionally, transmission of big genomic data between two geographical locations is done using general-purpose protocols, such as hypertext transfer protocol (HTTP) and file transfer protocol (FTP) secure. In this paper, we present a novel deep learning-based data minimization algorithm that 1) minimizes the datasets during transfer over the carrier channels; 2) protects the data from the man-in-the-middle (MITM) and other attacks by changing the binary representation (content-encoding) several times for the same dataset: we assign different codewords to the same character in different parts of the dataset. Our data minimization strategy exploits the alphabet limitation of DNA sequences and modifies the binary representation (codeword) of dataset characters using deep learning-based convolutional neural network (CNN) to ensure a minimum of code word uses to the high frequency characters at different time slots during the transfer time. This algorithm ensures transmission of big genomic DNA datasets with minimal bits and latency and yields an efficient and expedient process. Our tested heuristic model, simulation, and real implementation results indicate that the proposed data minimization algorithm is up to 99 times faster and more secure than the currently used content-encoding scheme used in HTTP of the HTTP content-encoding scheme and 96 times faster than FTP on tested datasets. The developed protocol in C# will be available to the wider genomics community and domain scientists.

Phase-engineered bosonic quantum codes

Abstract: Continuous-variable systems protected by bosonic quantum codes have emerged as a promising platform for quantum information. To date, the design of code words has centered on optimizing the state occupation in the relevant basis to generate the distance needed for error correction. Here, we show tuning the phase degree of freedom in the design of code words can affect, and potentially enhance, the protection against Markovian errors that involve excitation exchange with the environment. As illustrations, we first consider phase engineering bosonic codes with uniform spacing in the Fock basis that correct excitation loss with a Kerr unitary and show that these modified codes feature destructive interference between error code words and, with an adapted ``two-level'' recovery, the error protection is significantly enhanced. We then study protection against energy decay with the presence of mode nonlinearities and analyze the role of phase for optimal code designs. We extend the principle of phase engineering to bosonic codes defined in other bases and multiqubit codes, demonstrating its broad applicability in quantum error correction.

A Revisit to Ordered Statistics Decoding: Distance Distribution and Decoding Rules

Abstract: This paper revisits the ordered statistics decoding (OSD). It provides a comprehensive analysis of the OSD algorithm by characterizing the statistical properties, evolution and the distribution of the Hamming distance and weighted Hamming distance from codeword estimates to the received sequence in the reprocessing stages of the OSD algorithm. We prove that the Hamming distance and weighted Hamming distance distributions can be characterized as mixture models capturing the decoding error probability and code weight enumerator. Simulation and numerical results show that our proposed statistical approaches can accurately describe the distance distributions. Based on these distributions and with the aim to reduce the decoding complexity, several techniques, including stopping rules and discarding rules, are proposed, and their decoding error performance and complexity are accordingly analyzed. Simulation results for decoding various eBCH codes demonstrate that the proposed techniques can significantly reduce the decoding complexity with a negligible loss in the decoding error performance.

High-Throughput and Energy-Efficient VLSI Architecture for Ordered Reliability Bits GRAND

Abstract: Ultra-reliable low-latency communication (URLLC), a major 5G New-Radio use case, is the key enabler for applications with strict reliability and latency requirements. These applications necessitate the use of short-length and high-rate codes. Guessing Random Additive Noise Decoding (GRAND) is a recently proposed Maximum Likelihood (ML) decoding technique for these short-length and high-rate codes. Rather than decoding the received vector, GRAND tries to infer the noise that corrupted the transmitted codeword during transmission through the communication channel. As a result, GRAND can decode any code, structured or unstructured. GRAND has hard-input as well as soft-input variants. Among these variants, Ordered Reliability Bits GRAND (ORBGRAND) is a soft-input variant that outperforms hard-input GRAND and is suitable for parallel hardware implementation. This work reports the first hardware architecture for ORBGRAND, which achieves an average throughput of up to $42.5$ Gbps for a code length of $128$ at a target FER of $10^{-7}$. Furthermore, the proposed hardware can be used to decode any code as long as the length and rate constraints are met. In comparison to the GRANDAB, a hard-input variant of GRAND, the proposed architecture enhances decoding performance by at least $2$ dB. When compared to the state-of-the-art fast dynamic successive cancellation flip decoder (Fast-DSCF) using a 5G polar $(128,105)$ code, the proposed ORBGRAND VLSI implementation has $49\times$ higher average throughput, $32\times$ times more energy efficiency, and $5\times$ more area efficiency while maintaining similar decoding performance.

What is the Sugar Code

Abstract: A code is defined by the nature of the symbols, which are used to generate information-storing combinations (e. g. oligo- and polymers). Like nucleic acids and proteins, oligo- and polysaccharides are ubiquitous, and they are a biochemical platform for establishing molecular messages. Of note, the letters of the sugar code system (third alphabet of life) excel in coding capacity by making an unsurpassed versatility for isomer (code word) formation possible by variability in anomery and linkage position of the glycosidic bond, ring size and branching. The enzymatic machinery for glycan biosynthesis (writers) realizes this enormous potential for building a large vocabulary. It includes possibilities for dynamic editing/erasing as known from nucleic acids and proteins. Matching the glycome diversity, a large panel of sugar receptors (lectins) has developed based on more than a dozen folds. Lectins 'read' the glycan-encoded information. Hydrogen/coordination bonding and ionic pairing together with stacking and C-H/π-interactions as well as modes of spatial glycan presentation underlie the selectivity and specificity of glycan-lectin recognition. Modular design of lectins together with glycan display and the nature of the cognate glycoconjugate account for the large number of post-binding events. They give an entry to the glycan vocabulary its functional, often context-dependent meaning(s), hereby building the dictionary of the sugar code.

Implementation of Error Correction Techniques in Memory Applications

Abstract: As the technology scales down, various soft errors in SRAM memories occurs due to which the single cell and multiple cell upsets are formed. Error correction codes such as the first technique (7,4) hamming code, where 7 denotes total code word, four refers to data bits and 3 parity bits were implemented and verified its encoding and decoding process. But it is only useful for single bit error detection and also correction, which has been the main drawback of this hamming code. So, the second technique implemented was the extended hamming code (8,4) or SEC-DED code ("Single Error Correction-Double Error Detection"). This code has an extra bit and used for correction of single error and also detection of double error. But correction of double error doesn’t happen in SEC-DED code. So, the extension of (8,4) SEC-DED code was (14,8) SEC-DED-DAEC ("Single Error Correction-Double Error Detection-Double Adjacent Error Correction") code where 14 denotes total code word, 8 data bits, six parity bits which can be used for correction of single error, detection of double error and also correction of double adjacent error was proposed in this work. These techniques related Encoding and Decoding processes were studied and all the simulation results were verified and implemented by using Verilog Coding in Xilinx ISE 14.7 tool. This proposed SEC-DED-DAEC method was also implemented in memory application and its output is verified. The double error detection was adjacently corrected by using this method and the complexity was decreased. The advantage of the proposed technique is it has the ability to detect and correct errors adjacently up to 2 bits.

Timely Transmissions Using Optimized Variable Length Coding

Abstract: A status updating system is considered in which a variable length code is used to transmit messages to a receiver over a noisy channel. The goal is to optimize the codewords lengths such that successfully-decoded messages are timely. That is, such that the age-of-information (AoI) at the receiver is minimized. A hybrid ARQ (HARQ) scheme is employed, in which variable-length incremental redundancy (IR) bits are added to the originally-transmitted codeword until decoding is successful. With each decoding attempt, a non-zero processing delay is incurred. The optimal codewords lengths are analytically derived utilizing a sequential differential optimization (SDO) framework. The framework is general in that it only requires knowledge of an analytical expression of the positive feedback (ACK) probability as a function of the codeword length.

Concatenated Codes for Recovery From Multiple Reads of DNA Sequences

Abstract: 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 low-density parity-check code and either an inner convolutional code or a block code. We propose two new decoding algorithms for inference from multiple received sequences, both combining the inner code and channel to a joint hidden Markov model to infer symbolwise a posteriori probabilities (APPs). The first decoder computes the exact APPs by jointly decoding the received sequences, whereas the second decoder approximates the APPs by combining the results of separately decoded received sequences. Using the proposed algorithms, we evaluate the performance of decoding multiple received sequences by means of achievable information rates and Monte-Carlo simulations. We show significant performance gains compared to a single received sequence.

Blind Channel Codes Recognition via Deep Learning

Abstract: This paper considers the blind recognition of the type and the encoding parameters of channel codes from the Gaussian noisy signals. Specifically, based on the recurrent neural network (RNN), the attention mechanism, and the residual neural network (ResNet), three universal recognizers are proposed to identify the type, rate, and length of the target channel codes, with a training set generated by a small portion of all the possible code parameters. The proposed architectures need near zero a priori knowledge about the target channel code, and only require the length of the received signal to be dozen times of the codeword length. Numerical experiments show that the proposed deep learning methods own strong generalization to identify channel codes from the testing samples not generated by the encoding parameters utilized for the training set.

Permute, Quantize, and Fine-tune: Efficient Compression of Neural Networks

Abstract: Compressing large neural networks is an important step for their deployment in resource-constrained computational platforms. In this context, vector quantization is an appealing framework that expresses multiple parameters using a single code, and has recently achieved state-of-the-art network compression on a range of core vision and natural language processing tasks. Key to the success of vector quantization is deciding which parameter groups should be compressed together. Previous work has relied on heuristics that group the spatial dimension of individual convolutional filters, but a general solution remains unaddressed. This is desirable for pointwise convolutions (which dominate modern architectures), linear layers (which have no notion of spatial dimension), and convolutions (when more than one filter is compressed to the same codeword). In this paper we make the observation that the weights of two adjacent layers can be permuted while expressing the same function. We then establish a connection to rate-distortion theory and search for permutations that result in networks that are easier to compress. Finally, we rely on an annealed quantization algorithm to better compress the network and achieve higher final accuracy. We show results on image classification, object detection, and segmentation, reducing the gap with the uncompressed model by 40 to 70% w.r.t. the current state of the art. All our experiments can be reproduced using the code at https://github.com/uber-research/permute-quantize-finetune.

Non-malleable Codes for Bounded Parallel-Time Tampering

Abstract: Non-malleable codes allow one to encode data in such a way that once a codeword is being tampered with, the modified codeword is either an encoding of the original message, or a completely unrelated one. Since the introduction of this notion by Dziembowski, Pietrzak, and Wichs (ICS ’10 and J. ACM ’18), there has been a large body of works realizing such coding schemes secure against various classes of tampering functions. It is well known that there is no efficient non-malleable code secure against all polynomial size tampering functions. Nevertheless, no code which is non-malleable for bounded polynomial size attackers is known and obtaining such a code has been a major open problem.

Correcting Two Deletions with More Reads

Abstract: A two-deletion correcting code of length $n$ is defined to be a set of binary words such that a codeword can be uniquely identified from any one of its length- ( $n-2$ ) subsequence. A two-deletion correcting code requires at least $2\log n+O(1)$ , while the best known explicit construction uses $4\log n+o(\log n)$ redundant bits. In this work, we study this coding problem in the framework of the sequence reconstruction problem and require the receiver to uniquely reconstruct a codeword from any $N\geqslant 2$ of its length- ( $n-2$ ) subsequences. Specifically, we provide an explicit code construction that uniquely reconstructs a codeword from any five of its length-( $n-2$ ) subsequences, using only $2\log n+o(\log n)$ redundant bits.

A fixed latency ORBGRAND decoder architecture with LUT-aided error-pattern scheduling.

Abstract: Guessing Random Additive Noise Decoding (GRAND) is a universal decoding algorithm that has been recently proposed as a practical way to perform maximum likelihood decoding. It generates a sequence of possible error patterns and applies them to the received vector, checking if the result is a valid codeword. Ordered reliability bits GRAND (ORBGRAND) improves on GRAND by considering soft information received from the channel. Both GRAND and ORBGRAND have been implemented in hardware, focusing on average performance, sacrificing worst case throughput and latency. In this work, an improved pattern schedule for ORBGRAND is proposed. It provides $>0.5$dB gain over the standard schedule at a block error rate $\le 10^{-5}$, and outperforms more complex GRAND flavors with a fraction of the complexity. The proposed schedule is used within a novel code-agnositic decoder architecture: the decoder guarantees fixed high throughput and low latency, making it attractive for latency-constrained applications. It outperforms the worst-case performance of decoders by orders of magnitude, and outperforms many best-case figures. Decoding a code of length 128, it achieves a throughput of $79.21$Gb/s with $58.49$ns latency, and of $69.61$Gb/s with $40.58$ns latency, yielding better energy efficiency and comparable area efficiency with respect to the state of the art.

Coding for Sequence Reconstruction for Single Edits

Abstract: The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication scenario where the sender transmits a codeword from some codebook and the receiver obtains multiple noisy reads of the codeword. The common setup assumes the codebook to be the entire space and the problem is to determine the minimum number of distinct reads that is required to reconstruct the transmitted codeword. Motivated by modern storage devices, we study a variant of the problem where the number of noisy reads N is fixed. Specifically, we design reconstruction codes that reconstruct a codeword from N distinct noisy reads. We focus on channels that introduce single edit error (i.e. a single substitution, insertion, or deletion) and their variants, and design reconstruction codes for all values of N. In particular, for the case of a single edit, we show that as the number of noisy reads increases, the number of redundant symbols required can be gracefully reduced from logq n+O(1) to logq logq n+O(1), and then to O(1), where n denotes the length of a codeword. We also show that these reconstruction codes are asymptotically optimal. Finally, via computer simulations, we demonstrate that in certain cases, reconstruction codes can achieve similar performance as classical error-correcting codes with less redundant symbols.

On conflict free DNA codes

Abstract: DNA storage has emerged as an important area of research. The reliability of a DNA storage system depends on designing those DNA strings (called DNA codes) that are sufficiently dissimilar. In this work, we introduce DNA codes that satisfy the newly introduced constraint, a generalization of the non-homopolymers constraint. In particular, each codeword of the DNA code has the specific property that any two consecutive sub-strings of the DNA codeword will not be the same. This is apart from the usual constraints such as Hamming, reverse, reverse-complement and GC-content. We believe that the new constraints proposed in this paper will provide significant achievements in reducing the errors, during reading and writing data into the synthetic DNA strings. We also present a construction (based on a variant of stochastic local search algorithm) to determine the size of the DNA codes with a constraint that each DNA codeword is free from secondary structures in addition to the usual constraint. This further improves the lower bounds from the existing literature, in some specific cases. A recursive isometric map between binary vectors and DNA strings is also proposed. By applying this map over the well known binary codes, we obtain classes of DNA codes with all of the above constraints, including the property that the constructed DNA codewords are free from the hairpin like secondary structures.

On the Automorphism Group of Polar Codes

Abstract: The automorphism group of a code is the set of permutations of the codeword symbols that map the whole code onto itself. For polar codes, only a part of the automorphism group was known, namely the lower-triangular affine group (LTA), which is solely based upon the partial order of the code's synthetic channels. Depending on the design, however, polar codes can have a richer set of automorphisms. In this paper, we extend the LTA to a larger subgroup of the general affine group (GA), namely the block lower-triangular affine group (BLTA) and show that it is contained in the automorphism group of polar codes. Furthermore, we provide a low complexity algorithm for finding this group for a given information/frozen set and determining its size. Most importantly, we apply these findings in automorphism-based decoding of polar codes and report a comparable error-rate performance to that of successive cancellation list (SCL) decoding with significantly lower complexity.

Genetic algorithms with permutation-based representation for computing the distance of linear codes

Abstract: Finding the minimum distance of linear codes is an NP-hard problem. Traditionally, this computation has been addressed by means of the design of algorithms that find, by a clever exhaustive search, a linear combination of some generating matrix rows that provides a codeword with minimum weight. Therefore, as the dimension of the code or the size of the underlying finite field increase, so it does exponentially the run time. In this work, we prove that, given a generating matrix, there exists a column permutation which leads to a reduced row echelon form containing a row whose weight is the code distance. This result enables the use of permutations as representation scheme, in contrast to the usual discrete representation, which makes the search of the optimum polynomial time dependent from the base field. In particular, we have implemented genetic and CHC algorithms using this representation as a proof of concept. Experimental results have been carried out employing codes over fields with two and eight elements, which suggests that evolutionary algorithms with our proposed permutation encoding are competitive with regard to existing methods in the literature. As a by-product, we have found and amended some inaccuracies in the Magma Computational Algebra System concerning the stored distances of some linear codes.

Primitive Rateless Codes

Abstract: In this paper, we propose primitive rateless (PR) codes. A PR code is characterized by the message length and a primitive polynomial over $\mathbf {GF}(2)$ , which can generate a potentially limitless number of coded symbols. We show that codewords of a PR code truncated at any arbitrary length can be represented as subsequences of a maximum-length sequence ( $m$ -sequence). We characterize the Hamming weight distribution of PR codes and their duals and show that for a properly chosen primitive polynomial, the Hamming weight distribution of the PR code can be well approximated by the truncated binomial distribution. We further find a lower bound on the minimum Hamming weight of PR codes and show that there always exists a PR code that can meet this bound for any desired codeword length. We provide a list of primitive polynomials for message lengths up to 40 and show that the respective PR codes closely meet the Gilbert-Varshamov bound at various rates. Simulation results show that PR codes can achieve similar block error rates as their BCH counterparts at various signal-to-noise ratios (SNRs) and code rates. PR codes are rate-compatible and can generate as many coded symbols as required; thus, demonstrating a truly rateless performance.

Modulated Sparse Superposition Codes for the Complex AWGN Channel

Abstract: This paper studies a generalization of sparse superposition codes (SPARCs) for communication over the complex additive white Gaussian noise (AWGN) channel. In a SPARC, the codebook is defined in terms of a design matrix, and each codeword is a generated by multiplying the design matrix with a sparse message vector. In the standard SPARC construction, information is encoded in the locations of the non-zero entries of the message vector. In this paper we generalize the construction and consider modulated SPARCs, where information is encoded in both the locations and the values of the non-zero entries of the message vector. We focus on the case where the non-zero entries take values from a phase-shift keying (PSK) constellation. We propose a computationally efficient approximate message passing (AMP) decoder, and obtain analytical bounds on the state evolution parameters which predict the error performance of the decoder. Using these bounds we show that PSK-modulated SPARCs are asymptotically capacity achieving for the complex AWGN channel, with either spatial coupling or power allocation. We also provide numerical simulation results to demonstrate the error performance at finite code lengths. These results show that introducing modulation to the SPARC design can significantly reduce decoding complexity without sacrificing error performance.

An Algorithm for Constructing the Optimal Code Trees for Binary Alphabetic AIFV-m Codes

Abstract: We call the alphabetic version of the AIFV-m code the alphabetic AIFV-m codes. This paper defines binary alphabetic AIFV-m codes and proposes an algorithm to design the optimal binary alphabetic AIFV-m codes in terms of the minimum average codeword length for stationary memoryless sources. The proposed method is based on an iterative optimization algorithm and a dynamic programming algorithm.

Generalized Simple Streaming Codes from MDS Codes

Abstract: Streaming codes represent a packet-level FEC scheme for achieving reliable, low-latency communication. In the literature on streaming codes, the commonly-assumed Gilbert-Elliott channel model, is replaced by a more tractable, delay-constrained, sliding-window (DCSW) channel model that can introduce either random or burst erasures. The known streaming codes that are rate optimal over the DCSW channel model are constructed by diagonally embedding a scalar block code across successive packets. These code constructions have field size that is quadratic in the delay parameter $\tau$ and have a somewhat complex structure with an involved decoding procedure. This led to the introduction of simple streaming (SS) codes in which diagonal embedding is replaced by staggered-diagonal embedding (SDE). The SDE approach reduces the impact of a burst of erasures and makes it possible to construct near-rate-optimal streaming codes using Maximum Distance Separable (MDS) code having linear field size. The present paper takes this development one step further, by retaining the staggered-diagonal feature, but permitting the placement of more than one code symbol from a given scalar codeword within each packet. These generalized, simple streaming codes allow us to improve upon the rate of SS codes, while retaining the simplicity of working with MDS codes. We characterize the maximum code rate of streaming codes under a constraint on the number of contiguous packets over which symbols of the underlying scalar code are dispersed. Such a constraint leads to simplified code construction and reduced-complexity decoding.

On the Optimality of Binary AIFV Codes with Two Code Trees

Abstract: Huffman code is the optimal code in the class of uniquely decodable codes in the sense of the average length of codeword when a single code tree can represent the code. This paper defines hierarchical subclasses of noiseless source codes by allowing $k$ -bit decoding delay for positive integer $k$ and clarifies a necessary and sufficient condition for the uniquely decodable codes with $k$ -bit decoding delay. Furthermore, we show that AIFV code is the optimal code in the class of uniquely decodable codes with 2-bit decoding delay when two code trees represent the noiseless source code.

Systematic Convolutional Low Density Generator Matrix Code

Abstract: In this paper, we propose a systematic low density generator matrix (LDGM) code ensemble, which is defined by the Bernoulli process. We prove that, under maximum likelihood (ML) decoding, the proposed ensemble can achieve the capacity of binary-input output symmetric (BIOS) memoryless channels in terms of bit error rate (BER). The proof technique reveals a new mechanism, different from lowering down frame error rate (FER), that the BER can be lowered down by assigning light codeword vectors to light information vectors. The finite length performance is analyzed by deriving an upper bound and a lower bound, both of which are shown to be tight in the high signal-to-noise ratio (SNR) region. To improve the waterfall performance, we construct the systematic convolutional LDGM (SysConv-LDGM) codes by a random splitting process. The SysConv-LDGM codes are easily configurable in the sense that any rational code rate can be realized without complex optimization. As a universal construction, the main advantage of the SysConv-LDGM codes is their near-capacity performance in the waterfall region and predictable performance in the error-floor region that can be lowered down to any target as required by increasing the density of the uncoupled LDGM codes. Numerical results are also provided to verify our analysis.

High-Throughput VLSI Architecture for GRAND Markov Order

Abstract: Guessing Random Additive Noise Decoding (GRAND) is a recently proposed Maximum Likelihood (ML) decoding technique. Irrespective of the structure of the error correcting code, GRAND tries to guess the noise that corrupted the codeword in order to decode any linear error-correcting block code. GRAND Markov Order (GRAND-MO) is a variant of GRAND that is useful to decode error correcting code transmitted over communication channels with memory which are vulnerable to burst noise. Usually, interleavers and de-interleavers are used in communication systems to mitigate the effects of channel memory. Interleaving and de-interleaving introduce undesirable latency, which increases with channel memory. To prevent this added latency penalty, GRAND-MO can be directly used on the hard demodulated channel signals. This work reports the first GRAND-MO hardware architecture which achieves an average throughput of up to 52 Gbps and 64 Gbps for a code length of 128 and 79 respectively. Compared to the GRANDAB, hard-input variant of GRAND, the proposed architecture achieves 3 dB gain in decoding performance for a target FER of 10−5. Similarly, comparing the GRAND-MO decoder with a decoder tailored for a (79,64) BCH code showed that the proposed architecture achieves 33% higher worst case throughput and 2 dB gain in decoding performance.

On the Power of Relaxed Local Decoding Algorithms

Abstract: A locally decodable code (LDC) $C \colon \{0,1\}^k \to \{0,1\}^n$ is an error correcting code wherein individual bits of the message can be recovered by only querying a few bits of a noisy codeword...

Design of A Parallel Decoding Method for LDPC Code Generated via Primitive Polynomial

Abstract: An effective way of improving decoding performance of an LDPC code is to extend the single-decoder decoding method to a parallel decoding method with multiple sub-decoders To this end, this paper proposes a parallel decoding method for the LDPC codes constructed by m-sequence In this method, the sub-decoders have two types The first one contains only one decoding module using the original parity-check constraints to implement a belief propagation (BP) algorithm The second one consists of a pre-decode module and a decoding module The parity-check matrices for pre-decode modules are generated by the parity-check constraints of the sub-sequences sampled from an m-sequence Then, the number of iterations of the BP process in each pre-decode module is set as half of the girth of the parity-check matrix, resulting in the elimination of the impact of short cycles Using maximum a posterior (MAP), the least metric selector (LMS) finally picks out a codeword from the outputs of sub-decoders Our simulation results show that the performance gain of the proposed parallel decoding method with five sub-decoders is about 04 dB, compared to the single-decoder decoding method at the bit error rate (BER) of 10−5

Neural networks for decoding

Abstract: Methods and apparatus for training a Neural Network to recover a codeword of a Forward Error Correction code are provided. Trainable parameters of the Neural Network are optimised to minimise a loss function. The loss function is calculated by representing an estimated value of the message bit output from the Neural Network as a probability of the value of the bit in a predetermined real number domain and multiplying the representation of the estimated value of the message bit by a representation of a target value of the message bit. Training a neural network may be implemented via a loss function.