List Size Research Articles

Fast Iterative Soft-Output List Decoding of Polar Codes

Iterative detection and decoding (IDD) enjoys a higher capacity than separate detection and decoding (SDD). However, IDD requires both the detector and the decoder to support soft input and soft output. Considering the standard channel codes in 5G communication systems, the preferred decoder for polar codes, the successive cancellation list (SCL) decoder, outputs only hard decisions on the side of codeword. Yet, current soft-output polar decoders, such as belief propagation (BP) and soft cancellation (SCAN), are much inferior to the SCL decoders in terms of error correction performance. To this end, we propose a soft-output list (SOL) decoder in this paper, which considers both hypotheses of 0 and 1 for unreliable bits and keeps the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a-priori</i> likelihoods for reliable bits, so that it can provide soft output and satisfactory error-rate performance at the same time. Exploiting the property of special nodes, the resulting FastSOL decoder can directly return soft messages from these nodes, thus speeding up the decoding. The error-rate performance of the FastSOL decoder enhances as the number of iterations increases in the non-IDD setup. The proposed FastSOL decoder can also be applied in the IDD system. Concatenated with a maximum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a-posteriori</i> detector in ten IDD loops, our decoder with a list size of eight exhibits over 1 dB gain compared to using the SCAN decoder for polar codes with length 256 and half rate, which also outperforms the state-of-the-art soft list decoder by 0.12 dB in the same settings with a higher computational complexity, but comparable decoding latency.

Recursive Design of Precoded Polar Codes for SCL Decoding

A novel method to recursively construct a set of precoded polar codes of various rates and short-to-moderate lengths is presented. The proposed code design method minimizes the successive cancellation (SC) decoding error probability estimate under three constraints. The first constraint is the minimum distance requirement to improve the maximum-likelihood (ML) performance of the resulting code and therefore the performance under the SC list (SCL) decoding. The other two constraints introduce preselected supercode and subcode, where the supercode ensures fast computation of the minimum distance and the subcode ensures reduction of the search space size. The supercode is given by the Plotkin sum of shorter codes, which are nested to simplify computation of low-weight codewords. These low-weight codewords are needed to satisfy the minimum distance constraint. The simulation results indicate that the proposed precoded polar codes of lengths 128 and 256 provide a better frame error rate (FER) than polar codes with CRC and e-BCH polar subcodes under the SCL decoding algorithm with the list size <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$8-128$ </tex-math></inline-formula> .

On Sequential Decoding Metric Function of Polarization-Adjusted Convolutional (PAC) Codes

In this paper, we present a sequential decoding metric function, which leads to significantly improved computational complexity while maintaining the superiority of polarization-adjusted convolutional (PAC) codes’ error-correction performance. With the proposed metric function, the PAC codes’ decoding computational complexity is comparable to the computational complexity of sequential decoding of conventional convolutional codes (CCs). Moreover, simulation results show an improvement in the error-correction performance of low rate PAC codes when using the proposed metric function. Simulation results also show that using the proposed metric, the upper bound on the PAC codes’ computational complexity has a Pareto distribution. To reduce the worst-case latency of PAC sequential decoder, we limit the number of searches performed by sequential decoder. The results show that for PAC codes of length 128, search-limited sequential decoding can achieve an error-correction performance close to the error-correction performance of polar codes with successive cancellation list decoding with list size 64 and CRC length 11 with considerably less computational complexity.

Decision List Compression by Mild Random Restrictions

A decision list is an ordered list of rules. Each rule is specified by a term, which is a conjunction of literals, and a value. Given an input, the output of a decision list is the value corresponding to the first rule whose term is satisfied by the input. Decision lists generalize both CNFs and DNFs and have been studied both in complexity theory and in learning theory. The size of a decision list is the number of rules, and its width is the maximal number of variables in a term. We prove that decision lists of small width can always be approximated by decision lists of small size, where we obtain sharp bounds for such approximation. This also resolves a conjecture of Gopalan, Meka, and Reingold (Computational Complexity, 2013) on DNF sparsification. An ingredient in our proof is a new random restriction lemma, which allows to analyze how DNFs (and more generally, decision lists) simplify if a small fraction of the variables are fixed. This is in contrast to the more commonly used switching lemma, which requires most of the variables to be fixed.

Flexibility of planar graphs—Sharpening the tools to get lists of size four

A graph where each vertex v has a list L(v) of available colors is L-colorable if there is a proper coloring such that the color of v is in L(v) for each v. A graph is k-choosable if every assignment L of at least k colors to each vertex guarantees an L-coloring. Given a list assignment L, an L-request for a vertex v is a color c∈L(v). In this paper, we look at a variant of the widely studied class of precoloring extension problems from Dvořák, Norin, and Postle (J. Graph Theory, 2019), wherein one must satisfy “enough”, as opposed to all, of the requested set of precolors. A graph G is ɛ-flexible for list sizek if for any k-list assignment L, and any set S of L-requests, there is an L-coloring of G satisfying ɛ-fraction of the requests in S.It is conjectured that planar graphs are ɛ-flexible for list size 5, yet it is proved only for list size 6 and for certain subclasses of planar graphs. We give a stronger version of the main tool used in the proofs of the aforementioned results. By doing so, we improve upon a result by Masařík and show that planar graphs without K4− are ɛ-flexible for list size 5. We also prove that planar graphs without 4-cycles and 3-cycle distance at least 2 are ɛ-flexible for list size 4. Finally, we introduce a new (slightly weaker) form of ɛ-flexibility where each vertex has exactly one request. In that setting, we provide a stronger tool and we demonstrate its usefulness to further extend the class of graphs that are ɛ-flexible for list size 5.

Patient and practitioner views on cancer risk discussions in primary care: a qualitative study.

BackgroundIt is estimated that nearly 600 000 cancer cases in the UK could have been avoided in the past 5 years if people had healthier lifestyles, with the principle modifiable risk factors being smoking, obesity, alcohol consumption, and inactivity. There is growing interest in the use of cancer risk information in general practice to encourage lifestyle modification.AimTo explore the views and experiences of patients and practitioners in relation to cancer prevention and cancer risk discussions in general practice.Design & settingQualitative study among patients and practitioners in general practices in Glasgow, UK.MethodSemi-structured interviews were conducted with nine practitioners (five GPs and four practice nurses, recruited purposively from practices based on list size and deprivation status), and 13 patients (aged 30–60 years, with two or more specified comorbidities).ResultsCurrently, cancer risk discussions focus on smoking and cancer, with links between alcohol and/or obesity and cancer rarely made. There was support for the use of the personalised cancer risk tool as an additional resource in primary care. Practitioners felt practice nurses were best placed to use it. Use in planned appointments (for example, chronic disease reviews) was preferred over opportunistic use. Concerns were expressed, however, about generating anxiety, time constraints, and widening inequalities.ConclusionHealth behaviour change is complex and the provision of information alone is unlikely to have significant effects. Personalised risk tools may have a role, but important concerns about their use remain, particularly in areas of socioeconomic disadvantage.

Comparative analysis of routing techniques in chord overlay network

Overlay networks are not a new field or area of study. This domain of computing will someday drive P2P systems in various application areas such as block-chain, energy trading, video multicasting, and distributed file storage. This study highlights the two widely known methods of routing information employed in one of such overlay networks called chord. In this study, simulations of both routing modes (iterative and recursive) and their variations under no-churn (leaving and joining of nodes) and churn conditions was carried out. The routing parameter (successor list size) was varied for each of the routing techniques in a simulation study. The results obtained show that semi recursive routing gives a better routing performance under churn scenarios.

The Birthday Problem and Zero-Error List Codes

A key result of classical information theory states that if the rate of a randomly generated codebook is less than the mutual information between the channel's input and output, then the probability that that codebook has negligible error goes to one as the blocklength goes to infinity. In an attempt to bridge the gap between the probabilistic world of classical information theory and the combinatorial world of zero-error information theory, this work derives necessary and sufficient conditions on the rate so that the probability that a randomly generated codebook operated under list decoding (for any fixed list size) has zero error probability goes to one as the blocklength goes to infinity. Furthermore, this work extends the classical birthday problem to an information-theoretic setting, which results in the definition of a “noisy” counterpart of Rényi entropy, analogous to how mutual information can be considered a noisy counterpart of Shannon entropy.

Asymmetric List Sizes in Bipartite Graphs

Given a bipartite graph with parts A and B having maximum degrees at most Delta _A and Delta _B, respectively, consider a list assignment such that every vertex in A or B is given a list of colours of size k_A or k_B, respectively. We prove some general sufficient conditions in terms of Delta _A, Delta _B, k_A, k_B to be guaranteed a proper colouring such that each vertex is coloured using only a colour from its list. These are asymptotically nearly sharp in the very asymmetric cases. We establish one sufficient condition in particular, where Delta _A=Delta _B=Delta , k_A=log Delta and k_B=(1+o(1))Delta /log Delta as Delta rightarrow infty . This amounts to partial progress towards a conjecture from 1998 of Krivelevich and the first author. We also derive some necessary conditions through an intriguing connection between the complete case and the extremal size of approximate Steiner systems. We show that for complete bipartite graphs these conditions are asymptotically nearly sharp in a large part of the parameter space. This has provoked the following. In the setup above, we conjecture that a proper list colouring is always guaranteedif k_A ge Delta _A^varepsilon and k_B ge Delta _B^varepsilon for any varepsilon >0 provided Delta _A and Delta _B are large enough;if k_A ge C log Delta _B and k_B ge C log Delta _A for some absolute constant C>1; orif Delta _A=Delta _B = Delta and k_B ge C (Delta /log Delta )^{1/k_A}log Delta for some absolute constant C>0. These are asymmetric generalisations of the above-mentioned conjecture of Krivelevich and the first author, and if true are close to best possible. Our general sufficient conditions provide partial progress towards these conjectures.

Multi-stage guided stochastic search for optimization and standardization of free-form steel double-layer grids

There has been a growing interest in the use of free-form structures with irregularly curved yet aesthetically pleasing configurations in the recent decades. Although design optimization of regular steel grids has been well addressed in the literature of structural optimization, still limited work has been devoted to optimum design of real-size free-form grid structures. On the one hand, a main obstacle when dealing with real-size free-form steel grids is the excessive computational effort associated with contemporary evolutionary optimization algorithms. On the other hand, it is generally perceived that the obtained final designs using conventional optimization algorithms may not necessarily be favored in practice if certain provisions are not stipulated by the algorithm to preclude an abundance of distinct steel section sizes in the final design. Hence, instead of offering a single optimum or near optimum design, it would be more desirable to provide the designer or decision maker with a Pareto front set of non-dominated design alternatives taking into account both the minimum weight as well as the assortment of available steel section sizes in the final design. Accordingly, in this paper, a computationally efficient multi-stage guided stochastic search algorithm is proposed for optimization and standardization of real-size free-form steel double-layer grids. A gradual design-oriented section elimination approach is followed where in the first optimization stage, a complete set of commercially available steel sections is introduced to the algorithm and in the succeeding stages, the size of section list is reduced by eliminating the redundant sizes. Two variants of the algorithm are employed to demonstrate the usefulness of the proposed technique in challenging test examples of free-form steel double-layer grids, and the obtained Pareto fronts are plotted to illustrate the trade-off between minimum weight and assortment of steel section sizes in the final design.

Still 'being bothered about Billy': managing the physical health of people with severe mental illness.

People with severe mental illness (SMI) face a future not only limited by stigmatising psychiatric illness, but also a life shortened by 15–20 years through physical comorbidities. Social and behavioural determinants help explain why many of these comorbidities cluster together. Moreover, the experience of multiple conditions, sometimes with conflicting management requirements and multiple healthcare providers, creates a disproportionate treatment burden accompanied by often poorer individual disease outcomes, a situation compounded by discriminatory health care.1 The late Professor Helen Lester called upon GP colleagues to make the care of people with SMI core business in her 2012 James Mackenzie Lecture, ‘Being Bothered about Billy’, to the Royal College of General Practitioners (RCGP) Annual General Meeting. Recognising the particular contribution of cardiovascular disease (CVD) and diabetes to reduced life expectancy, Professor Lester urged GPs to ‘Don’t just screen, intervene’ for cardiometabolic risks. This advice was seemingly unheeded when GP contract negotiators retired three key cardiometabolic indicators from the 2014/2015 Quality and Outcomes Framework (QOF),2 with the predictable detrimental impact of this decision.3 While CVD remains the commonest cause of a still widening mortality gap,4 this population also experiences elevated rates of other physical comorbidities compared with the general population.5 We will argue that tackling this health inequality should remain core business for GPs. ### Why this matters to primary care In the UK, the lifetime prevalence of psychotic disorders such as schizophrenia and bipolar disorder are 0.72%6 and 1–2%7 respectively. A GP with an average list size can expect about one patient per year to present with a new psychotic illness, characterised by changes in perception, thinking, mood, and behaviour. Stigma and social isolation compound disrupted education and employment, and financial and accommodation uncertainties. About 20% of individuals will fully recover following a single episode. However, most continue to experience psychological and …

Erasures versus errors in local decoding and property testing

AbstractWe initiate the study of the role of erasures in local decoding and use our understanding to prove a separation between erasure‐resilient and tolerant property testing. We first investigate local list‐decoding in the presence of erasures. We prove an analog of a famous result of Goldreich and Levin on local list‐decodability of the Hadamard code. Specifically, we show that the Hadamard code is locally list‐decodable in the presence of a constant fraction of erasures, arbitrarily close to 1, with list sizes and query complexity better than in the Goldreich–Levin theorem. We further study approximate locally erasure list‐decodable codes and use them to construct a property that is erasure‐resiliently testable with query complexity independent of the input length, , but requires queries for tolerant testing. We also investigate the general relationship between local decoding in the presence of errors and in the presence of erasures.

List Decoding of Arıkan's PAC Codes.

Polar coding gives rise to the first explicit family of codes that provably achieve capacity with efficient encoding and decoding for a wide range of channels. However, its performance at short blocklengths under standard successive cancellation decoding is far from optimal. A well-known way to improve the performance of polar codes at short blocklengths is CRC precoding followed by successive-cancellation list decoding. This approach, along with various refinements thereof, has largely remained the state of the art in polar coding since it was introduced in 2011. Recently, Arıkan presented a new polar coding scheme, which he called polarization-adjusted convolutional (PAC) codes. At short blocklengths, such codes offer a dramatic improvement in performance as compared to CRC-aided list decoding of conventional polar codes. PAC codes are based primarily upon the following main ideas: replacing CRC codes with convolutional precoding (under appropriate rate profiling) and replacing list decoding by sequential decoding. One of our primary goals in this paper is to answer the following question: is sequential decoding essential for the superior performance of PAC codes? We show that similar performance can be achieved using list decoding when the list size L is moderately large (say, ). List decoding has distinct advantages over sequential decoding in certain scenarios, such as low-SNR regimes or situations where the worst-case complexity/latency is the primary constraint. Another objective is to provide some insights into the remarkable performance of PAC codes. We first observe that both sequential decoding and list decoding of PAC codes closely match ML decoding thereof. We then estimate the number of low weight codewords in PAC codes, and use these estimates to approximate the union bound on their performance. These results indicate that PAC codes are superior to both polar codes and Reed–Muller codes. We also consider random time-varying convolutional precoding for PAC codes, and observe that this scheme achieves the same superior performance with constraint length as low as .

A new formula for managing family doctors' patient list in Portugal.

In Portugal, family doctors work with a well-defined list of patients to whom they provide healthcare throughout their lives. Several studies showed that larger list sizes are associa- ted with poorer health outcomes and compromise the quality of care. A significant increase in the average list size has been observed in recent years due to the Portuguese unfavorable socioeconomic context and the lack of family doctors. In 2017, the Portuguese Association of General and Fa- mily Medicine (APMGF) developed technical and scientific research that ultimately typified a set of different clinical practice contexts. It considers the geographic and socioeconomic characteristics and a set of population-based indicators, adjusting the list size according to the population's specific needs. Such adjustments ensure health care services with better quality, safety, efficacy, and personalized to their features. In this paper, a brief review is made on this topic, focusing on the work developed by APMGF and its main results.

Improving the Tradeoff Between Error Correction and Detection of Concatenated Polar Codes

Concatenated polar codes under successive cancellation list (SCL) decoding have excellent error-correction performance. However, their expected error-detection capability becomes degraded, when we increase the list size of the SCL decoder in order to improve their error-correction performance. In this paper, we propose a configuration design scheme for the SCL decoder and a post-decoding validation check scheme in order to provide a better tradeoff between error-detection and error-correction performance. Firstly, a configuration of the SCL decoder is designed to improve its own error detection capability. Specifically, a part of dynamic frozen bits (also called parity-check bits) is used for path checking during SCL decoding rather than their original purpose of use, path pruning. Furthermore, the number of paths to be checked by the applied cyclic redundancy check (CRC) code is limited. Secondly, a new metric corresponding to the correlation between the received signal vector and the decoded one is presented to check the validity of the decoding result. These proposed schemes are analyzed to provide a proper configuration of the SCL decoder and determine a threshold for post-decoding validation check. Numerical results show that a better tradeoff between error correction and detection is achieved, compared with conventional schemes.

Uncertainty of Reconstruction With List-Decoding From Uniform-Tandem-Duplication Noise

We propose a list-decoding scheme for reconstruction codes in the context of uniform-tandem-duplication noise, which can be viewed as an application of the associative memory model to this setting. We find the uncertainty associated with $m>2$ strings (where a previous paper considered $m=2$) in asymptotic terms, where code-words are taken from an error-correcting code. Thus, we find the trade-off between the design minimum distance, the number of errors, the acceptable list size and the resulting uncertainty, which corresponds to the required number of distinct retrieved outputs for successful reconstruction. It is therefore seen that by accepting list-decoding one may decrease coding redundancy, or the required number of reads, or both.

Efficient Dynamic Group Signature Scheme with Verifier Local Revocation and Time-Bound Keys using Lattices

Revocation is an important feature of group signature schemes. Verifier Local Revocation (VLR) is a popular revocation mechanism which involves only verifiers in the revocation process. In VLR, a revocation list is maintained to store the information about revoked users. The verification cost of VLR based schemes islinearly proportional to the size of recvocation list. In many applications, the size of revocation list grows with time, which makes the verification process expensive. In this paper, we propose a lattice based dynamic group signature using VLR and time bound keys to reduce the size of revocation list to speed up the verification process. In the proposed scheme, an expiration date is fixed for signing key of each group member, and verifiers can find out (at constantcost) if a signature is generated using an expired key. Hence revocation information of members who are revoked before signing key expiry date (premature revocation) are kept in revocation list, and other members are part of natural revocation. This leads to a significant saving on the revocation check by assuming natural revocation accounts for large fraction of the total revocation. This scheme also takes care of non-forgeability of signing key expiry date.

An improved path splitting strategy on successive cancellation list decoder for polar codes

The performance of the cyclic redundancy check aided successive cancellation list (CA-SCL) decoder for polar codes exceeds that of the Turbo codes and the Low Density Parity Check (LDPC) codes adopted in the World Interoperability for Microwave Access (WiMAX) proposal. However, CA-SCL decoder has a high computational complexity, resulting in a long time delay and high memory complexity. In order to alleviate this problem, an improved path splitting strategy on successive cancellation list (IPSS-SCL) decoder was proposed, which can significantly reduce the average list size. The influence of splitting on CA-SCL decoder was analysed at first and a new selective splitting criterion using the Gaussian approximation method was proposed according to the analysis. In addition, a path contraction mechanism based on the location estimation of the correct path was proposed to further reduce the average number of unnecessary candidate paths. Compared with existing path splitting strategies, simulation results show that the proposed IPSS-SCL decoding algorithm can reduce the average computational complexity significantly over the additive white Gaussian noise (AWGN) channel with almost no performance loss.

Crypt-DAC: Cryptographically Enforced Dynamic Access Control in the Cloud

Enabling cryptographically enforced access controls for data hosted in untrusted cloud is attractive for many users and organizations. However, designing efficient cryptographically enforced dynamic access control system in the cloud is still challenging. In this paper, we propose Crypt-DAC, a system that provides practical cryptographic enforcement of dynamic access control. Crypt-DAC revokes access permissions by delegating the cloud to update encrypted data. In Crypt-DAC, a file is encrypted by a symmetric key list which records a file key and a sequence of revocation keys. In each revocation, a dedicated administrator uploads a new revocation key to the cloud and requests it to encrypt the file with a new layer of encryption and update the encrypted key list accordingly. Crypt-DAC proposes three key techniques to constrain the size of key list and encryption layers. As a result, Crypt-DAC enforces dynamic access control that provides efficiency, as it does not require expensive decryption/re-encryption and uploading/re-uploading of large data at the administrator side, and security, as it immediately revokes access permissions. We use formalization framework and system implementation to demonstrate the security and efficiency of our construction.

Two-Stage Biometric Identification Systems Without Privacy Leakage

We study two-stage biometric identification systems that allow authentication without privacy leakage. In the enrollment phase, secret keys and two layers of the helper data for each user are generated. Additional to the helper data and secret keys, we also introduce private keys in the systems. In the identification phase, an unknown but previously enrolled user is observed, and the user's private key is also presented to the system. The system firstly compares the user with the first layer helper database, outputs a list, and obtains a set of user indices. Then the system compares the observed user with the users in the set. Therefore, the identification procedure avoids an exhaustive search and only has to do a comparison with some part of the users in the system, which leads to a systematic reduction of the search complexity. Fundamental trade-offs among the identification rate, the secret key rate, the private key rate, the helper data rate, and the list size rate are derived in the imposed two-stage biometric identification systems without privacy leakage. Moreover, the obtained results show that a private key can boost the identification rate and the secret key rate, as well as preserve privacy.