Small List Size Research Articles

On Tail-Biting Polarization-Adjusted Convolutional (TB-PAC) Codes and Small-Sizes List Decoding

Polarization-adjusted convolutional (PAC) coding is a good concatenation of convolutional codes and polar codes. For short block-length codes ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N\leq 128$ </tex-math></inline-formula> ), PAC codes with a sequential decoding or a list decoding with large list-sizes ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L\geq 128$ </tex-math></inline-formula> ) can achieve better block-error-rate (BLER) performance than polar codes with CRC-aided list decoding. However, the PAC codes have no BLER performance advantage when the list decoding is with small list-sizes ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L\leq 8$ </tex-math></inline-formula> ). In this letter, tail-biting PAC (TB-PAC) coding is proposed, in which tail-biting convolutional pre-transformation is applied. A multi-round list decoding with small list-sizes is provided for TB-PAC codes, in which an early-stopping method is designed to control the number of rounds. In each round, the tail-biting bits are assigned various initial path-values and also used as a check at the end, which helps the correct path be distinguishable. The proposed small-sizes list decoding can help the TB-PAC codes achieve much better BLER performance than the polar/PAC codes.

How do the working lives of general practitioners in rural areas compare with elsewhere in Scotland? Cross-sectional analysis of the Scottish School of Primary Care National GP Survey.

Like many countries around the world, Scotland faces a shortage of general practitioners (GPs) due to both recruitment and retention issues. Such workforce shortages are of particular concern in rural areas. There are many reasons why GPs are leaving general practice; however, satisfaction with working life is an important predictor of GP retention. It is important, therefore, to understand working life satisfaction of rural GPs. The purpose of this study was to compare the working lives and intentions to reduce work participation of rural GPs and GPs working elsewhere in Scotland. This study was a quantitative analysis of survey data from the Scottish School of Primary Care national working lives survey. GPs were classified as working in 'non-rural' or 'rural' practices based on the Scottish Government's rural binary classification system, and were compared using univariate and multivariate statistical analysis on four domains of working lives: job satisfaction, job stressors, positive and negative job attributes, and four intentions to reduce work participation: reducing working hours, working abroad, leaving direct patient care and leaving medical work entirely. A total of 2465 GPs returned the survey, giving a response rate of 56%. Three-hundred and forty seven GPs who returned the survey worked in practices in rural areas (14.1%). Rural GPs were more likely to do out-of-hours work (p<0.001), to have worked in their practice for fewer years (p=0.014), to work in single-GP partnerships (p<0.001), and to work in practices with smaller list sizes (p<0.001), than GPs in non-rural settings. Compared with GPs elsewhere, rural GPs reported higher mean job satisfaction (5.23 v 5.39, respectively; p<0.005), lower mean job stressors (3.58 v 3.29; p<0.001) and lower mean negative job attributes (4.08 vs 3.78; p<0.001). These differences remained highly significant after controlling for potential confounders (age, gender and the differences in work practices shown above). In regression analysis, a significant interaction was found between gender and rurality for job satisfaction (p=0.008), which indicated that rural female GPs' higher job satisfaction mainly accounted for rural GPs' increased job satisfaction. No significant interaction was found between gender and rurality for the other domains of working lives. Compared with GPs elsewhere, however, rural GPs were more likely to intend to work abroad (mean 1.39 v 1.55; p=0.013) and leave medical work entirely within 5 years (mean 2.15 v 2.36; p=0.039). These intentions remained significant after controlling for potential confounders. No significant interaction was found between gender and rurality for variables for intentions to reduce work participation. Rural GPs in Scotland are more satisfied with their working lives than GPs working elsewhere in Scotland, which is mainly due to higher job satisfaction in female GPs in rural areas. Despite this, rural GPs as a whole have a higher intention to leave their job in the next 5 years than their non-rural counterparts. Although some of these differences are small, they may signal serious implications for the future care of patients in rural areas and require further research to understand the drivers of this.

Optimal Rate List Decoding over Bounded Alphabets Using Algebraic-geometric Codes

We give new constructions of two classes of algebraic code families that are efficiently list decodable with small output list size from a fraction 1-R-ε of adversarial errors, where R is the rate of the code, for any desired positive constant ε. The alphabet size depends only ε and is nearly optimal. The first class of codes are obtained by folding algebraic-geometric codes using automorphisms of the underlying function field. The second class of codes are obtained by restricting evaluation points of an algebraic-geometric code to rational points from a subfield . In both cases, we develop a linear-algebraic approach to perform list decoding, which pins down the candidate messages to a subspace with a nice “periodic” structure. To prune this subspace and obtain a good bound on the list size, we pick subcodes of these codes by pre-coding into certain subspace-evasive sets that are guaranteed to have small intersection with the sort of periodic subspaces that arise in our list decoding. We develop two approaches for constructing such subspace-evasive sets. The first is a Monte Carlo construction of hierearchical subspace-evasive (h.s.e.) sets that leads to excellent list size but is not explicit. The second approach exploits a further ultra-periodicity of our subspaces and uses a novel construct called subspace designs , which were subsequently constructed explicitly and also found further applications in pseudorandomness. To get a family of codes over a fixed alphabet size, we instantiate our approach with algebraic-geometric codes based on the Garcia–Stichtenoth tower of function fields. Combining this with pruning via h.s.e. sets yields codes list-decodable up to a 1-R-ε error fraction with list size bounded by O (1/ε), matching the existential bound for random codes up to constant factors. Further, the alphabet size can be made exp ( Õ (1/ε 2 )), which is not much worse than the lower bound of exp (Ω (1/ε)). The parameters we achieve are thus quite close to the existential bounds in all three aspects (error-correction radius, alphabet size, and list size) simultaneously. This construction is, however, Monte Carlo and the claimed list-decoding property only holds with high probability. Once the code is (efficiently) sampled, the encoding/decoding algorithms are deterministic with a running time O _ε ( N c ) for an absolute constant c , where N is the code’s block length. Using subspace designs instead for the pruning, our approach yields the first deterministic construction of an algebraic code family of rate R with efficient list decoding from 1-R-ε fraction of errors over an alphabet of constant size exp (Õ(1/ε 2 )). The list-size bound is upper bounded by a very slowly growing function of the block length N ; in particular, it is at most O(log ( r ) N ) (the r th iterated logarithm) for any fixed integer r . The explicit construction avoids the shortcoming of the Monte Carlo sampling at the expense of a slightly worse list size.

Post-Processing for CRC-Aided Successive Cancellation List Decoding of Polar Codes

In this letter, three post-processing schemes for cyclic redundancy check (CRC-)aided successive cancellation list (CA-SCL) decoding are presented for polar codes. The re-decoding based on our post-processing schemes can effectively alleviate both the channel and decision errors encountered via CA-SCL decoding. Simulation results show that our schemes perform better than conventional re-decoding schemes and can be incorporated into a polar decoder that has a small list size to achieve a performance that is expected for a large list size.

Bridging the Gap Between MMSE-DFE and Optimal Detection of MIMO Systems

In this paper, we propose a novel low-complexity, near-optimal soft-input soft-output detector for $\text {N}\times \text {M}$ multiple-input multiple-output (MIMO) systems. Our algorithm is based on the combination of minimum mean square error decision feedback equalization (MMSE-DFE) and conditional optimization. In a round-robin fashion, one symbol is detected using exhaustive search in such a way that all $\text {N}\times (\text {M}-1)$ submatrices of the baseband channel matrix are considered and the one with the best metric is chosen. This search over all columns of the channel matrix, which can be performed in parallel, has the advantages of improving the performance of the hard-output version of the detector, and refining the list of candidates for efficient implementation of the soft-output detector for MIMO systems with error correcting codes. In particular, it is shown that the error performance of the soft-output system is comparable to that of the list sphere decoder (LSD) but with much smaller list size, and hence smaller complexity than the latter. We also analyze the performance and complexity of the proposed algorithm and discuss different techniques to further reduce its complexity without affecting the performance. Finally, the obtained theoretical results are validated via simulations.

A Multimode Area-Efficient SCL Polar Decoder

Polar codes are of great interest, since they are the first provably capacity-achieving forward error correction codes. To improve throughput and to reduce decoding latency of polar decoders, maximum likelihood (ML) decoding units are used by successive cancellation list (SCL) decoders as well as SC decoders. This paper proposes an approximate ML (AML) decoding unit for SCL decoders first. In particular, we investigate the distribution of frozen bits of polar codes designed for both the binary erasure and additive white Gaussian noise channels, and take advantage of the distribution to reduce the complexity of the AML decoding unit, improving the throughput-area efficiency of the SCL decoders. Furthermore, a multimode (MM) SCL decoder with variable list sizes and parallelism is proposed. If high throughput or small latency is required, the decoder decodes multiple received words in parallel with a small list size. However, if error performance is of higher priority, the MM-SCL decoder switches to a serial mode with a bigger list size. Therefore, the MM-SCL decoder provides a flexible tradeoff between latency, throughput, and error performance at the expense of small overhead. Hardware implementation and synthesis results show that our polar decoders not only have a better throughput-area efficiency but also easily adapt to different communication channels and applications.

Exploration of population and practice characteristics explaining differences between practices in the proportion of hospital admissions that are emergencies.

BackgroundEmergency (unscheduled) and elective (scheduled) use of secondary care varies between practices. Past studies have described factors associated with the number of emergency admissions; however, high quality care of chronic conditions, which might include increased specialist referrals, could be followed by reduced unscheduled care. We sought to characterise practices according to the proportion of total hospital admissions that were emergency admissions, and identify predictors of this proportion.MethodThe study included 229 general practices in Leicestershire, Northamptonshire and Rutland, England. Publicly available data were obtained on scheduled and unscheduled secondary care usage, and on practice and patient characteristics: age; gender; list size; observed prevalence, expected prevalence and the prevalence gap of coronary heart disease, hypertension and stroke; deprivation; headcount number of GPs per 1000 patients; total and clinical quality and outcomes framework (QOF) scores; ethnicity; proportion of patients seen within two days by a GP; proportion able to see their preferred GP. Using the proportion of admissions that were emergency admissions, seven categories of practices were created, and a regression analysis was undertaken to identify predictors of the proportion.ResultsIn univariate analysis, practices with higher proportions of admissions that were emergencies tended to have fewer older patients, higher proportions of male patients, fewer white patients, greater levels of deprivation, smaller list sizes, lower recorded prevalence of coronary heart disease and stroke, a bigger gap between the expected and recorded levels of stroke, and lower proportions of total and clinical QOF points achieved. In the multivariate regression, higher deprivation, fewer white patients, more male patients, lower recorded prevalence of hypertension, more outpatient appointments, and smaller practice list size were associated with higher proportions of total admissions being emergencies.ConclusionIn monitoring use of secondary care services, the role of population characteristics in determining levels of use is important, but so too is the ability of practices to meet the demands for care that face them. The level of resources, and the way in which available resources are used, are likely to be key in determining whether a practice is able to meet the health care needs of its patients.

A Lattice-Reduction-Aided Max-Log List Demapper for Coded MIMO Receivers

The max-log list demapper has been widely employed in the implementations of a coded multiple-input-multiple-output (MIMO) receiver, where only a candidate list of signal vectors is examined in the likelihood-ratio calculation to reduce complexity. Traditionally, the candidate list is generated in the original-lattice domain, which, unfortunately, results in severe degradation in the performance of the demapper if the channel is in ill-condition. In this paper, two new lattice-reduction-aided max-log list demappers are proposed, i.e., one for an iterative receiver and the other for a noniterative receiver. With similar complexity, the proposed demappers provide significant gains over existing demappers, particularly for the cases with a small list size and/or under a spatially correlated channel, due to the new algorithms for the generation of the candidate list. In addition, for the iterative receiver, the prior information coming out of the decoder is exploited to lower the complexity of the demapper.

Signal Vector Based List Detection for Spatial Modulation

In this Letter, a list variant of the signal vector based detection (SVD) for the spatial modulation system is proposed. In the proposed list SVD, the transmit antenna index detection is first performed and a list of the best candidates survives, then the constellation symbol detection is performed conditioned on the candidate list. Simulation results show that the proposed list SVD can approach the optimal detection performance with a small list size, i.e., an excellent performance-complexity tradeoff is achieved.

Progressive List-Enlarged Algebraic Soft Decoding of Reed-Solomon Codes

A progressive algebraic soft decoding algorithm is proposed for Reed-Solomon (RS) codes, aiming to reduce the computational complexity. The decoding starts with a small initial factorization output list size (OLS), then updates the OLS progressively leading to an incremental interpolation. Decoding will terminate either when the output contains a codeword that can be identified as the most likely one or the predefined maximal OLS is reached. The algorithm can adjust the decoding parameter according to the quality of the received information, optimizing its complexity to the minimal but necessary level.

Characteristics of general practices associated with emergency admission rates to hospital: a cross-sectional study

ObjectivesTo identify characteristics of general practices associated with emergency hospital admission rates, and determine whether levels of performance and patient reports of access are associated with admission rates.DesignA cross-sectional study.SettingTwo...

Identifying Poorly Performing General Practices in England: A Longitudinal Study Using Data from the Quality and Outcomes Framework

to determine the characteristics of general practices which perform poorly in terms of Quality and Outcome (QOF) performance indicators in England's NHS. retrospective, four year longitudinal study, 2005 to 2008. Data were obtained from 8515 practices (99% of practices in England) in year 1, 8264 (98%) in year 2, 8192 (98%) in year 3 and 8256 (99%) in year 4. QOF performance scores; social deprivation (IMD-2007) and ethnicity from the 2001 national census; general practice characteristics. we identified a cohort of 212 (2.7%) practices which remained in the lowest decile for total QOF scores in the four years following the introduction of the QOF. A total of 705,386 patients were registered at these practices in year 4. These practices were more likely to be singlehanded (odds ratio [OR], 13.8), non-training practices (OR, 3.9) and located in deprived areas (OR, 2.6; most vs least deprived quintiles). General practitioners (GPs) in these practices were more often aged ≥ 65 years or more (OR, 7.3; mean GP age ≥ 65 years vs <45 years), male (OR 2.0), UK qualified (OR 2.0) with small list sizes (OR 3.2; list size <1000 vs 1500-2000 patients). We identified individual QOF indicators which were poorly achieved. The reported prevalence of most chronic diseases was lower in the poorly performing cohort. a small minority of practices have remained poor performers in terms of measurable performance indicators over a four-year period. The strongest predictors of poor QOF performance were singlehanded and small practices, and practices staffed by elderly GPs.

Iterative Joint Detection, Decoding, and Channel Estimation in Turbo-Coded MIMO-OFDM

An iterative receiver for a multiple-input-multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) system is considered to jointly decode the transmitted bits and estimate the channel state. The receiver consists of a list detector, a turbo decoder, and a channel estimator that is based on the space-alternating generalized expectation-maximization (SAGE) algorithm. This paper proposes a way to improve the convergence of the iterative detection and decoding by using a priori information to also recalculate the candidate list, aside from the log-likelihood ratios (LLRs) of the coded bits. A new list parallel interference cancellation (PIC) detector is derived to approximate an a posteriori probability (APP) algorithm with reduced complexity and minimal losses of performance. Furthermore, the organization of spectrally efficient decision-directed (DD) SAGE channel estimation under a constrained number of detector-decoder iterations is optimized by computer simulations, and the SAGE algorithm itself is modified for nonconstant envelope constellations. The list recalculation is shown to improve convergence. It is also shown that the list PIC detector with good initialization outperforms the K-best list sphere detector (LSD) in the case of small list sizes, whereas the complexities of the algorithms are of the same order. Despite the low preamble density and fast-fading channel, the proposed iterative receiver shows robust performance.

Convergence Behavior Analysis and Detection Switching for the Iterative Receiver of MIMO-BICM Systems

The iterative receivers with a list sphere detector (LSD) and a parallel interference canceller (PIC) for multiple-input-multiple-output (MIMO) bit-interleaved coded modulation systems are considered. The convergence behaviors of these iterative detection and decoding schemes are analyzed via variance transfer (VT) functions. For ergodic channels, we show that the waterfall region of an iterative receiver can be predicted using a variance exchange graph. For slow fading channels, we show that the frame error rate of the iterative receiver is essentially limited by the early interception rate of the iterative receiver. Moreover, we show that the VT function of an LSD with a small list size is superior to that of a PIC at a high-variance region, whereas it is worse than that of a PIC at a low-variance region. Then, we propose a detection switching (DSW) approach for the iterative receiver and present a DSW criterion based on cross entropy. By applying the DSW, we show that the near-capacity performance can be achieved with a significantly reduced complexity.

Iterative Reconfigurable Tree Search Detection of MIMO Systems

This paper is concerned with reduced-complexity detection, referred to as iterative reconfigurable tree search (IRTS) detection, with application in iterative receivers for multiple-input multiple-output (MIMO) systems. Instead of the optimum maximum a posteriori probability detector, which performs brute force search over all possible transmitted symbol vectors, the new scheme evaluates only the symbol vectors that contribute significantly to the soft output of the detector. The IRTS algorithm is facilitated by carrying out the search on a reconfigurable tree, constructed by computing the reliabilities of symbols based on minimum mean-square error (MMSE) criterion and reordering the symbols according to their reliabilities. Results from computer simulations are presented, which proves the good performance of IRTS algorithm over a quasistatic Rayleigh channel even for relatively small list sizes.

Improving access for patients – a practice manager questionnaire

BackgroundThe administrative and professional consequences of access targets for general practices, as detailed in the new GMS contract, are unknown. This study researched the effect of implementing the access targets of the new GP contract on general practice appointment systems, and practice manager satisfaction in a UK primary health care setting.MethodsA four-part postal questionnaire was administered. The questionnaire was modified from previously validated questionnaires and the findings compared with data obtained from the Western Health and Social Services Board (WHSSB) in N Ireland. Practice managers from the 59 general practices in the WHSSB responded to the questionnaire.ResultsThere was a 94.9% response rate. Practice managers were generally satisfied with the introduction of access targets for patients. Some 57.1% of responding practices, most in deprived areas (Odds ratio 3.13 -95% CI 1.01 – 9.80, p = 0.0256) had modified their appointment systems. Less booking flexibility was reported among group practices (p = 0.006), urban practices (p < 0.001) and those with above average patient list sizes (p < 0.001). Receptionists had not received training in patient appointment management in a quarter of practices. Practices with smaller list sizes were more likely than larger ones to utilise nurses in seeing extra patients (p = 0.007) or to undertake triage procedures (p = 0.062).ConclusionThe findings demonstrated the ability of general practices within the WHSSB to adjust to a demanding component of the new GP contract. Issues relating to the flexibility of patient appointment booking systems, receptionists' training and the development of the primary care nursing role were highlighted by the study.

How do general practitioners choose their practice? Preferences for practice and job characteristics.

To investigate the strength of preferences for practice and job characteristics among recently appointed general practitioners (GPs) in south-east England. Conjoint analysis based on a postal questionnaire survey of all 293 GPs who joined a new practice between April 1997 and March 1998 in London, Essex and Hertfordshire. GPs were presented with descriptions of practices in pairs, which varied systematically for key characteristics, and asked to indicate their preferred practice in each pair. The response rate was 58.7%. The most important influence on GPs' choice of practice was aversion to location in an area of high deprivation. They were more likely to choose a practice that: had an extended primary health care team; offered opportunities to develop outside interests; and offered them higher income, shorter working hours and smaller list sizes. The model generated estimates of the strength of these preferences. For example, GPs would require additional income of just over 5000 Pounds per annum to work in an area with a high proportion of deprived patients. Potential policy interventions to attract GPs to under-served areas include increasing their level of remuneration, providing opportunities to develop outside interests and ensuring that practices have a primary health care team.

Diffusion of new drugs in Danish general practice.

There is a large variation in implementing research findings in clinical practice. We examined whether the concept of early or late adopters is universal for the diffusion of all new drugs, and whether it is associated with non-scientific factors in general practice. We identified all prescriptions for five new drugs from the population-based prescription database in North Jutland County, Denmark (490000 inhabitants) from 1993 to 1996, and calculated the period from release of the drugs to the issuing of the first prescription by each GP. Logistic regression was performed to predict early or late prescribing from physician characteristics, practice activity and the number of prescriptions, adjusted for age and sex. The distributions of the diffusion time of the drugs by 95 solo practitioners were asymmetrical, with a long upper tail representing the late prescribers. The shape and slope of the diffusion curve were highly drug dependent. There was poor agreement of the three adopter categories (early, intermediate and late prescribers) between the five drugs (kappa < 0.35), but being a late prescriber was the most consistent condition. Late prescribing of tramadol, compared with intermediate prescribing, was associated with female physicians (odds ratio (OR) 5.7; 95% CI 1.5-21.3), smaller list size (OR 0.1; 95% CI 0.0-0.8), a strong general restrictive attitude to pharmacotherapy (OR 0.07; 95% CI 0.01-0.68) and a tendency to lower diagnostic activity per patient (OR 0.4; 95% CI 0.1-1.9). The slope and shape of the diffusion curve are both dependent on physician and drug characteristics, but late prescribers share some common characteristics.

A total audit of preventive procedures in 45 practices caring for 430,000 patients.

To develop and report the results of a system of audit of computer records in general practice. A retrospective audit of records in practices using the same computer system. Information about recorded preventive procedures was collected by sending the same audit program to each practice on floppy disk. Other characteristics of the practices were determined by postal questionnaire. Forty five general practices, widely distributed in England and Wales. All 430,901 patients registered with the practices. Within each practice the percentage of patients in specified age groups for whom certain preventive procedures were recorded as having been carried out. These measures were analysed in relation to practice characteristics. Practice characteristics and recording rates for preventive procedures varied over a wide range. Recording rates were higher in practices with computer terminals on every doctor's desk. Only one practice achieved the new contract target of 90% coverage for recorded primary immunisations, and fewer than two thirds recorded 80% coverage for cervical cytology in the past five years. Practices holding clinics did no better than those without. Smaller partnerships and smaller doctors' list sizes were associated with better performance. Centrally programmed audit of computerised records is a feasible method of providing data on a regular basis for epidemiological purposes and for performance review. The fact that practices with smaller list sizes had higher levels of recorded preventive care suggests that the trend towards larger lists promoted by the new contract might militate against the intended effect of better preventive care.

List size, screening methods, and other characteristics of practices in relation to preventive care.

Twenty eight practices carried out a review of patient records for information about preventive procedures on two occasions in 1980 and 1982. We have now undertaken a survey of certain characteristics of the practices in an attempt to demonstrate features associated with effective preventive care. Significant favourable factors are a small list size, the setting up of a formal screening programme for cervical cytology and measuring blood pressure, and few registered patients in social classes IV and V. More successful practices also tend to be training practices, have principals with higher qualifications, and have developed good records organization. Opportunistic screening for cervical cytology and measuring blood pressure was not shown to be more effective than no policy of screening at all.