Time-sharing vs. source-splitting in the Slepian-Wolf problem: error exponents analysis

We discuss two approaches for decoding at arbitrary rates in the Slepian-Wolf problem - time sharing and source splitting - both of which rely on constituent vertex decoders. We consider the error exponents for both schemes and conclude that source-splitting is more robust at coding at arbitrary rates, as the error exponent for time-sharing degrades significantly at rates near vertices. As a by-product of our analysis, we exhibit an interesting connection between minimum mean-squared error estimation and error exponents

Linear complexity universal decoding with exponential error probability decay

In this manuscript we consider linear complexity binary linear block encoders and decoders that operate universally with exponential error probability decay. Such scenarios may be relevant in wireless scenarios where probability distributions may not be fully characterized due to the dynamic nature of wireless environments. More specifically, we consider the setting of fixed length-to-fixed length near-lossless data compression of a memoryless binary source of unknown probability distribution as well as the dual setting of communicating on a binary symmetric channel (BSC) with unknown crossover probability. We introduce a new 'min-max distance' metric, analogous to minimum distance, that addresses the universal binary setting and has the same properties as that of minimum distance on BSCs with known crossover probability. The code construction and decoding algorithm are universal extensions of the 'expander codes' framework of Barg and Zemor and have identical complexity and exponential error probability performance

Towards practical minimum-entropy universal decoding

Minimum-entropy decoding is a universal decoding algorithm used in decoding block compression of discrete memoryless sources as well as block transmission of information across discrete memoryless channels. Extensions can also be applied for multiterminal decoding problems, such as the Slepian-Wolf source coding problem. The 'method of types' has been used to show that there exist linear codes for which minimum-entropy decoders achieve the same error exponent as maximum-likelihood decoders. Since minimum-entropy decoding is NP-hard in general, minimum-entropy decoders have existed primarily in the theory literature. We introduce practical approximation algorithms for minimum-entropy decoding. Our approach, which relies on ideas from linear programming, exploits two key observations. First, the 'method of types' shows that that the number of distinct types grows polynomially in n. Second, recent results in the optimization literature have illustrated polytope projection algorithms with complexity that is a function of the number of vertices of the projected polytope. Combining these two ideas, we leverage recent results on linear programming relaxations for error correcting codes to construct polynomial complexity algorithms for this setting. In the binary case, we explicitly demonstrate linear code constructions that admit provably good performance

A new source-splitting approach to the Slepian-Wolf problem

It is shown that achieving an arbitrary rate-point in the achievable region of the M-source Slepian-Wolf [1] problem may be reduced via a practical source-splitting transformation to achieving a corner point in a 2M − 1 source Slepian-Wolf problem. Moreover, each source must be split at most once. This approach extends the ideas introduced in [2] to a practical setting: it does not require common randomness shared between splitters and the decoders, the cardinality of each source split is strictly smaller than the original, and practical iterative decoding methods can achieve rates near the theoretical bound

Rate-splitting for the deterministic broadcast channel

We show that the deterministic broadcast channel, where a single source transmits to M receivers across a deterministic mechanism, may be reduced, via a rate-splitting transformation, to another (2M−1)-receiver deterministic broadcast channel problem where a successive encoding approach suffices. Analogous to rate-splitting for the multiple access channel and source-splitting for the Slepian-Wolf problem, all achievable rates (including non-vertices) apply. This amounts to significant complexity reduction at the encoder

On some new approaches to practical Slepian-Wolf compression inspired by channel coding

This paper considers the problem, first introduced by Ahlswede and Körner in 1975, of lossless source coding with coded side information. Specifically, let X and Y be two random variables such that X is desired losslessly at the decoder while Y serves as side information. The random variables are encoded independently, and both descriptions are used by the decoder to reconstruct X. Ahlswede and Körner describe the achievable rate region in terms of an auxiliary random variable. This paper gives a partial solution for the optimal auxiliary random variable, thereby describing part of the rate region explicitly in terms of the distribution of X and Y

Longevity perceptions in patients who have had their kidney transplant for 25 years or longer [abstract]

Survival of a renal transplant beyond 25 years is a relatively rare event with median length of graft survival 11 years. Numerous outcomes, but no studies have described longevity perceptions of individuals who have had their kidneys for 25 years or longer. The purpose of this qualitative study was to examine longevity perceptions of 19 renal transplant recipients who had their transplants for 25 years or longer. The question asked of the subjects was "To what do you attribute keeping your kidney for such a long time?" Appropriate institutional approval and human subjects during the study. The sample was obtained from an informal support group which includes only those who have had their kidney transplant for 25 years or longer. A semi interview was audio-taped and transcribed. Data sample consisted of 19 participants (7 male, 12 female) ranging in age from 43 to 67 years, with a mean age of 52.8 years (S.D. = 6.82). Transplants were performed between 26 and 36 years ago, with a mean of 30.7 years (S.D. = 3.2). Themes emerged included competence, autonomy, relatedness, faith, normalcy, and luck. The participants voiced statements of competence in the care of their kidney, autonomy in health decisions, and relatedness to support group member transplant games, and/or to the donor's family. Striving for a sense of normalcy, faith, and luck were also shared by the participants Michelle Matteson (Doctoral Candidate) RN, PhD (Postdoctoral Fellow) (Cynthia Russell RN, PhD) Sinclair School of Nursing Numerous studies have described predictors of poor renal transplant ceptions protection was followed semi-structured phone were examined using thematic analyses. The 7 participants

Low-Complexity Approaches to Slepian–Wolf Near-Lossless Distributed Data Compression

This paper discusses the Slepian–Wolf problem of distributed near-lossless compression of correlated sources. We introduce practical new tools for communicating at all rates in the achievable region. The technique employs a simple “source-splitting” strategy that does not require common sources of randomness at the encoders and decoders. This approach allows for pipelined encoding and decoding so that the system operates with the complexity of a single user encoder and decoder. Moreover, when this splitting approach is used in conjunction with iterative decoding methods, it produces a significant simplification of the decoding process. We demonstrate this approach for synthetically generated data. Finally, we consider the Slepian–Wolf problem when linear codes are used as syndrome-formers and consider a linear programming relaxation to maximum-likelihood (ML) sequence decoding. We note that the fractional vertices of the relaxed polytope compete with the optimal solution in a manner analogous to that observed when the “min-sum” iterative decoding algorithm is applied. This relaxation exhibits the ML-certificate property: if an integral solution is found, it is the ML solution. For symmetric binary joint distributions, we show that selecting easily constructable “expander”-style low-density parity check codes (LDPCs) as syndrome-formers admits a positive error exponent and therefore provably good performance

Contextual determinants of re-reporting for families receiving alternative response: A survival analysis in a Midwestern State

Differential response (DR) has been widely adopted in over 30 states to address shortcomings of the traditional approach to child maltreatment reports in complex family and case circumstances. However, despite continued evaluation efforts, evidence of the effectiveness of DR remains inconclusive. The current study aims to assess the impact of a DR program and potential predictors, including service match and number of family case workers, on maltreatment re-reports in a Midwestern state. The study utilized a randomized control trial and assigned eligible families to either the Alternative Response (AR) track or Traditional Response (TR) track. The enrollment was implemented in a phased rollout covering all counties in the state. Data were drawn from state child welfare administrative datasets and case worker surveys. The probability and time to re-reporting was calculated using survival analysis, while adjusting for case-level covariates. Prior ongoing case (HR = 3.24, p \u3c 0.001), high risk level (HR = 1.43, p \u3c 0.05), and having only one worker (HR = 1.92, p \u3c 0.001) serve the case were strong predictors of re-reporting. The effect of service match within each level of prior ongoing case (No, Yes) was also a significant predictor of re-reporting (p \u3c 0.05). AR had limited, but nonsignificant, impact on preventing re-reporting after adjusting for these factors, as there was no difference in terms of re-reporting between DR tracks. However, findings suggest that matching child welfare service with family needs is an important component of child welfare practice. Implications for DR policy and practice are discussed