EXTREMAL ABSORBING SETS IN LOW-DENSITY PARITY-CHECK CODES

Absorbing sets are combinatorial structures in the Tanner graphs of low-density parity-check (LDPC) codes that have been shown to inhibit the high signal-to-noise ratio performance of iterative decoders over many communication channels. Absorbing sets of minimum size are the most likely to cause errors, and thus have been the focus of much research. In this paper, we determine the sizes of absorbing sets that can occur in general and left-regular LDPC code graphs, with emphasis on the range of b for a given a for which an (a, b)-absorbing set may exist. We identify certain cases of extremal absorbing sets that are elementary, a particularly harmful class of absorbing sets, and also introduce the notion of minimal absorbing sets which will help in designing absorbing set removal algorithms

Federal Research, Additional Actions Needed to Improve Public Access to Research Results: Report to Congressional Requesters [with Responses from Federal Agencies]

Why GAO Did This Study Research and development helps catalyze breakthroughs that improve the overall health and wellbeing of our society. Federal research and development expenditures averaged about $135 billion annually for fiscal years 2015 to 2017. According to OSTP, providing free public access to federally funded research results can improve both the impact and accountability of this important federal investment. In February 2013, OSTP directed federal agencies with more than$100 million in annual research and development expenditures to develop a plan to support increased public access to the results of federally funded research. GAO was asked to examine public access to federally funded research results. This report examines the extent of agencies’ (1) progress implementing plans to increase public access to federally funded research results and (2) coordination on public access plan implementation. GAO administered a questionnaire to 19 federal agencies selected based on annual research and development expenditure amounts, among other criteria; reviewed agency documents; and interviewed officials from 11 agencies, OSTP, and 21 stakeholder organizations. What GAO Found The 19 agencies that GAO reviewed have made progress implementing their plans to increase public access to federally funded research results (publications and data), as called for in a 2013 Office of Science and Technology Policy (OSTP) memorandum. However, some agencies have not fully implemented some aspects of their plans, in particular those related to data access and mechanisms to ensure researchers comply with public access requirements. Agencies are coordinating with each other and with nonfederal stakeholders to implement public access plans, including through an interagency group led by OSTP and five other agencies. However, the group has not fully implemented selected leading practices identified by GAO that can enhance and sustain interagency collaboration, such as defining and articulating common outcomes. For example, according to OSTP staff, key outcomes have not yet been decided upon. Agency officials and stakeholders identified several challenges to implementing public access plans that interagency coordination might help them address, such as • Absence of common standards in several areas; • Measuring effectiveness of public access plan implementation; and • Balancing providing public access with safeguarding sensitive information. By taking steps to fully implement relevant leading collaboration practices, the interagency group could help agencies better marshal their collective efforts to address common challenges to public access plan implementation. What GAO Recommends GAO is making 37 recommendations to 16 agencies to promote full and effective implementation of agency public access plans. For example, GAO recommends that OSTP and 5 agencies leading a public access interagency group take steps to fully implement selected leading collaboration practices. Of the 16 agencies, 15 agreed with GAO’s recommendations while 1 (OSTP) disagreed. GAO continues to believe the recommendation to OSTP is warranted

Theory and Design of Graph-Based Codes for Improved Iterative and Windowed Decoding

Mathematical coding theory addresses the problem of transmitting information reliably and efficiently across noisy channels. This dissertation focuses on graph-based codes, which are codes whose representation, encoding, and/or decoding can be visualized using a sparse graph. We examine a variety of problems for understanding and improving low density parity check (LDPC) codes. While iterative decoding is efficient on these graph-based codes, it is also sub-optimal and sometimes fails to output a codeword. This failure is caused by combinatorial structures in the graph called absorbing sets. We obtain bounds on the sizes of absorbing sets that can exist in certain classes of codes and give a novel connection that links absorbing sets to cosets and syndromes. This connection is used to design an innovative absorbing set search algorithm. In addition, we consider spatially-coupled LDPC (SC-LDPC) codes, a type of code amenable to windowed decoding, which allows information to be decoded sequentially rather than all at once. We examine the inherent properties of the code within a decoding window, which we call a window code. We provide foundational results on the existence and properties of SC-LDPC codes with cycle-free window codes. We provide distance relationships between an SC-LDPC code and its window codes and show that SC-LDPC codes with maximum distance separable (MDS) window codes have bad code rates

Federal Research, Additional Actions Needed to Improve Public Access to Research Results: Report to Congressional Requesters [with Responses from Federal Agencies]

Why GAO Did This Study Research and development helps catalyze breakthroughs that improve the overall health and wellbeing of our society. Federal research and development expenditures averaged about $135 billion annually for fiscal years 2015 to 2017. According to OSTP, providing free public access to federally funded research results can improve both the impact and accountability of this important federal investment. In February 2013, OSTP directed federal agencies with more than$100 million in annual research and development expenditures to develop a plan to support increased public access to the results of federally funded research. GAO was asked to examine public access to federally funded research results. This report examines the extent of agencies’ (1) progress implementing plans to increase public access to federally funded research results and (2) coordination on public access plan implementation. GAO administered a questionnaire to 19 federal agencies selected based on annual research and development expenditure amounts, among other criteria; reviewed agency documents; and interviewed officials from 11 agencies, OSTP, and 21 stakeholder organizations. What GAO Found The 19 agencies that GAO reviewed have made progress implementing their plans to increase public access to federally funded research results (publications and data), as called for in a 2013 Office of Science and Technology Policy (OSTP) memorandum. However, some agencies have not fully implemented some aspects of their plans, in particular those related to data access and mechanisms to ensure researchers comply with public access requirements. Agencies are coordinating with each other and with nonfederal stakeholders to implement public access plans, including through an interagency group led by OSTP and five other agencies. However, the group has not fully implemented selected leading practices identified by GAO that can enhance and sustain interagency collaboration, such as defining and articulating common outcomes. For example, according to OSTP staff, key outcomes have not yet been decided upon. Agency officials and stakeholders identified several challenges to implementing public access plans that interagency coordination might help them address, such as • Absence of common standards in several areas; • Measuring effectiveness of public access plan implementation; and • Balancing providing public access with safeguarding sensitive information. By taking steps to fully implement relevant leading collaboration practices, the interagency group could help agencies better marshal their collective efforts to address common challenges to public access plan implementation. What GAO Recommends GAO is making 37 recommendations to 16 agencies to promote full and effective implementation of agency public access plans. For example, GAO recommends that OSTP and 5 agencies leading a public access interagency group take steps to fully implement selected leading collaboration practices. Of the 16 agencies, 15 agreed with GAO’s recommendations while 1 (OSTP) disagreed. GAO continues to believe the recommendation to OSTP is warranted