Spatially Coupled Sparse Codes On Graphs - Theory, Practice & Extensions
Investigator(s): Daniel Costello Jr. and Thomas Fuja (Co-PI)
Sponsor: National Science Foundation
Timeframe: 5/12 to 4/15
Abstract: This research investigates a new approach to protecting the reliability of digital communication and digital storage systems. This approach takes advantage of recent work (by the research team and others) that formulates the "encoding" and "decoding" of data in terms of a novel graphical representation; this formulation has several advantages over existing techniques for insuring data integrity, including better performance at very low power and the absence of an 'error floor', i.e., the ability to consistently (and significantly) lower the decoded error probability with incremental expenditures of power. The ultimate goal of the research is more reliable delivery of digital data, text, computer files, speech and audio signals, video, etc. - using devices that require less power (and thus have longer battery life) and shorter processing delay.
More specifically, the research investigates the use of spatially coupled sparse codes - channel (error control) codes with a sparse parity check representation formed by coupling together a chain of small "protographs". This approach, which was pioneered by the research team in the context of terminated low-density parity check convolutional codes, has recently been shown to possess a unique combination of properties - iterative decoding performance that approaches channel capacity and minimum distance that grows linearly with block length - as the code size gets large. The research follows four tracks: (1) the design and analysis of low latency/memory decoding strategies; (2) decoded error probability performance guarantees; (3) the development and analysis of spatially coupled sparse codes with algebraic structure; and (4) the application of spatial coupling outside the immediate domain of channel coding, including cooperative diversity, compressed sensing, and multi-terminal source/channel coding.