Adaptive Linear Programming Decoding of Polar Codes

Polar codes are high density parity check codes and hence the sparse factor graph, instead of the parity check matrix, has been used to practically represent an LP polytope for LP decoding. Although LP decoding on this polytope has the ML-certificate property, it performs poorly over a BAWGN channel. In this paper, we propose modifications to adaptive cut generation based LP decoding techniques and apply the modified-adaptive LP decoder to short blocklength polar codes over a BAWGN channel. The proposed decoder provides significant FER performance gain compared to the previously proposed LP decoder and its performance approaches that of ML decoding at high SNRs. We also present an algorithm to obtain a smaller factor graph from the original sparse factor graph of a polar code. This reduced factor graph preserves the small check node degrees needed to represent the LP polytope in practice. We show that the fundamental polytope of the reduced factor graph can be obtained from the projection of the polytope represented by the original sparse factor graph and the frozen bit information. Thus, the LP decoding time complexity is decreased without changing the FER performance by using the reduced factor graph representation.Comment: 5 pages, 8 figures, to be presented at the IEEE Symposium on Information Theory (ISIT) 201

Error Characterization, Channel Modeling and Coding for Flash Memories

NAND Flash memories have become a widely used non-volatile data storage technology and their application areas are expected to grow in the future with the advent of cloud computing, big data and the internet-of-things. This has led to aggressive scaling down of the NAND flash memory cell feature sizes and also increased adoption of flash memories with multiple cell levels to increase the data storage density. These factors have adversely affected the reliability of flash memories.In this dissertation, our main goal is to perform detailed characterization of the errors that occur in multi-level cell (MLC) flash memories and develop novel mathematical channel models that better reflect the measured error characteristics than do current models. The channel models thus developed are applied to error correcting code (ECC) frame error rate (FER) performance estimation in MLC flash memories and to estimating the flash memory channel capacity as represented by the channel models. We also utilize the characterization of inter-cell interference (ICI) errors to evaluate the performance of constrained coding schemes that mitigate ICI and improve the reliability of flash memories.In Chapter 5, which is self-contained, we propose and study modifications to adaptive linear programming decoding techniques applied to decoding polar codes. We also propose a reduced complexity representation of the polar code sparse factor graph, resulting in time complexity improvements in the adaptive LP decoder