Linear-time list recovery of high-rate expander codes

We show that expander codes, when properly instantiated, are high-rate list recoverable codes with linear-time list recovery algorithms. List recoverable codes have been useful recently in constructing efficiently list-decodable codes, as well as explicit constructions of matrices for compressive sensing and group testing. Previous list recoverable codes with linear-time decoding algorithms have all had rate at most 1/2; in contrast, our codes can have rate $1 - \epsilon$ for any $\epsilon > 0$. We can plug our high-rate codes into a construction of Meir (2014) to obtain linear-time list recoverable codes of arbitrary rates, which approach the optimal trade-off between the number of non-trivial lists provided and the rate of the code. While list-recovery is interesting on its own, our primary motivation is applications to list-decoding. A slight strengthening of our result would implies linear-time and optimally list-decodable codes for all rates, and our work is a step in the direction of solving this important problem

Write-isolated memories (WIMs)

AbstractA write-isolated memory (WIM) is a binary storage medium on which no change of two consecutive positions is allowed when updating the information stored. We prove that the optimal rate for writing on a WIM is log2(1+5)2=0.69. We give asymptotic constructions achieving 0.6

Generalized low-density codes with BCH constituents for full-diversity near-outage performance

Comunicació presentada en el International Symposium on Information Theory (ISIT '08), celebrat els dies 6, 7, 8, 9, 10 i 11 de juliol de 2008 a Toronto (Ontario, Canadà), organitzat per Institute of Electrical and Electronics Engineers (IEEE).A new graph-based construction of generalized low density codes (GLD-Tanner) with binary BCH constituents is described. The proposed family of GLD codes is optimal on block erasure channels and quasi-optimal on block fading channels. Optimality is considered in the outage probability sense. A/nclassical GLD code for ergodic channels (e.g., the AWGN channel,/nthe i.i.d. Rayleigh fading channel, and the i.i.d. binary erasure channel) is built by connecting bitnodes and subcode nodes via a unique random edge permutation. In the proposed construction of full-diversity GLD codes (referred to as root GLD), bitnodes are divided into 4 classes, subcodes are divided into 2 classes, and finally both sides of the Tanner graph are linked via 4 random edge permutations. The study focuses on non-ergodic channels with two states and can be easily extended to channels with 3 states or more.The work of Ezio Biglieri was supported by the STREP project "DA/nVINCI" within the 7th FP of the European Commission

Full-diversity product codes for block erasure and block fading channels

Comunicació presentada en el Information Theory Workshop (ITW '08), celebrat els dies 5, 6, 7, 8 i 9 de maig de 2008 a Porto (Portugal), organitzat per l’Institute of Electrical and Electronics Engineers (IEEE).We show how to build full-diversity product codes under both iterative encoding and decoding over non-ergodic channels, in presence of block erasure and block fading. The concept of a rootcheck or a root subcode is introduced by generalizing the same principle recently invented for low-density parity-check codes. We also describe some channel related graphical properties of the new family of product codes, a family/nreferred to as root product codes.The work of Ezio Biglieri was supported by the STREP project "DA/nVINCI" within the 7th FP of the European Commission