Presence Of Erasures Research Articles

A family of codes with variable locality and availability

In this work we present a class of locally recoverable codes, i.e. codes where an erasure at a position P of a codeword may be recovered from the knowledge of the entries in the positions of a recovery set $$R_P$$ . The codes in the class that we define have availability, meaning that for each position P there are several distinct recovery sets. Also, the entry at position P may be recovered even in the presence of erasures in some of the positions of the recovery sets, and the number of supported erasures may vary among the various recovery sets.

Erasures versus errors in local decoding and property testing

AbstractWe initiate the study of the role of erasures in local decoding and use our understanding to prove a separation between erasure‐resilient and tolerant property testing. We first investigate local list‐decoding in the presence of erasures. We prove an analog of a famous result of Goldreich and Levin on local list‐decodability of the Hadamard code. Specifically, we show that the Hadamard code is locally list‐decodable in the presence of a constant fraction of erasures, arbitrarily close to 1, with list sizes and query complexity better than in the Goldreich–Levin theorem. We further study approximate locally erasure list‐decodable codes and use them to construct a property that is erasure‐resiliently testable with query complexity independent of the input length, , but requires queries for tolerant testing. We also investigate the general relationship between local decoding in the presence of errors and in the presence of erasures.

A Nonuniform-Quantized Successive Cancellation Decoding of Polar Codes Over AWGN Channels

Since polar codes are capacity-achieving codes, there have been various research works devoted to devising efficient implementation methods as well as improving error-correction performance. Since quantization is a critical implementation issue, in this paper, a nonuniform quantization method is proposed for the successive cancellation (SC) decoder of polar codes, which finds quantization boundary values based on the analysis of various quantization levels over the additive white Gaussian noise channel. Since low computational complexity, high reliability, and efficient memory management are required in the next-generation communication and memory systems, 2-4 bit precision levels are mainly considered in the proposed nonuniform quantization method. Depending on the presence of erasure, quantization levels are divided into three types, and the message alphabets and update rules are derived for each type. Also, a construction method of polar codes suitable for the proposed nonuniform-quantized SC decoder is proposed, which simultaneously determines the information set and the quantization boundary values based on the density evolution analysis and an upper bound of the block error probability. To determine quantization boundary values, a multivariate objective function is defined and an iterative coarse-to-fine search algorithm to minimize this objective function is proposed. In addition, a scaling method of quantizer output values is proposed when the number of quantization levels of quantizer is smaller than the number of quantization levels of decoder. Finally, simulation results confirm that the proposed nonuniform-quantized SC decoder shows better error-correction performance, lower decoding complexity, and higher memory efficiency compared to the best known uniform-quantized SC decoder.

“Error: No Such Entry”

“Error: No Such Entry”

Precompensation for anticipated erasures in LTI interpolation systems

This paper considers compensation of anticipated erasures in a discrete-time (DT) signal such that the desired interpolation can still be accomplished, with minimum error, through a linear time-invariant (LTI) filter. The algorithms presented may potentially be useful in the compensation of a fault in a digital-to-analog converter where samples are dropped at known locations prior to reconstruction. Four algorithms are developed. The first is a general solution that, in the presence of erasures, minimizes the squared error for arbitrary LTI interpolation filters. In certain cases, e.g., oversampling and a sinc-interpolating filter, this solution is specialized so it perfectly compensates for erasures. The second solution is an approximation to the general solution that computes the optimal, finite-length compensation for arbitrary LTI interpolation filters. The third is a finite-length windowed version of the oversampled, sinc-interpolating solution using discrete prolate spheroidal sequences. The last is an iterative algorithm in the class of projection onto convex sets. Analysis and results from numerical simulations are presented.

Application of parallel forward-error correction in two-dimensional optical-data links

We propose the use of on-chip parallel forward-error correction (FEC) to improve the performance of two-dimensional (2-D) optical-data links (2-D-ODLs). Using an optical system model that describes a 2-D-ODL, we show the merits of using the Golay code as an FEC scheme to enable the reliable operation of 2-D-ODLs in the presence of erasures [e.g., a dead laser or photodetector, a dark fiber, an alignment problem, or a fault on the application-specific integrated circuit (ASIC)]. In addition, we study the impact of using on-chip FEC in 2-D-ODLs and show that FEC can reduce the launched optical power requirements, reduce on-chip power consumption, and relax the throughput requirements of the optical system.