Binary optimal linear rate 1/2 codes

Binary Optimal Linear Rate 1/2 Codes

Binary Linear Codes with Optimal Scaling and Quasi-Linear Complexity

We present the first family of binary codes that attains optimal scaling and quasi-linear complexity, at least for the binary erasure channel (BEC). In other words, for any fixed δ > 0, we provide codes that ensure reliable communication at rates within ε > 0 of the Shannon capacity with block length n = O(1/ε2+δ), construction complexity Θ(n), and encoding/decoding complexity Θ(n log n). Furth...

Optimal Rate Irregular LDPC Codes in Binary Erasure Channel

In this paper, we design the optimal rate capacity approaching irregular Low-Density ParityCheck code ensemble over Binary Erasure Channel, by using practical Semi-Definite Programming approach. Our method does not use any relaxation or any approximate solution unlike previous works. Our simulation results include two parts; first, we present some codes and their degree distribution functions t...

Robustly optimal rate one-half binary convolutional codes (Corresp.)

Optimal binary linear locally repairable codes with disjoint repair groups

In recent years, several classes of codes are introduced to provide some fault-tolerance and guarantee system reliability in distributed storage systems, among which locally repairable codes (LRCs for short) play an important role. However, most known constructions are over large fields with sizes close to the code length, which lead to the systems computationally expensive. Due to this, binary...