Introduction: In modern systems for communication, data storage and processing the error-correction capability of codes are estimated memoryless channels. real channels noise is correlated, which leads to grouping error in bursts. A traditional method fight this phenomenon channel decorrelation, does not allow developing coding schemes, mostly utilizing capacity. Thus development bursts decodin...

Introduction: The family of low-density parity-check (LDPC) codes proposed by Gallager [1] has attracted substantial research interest in the information theory community. LDPC codes can be decoded using various decoding schemes [1–4] such as hard-decisions, softdecisions and hybrid decoding schemes. The high-complexity sum-product algorithm (SPA) was shown to achieve a near-capacity performanc...

We introduce new reliability definitions for bit and check nodes. Maximizing global reliability, which is the sum reliability of all bit nodes, is shown to be equivalent to minimizing a decoding metric which is closely related to the maximum likelihood decoding metric. We then propose novel bit-flipping (BF) decoding algorithms that take into account the check node reliability. Both hard-decisi...

Forward error correction codes (FEC) are used for error detection and correction in communication systems. Low density parity check code (LDPC) is used as a powerful Forward Error Correction code in long distance communication systems which works close to the Shannon limit. Unlike other conventional channel code, the decoding algorithm used for LDPC codes is an iterative message passing algorit...

God does not play dice. He flips coins instead.” And though for some reason He has denied us quantum bit commitment. And though for some reason he has even denied us strong coin flipping. He has, in His infinite mercy, granted us quantum weak coin flipping so that we too may flip coins. Instructions for the flipping of coins are contained herein. But be warned! Only those who have mastered Kita...

In this paper, we investigate the error correction capability of column-weight-three LDPC codes when decoded using the Gallager A algorithm. We prove that the necessary condition for a code to correct k ≥ 5 errors is to avoid cycles of length up to 2k in its Tanner graph. As a consequence of this result, we show that given any α > 0,∃N such that ∀n > N , no code in the ensemble of column-weight...