We construct new families of error-correcting codes based on Gallager’s low-density parity-check codes, which we call irregular codes. When decoded using belief propagation, our codes can correct more errors than previously known low-density parity-check codes. For example, for rate 1/4 codes on 16,000 bits over a binary symmetric channel, previous low-density parity-check codes can correct up ...

in this paper, we consider a class of column-weight two quasi-cyclic low-density paritycheck codes in which the girth can be large enough, as an arbitrary multiple of 8. then we devote a convolutional form to these codes, such that their generator matrix can be obtained by elementary row and column operations on the parity-check matrix. finally, we show that the free distance of the convolution...

Trapping sets have been identified as one of the main factors causing error floors of low-density parity-check (LDPC) codes at high SNR values. By adding several new rows to the original parity-check matrix, a novel method is proposed to eliminate small trapping sets in the LDPC code’s Tanner graph. Based on this parity-check matrix extension, we design new codes with low error floors from the ...

Introduction: Multilevel coding (MLC) was proposed by Imai and Hirawaki [1] as a bandwidth-efficient coded modulation scheme designed for protecting each bit of a non-binary symbol with the aid of binary codes, while maintaining different target bit error rates (BERs). Parallel independent decoding (PID) [2] is employed as an efficient decoding strategy with reduced decoding delay, where there ...

This thesis focuses on designing Low-Density Parity-Check (LDPC) codes for forward-error-correction. The target application is real-time multimedia communications over packet networks. We investigate two code design issues, which are important in the target application scenarios, designing LDPC codes with low decoding latency, and constructing capacity-approaching LDPC codes with very low error...

Abstract – In this paper a formal theory, construction methods, and a random ensemble approach for low-density parity-check convolutional codes (including turbo-codes) are presented. The principles of iterative decoding of low-density parity-check (LDPC) convolutional codes are given, and an iterative algorithm for decoding of homogeneous LDPC convolutional codes is described. Some simulation r...