Optimization of LDPC Codes Using Convex Relaxation

On the Design of Fast Convergent LDPC Codes: An Optimization Approach

The complexity-performance trade-off is a fundamental aspect of the design of low-density parity-check (LDPC) codes. In this paper, we consider LDPC codes for the binary erasure channel (BEC), use code rate for performance metric, and number of decoding iterations to achieve a certain residual erasure probability for complexity metric. We first propose a quite accurate approximation of the numb...

Design of Low-Density Parity-Check Codes with Optimized Complexity-Rate Tradeoff

The optimal complexity-rate tradeoff for errorcorrecting codes at rates strictly below the Shannon limit is a central question in coding theory. This paper proposes a numerical approach for the joint optimization of rate and decoding complexity for long-block-length irregular low-density parity-check (LDPC) codes. The proposed design methodology is applicable to any binary-input memoryless symm...

A Joint Optimization Technique for Multi-Edge Type LDPC Codes

This paper considers the optimization of multi-edge type low-density parity-check (METLDPC) codes to maximize the decoding threshold. We propose an algorithm to jointly optimize the node degree distribution and the multi-edge structure of MET-LDPC codes for given values of the maximum number of edge-types and maximum node degrees. This joint optimization is particularly important for MET-LDPC c...

Improving the Rao-Nam secret key cryptosystem using regular EDF-QC-LDPC codes

This paper proposes an efficient joint secret key encryption-channel coding cryptosystem, based on regular Extended Difference Family Quasi-Cyclic Low-Density Parity-Check codes. The key length of the proposed cryptosystem decreases up to 85 percent using a new efficient compression algorithm. Cryptanalytic methods show that the improved cryptosystem has a significant security advantage over Ra...

On the Grobner Basis of a Family of Quasi-Cyclic LDPC Codes