Non-Systematic LDPC Codes via Scrambling and Splitting

摘要

We consider design of non-systematic low-density parity-check (LDPC) codes for channel decoding of redundant sequences. We demonstrate that in the presence of source redundancy in channel coded sequences there may be a significant advantage to well designed non-systematic channel encoding over systematic encoding. In particular, we study methods we recently proposed for designing non-systematic LDPC codes by scrambling or splitting redundant data bits into coded bits. These methods consist of cascading a sparse matrix or an inverse of a sparse matrix with an LDPC code. We propose a method to perform density evolution on splitting based LDPC codes, and show that splitting based LDPC codes achieve better gains in the presence of redundancy than other known codes, including MacKay-Neal (MN) codes, without significant loss even if the data contains no redundancy. Using density evolution, we show that for independently identically distributed (i.i.d.) nonuniform (redundant) sequences, splitting based non-systematic codes can theoretically achieve very good performance.