We introduce a new family of unequal error protection (UEP) codes, based on low-density parity-check (LDPC) component codes and Plotkin-type constructions. The codes are decoded iteratively in multiple stages, and the order of decoding determines the level of error protection. The level of UEP among the code bits is also influenced by the choice of the LDPC component codes and by some new reliability features incorporated into the decoding process. The proposed scheme offers a very good tradeoff between code performance on one side and encoding/decoding and storage complexity on the other side. The novel approach to UEP also allows for finding simple approximations for the achievable degrees of UEP, which can be used to govern practical code design implementations

A family of unequal error-protection (UEP) low-density parity-check (LDPC) codes, based on Plotkin-type constructions, is introduced. The codes are decoded in multiple stages in such a manner that the order of decoding determines the level of error protection. The level of UEP among the code bits can be further increased by properly combining structured and random-like LDPC component codes with carefully chosen properties, and by using some new reliability features. The proposed scheme also offers a good trade-off between code performance on the one hand and encoding/decoding and storage complexity on the other. To the best of our knowledge, the proposed approach represents the first iterative UEP method with analytically provable properties.

It is well known that random-like low-density parity-check (LDPC) codes over the extension fields GF(2/sup m/) of GF(2), for m>1, tend to outperform their binary counterparts of comparable length and rate. At the same time, structured LDPC codes offer the advantage of reduced implementation and storage complexity, so that it is of interest to investigate mathematical design methods for codes on graphs over fields of large order. We propose a new class of combinatorially developed codes obtained by properly combining Reed-Solomon (RS) type parity-check matrices and sparse parity-check matrices based on permutation matrices. The proposed codes have large girth and minimum distance. In order to further reduce the decoding complexity of the proposed scheme, we introduce a new decoding algorithm based on matrix representations of the underlying field, which trades performance for complexity. The particular field representation described in this abstract is based on a power basis generated by a companion matrix of a primitive polynomial of the field GF(2/sup m/). It is observed that the choice of the primitive polynomial influences the cycle distribution of the code graph.