European Journal of Combinatorics
Good Codes Based on Very Sparse Matrices
Proceedings of the 5th IMA Conference on Cryptography and Coding
On the classification of all self-dual additive codes over GF(4) of length up to 12
Journal of Combinatorial Theory Series A
Edge local complementation and equivalence of binary linear codes
Designs, Codes and Cryptography
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Low-density parity-check codes based on finite geometries: a rediscovery and new results
IEEE Transactions on Information Theory
Finite-length analysis of low-density parity-check codes on the binary erasure channel
IEEE Transactions on Information Theory
Iterative Soft-Input Soft-Output Decoding of Reed–Solomon Codes by Adapting the Parity-Check Matrix
IEEE Transactions on Information Theory
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We describe an operation to dynamically adapt the structure of the Tanner graph used during iterative decoding. Codes on graphs---most importantly, low-density parity-check (LDPC) codes---exploit randomness in the structure of the code. Our approach is to introduce a similar degree of controlled randomness into the operation of the message-passing decoder, to improve the performance of iterative decoding of classical structured (i.e., non-random) codes for which strong code properties are known. We use ideas similar to Halford and Chugg (IEEE Trans. on Commun., April 2008), where permutations on the columns of the parity-check matrix are drawn from the automorphism group of the code, Aut$\mathcal{(C)}$. The main contributions of our work are: 1) We maintain a graph-local perspective, which not only gives a low-complexity, distributed implementation, but also suggests novel applications of our work, and 2) we present an operation to draw from Aut$\mathcal{(C)}$ such that graph isomorphism is preserved, which maintains desirable properties while the graph is being updated. We present simulation results for the additive white Gaussian noise (AWGN) channel, which show an improvement over standard sum-product algorithm (SPA) decoding.