New Sequences of Linear Time Erasure Codes Approaching the Channel Capacity
AAECC-13 Proceedings of the 13th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes
Wireless Communications
Modern Coding Theory
Capacity of fading channels with channel side information
IEEE Transactions on Information Theory
Bit-interleaved coded modulation
IEEE Transactions on Information Theory
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
Improved low-density parity-check codes using irregular graphs
IEEE Transactions on Information Theory
The capacity of low-density parity-check codes under message-passing decoding
IEEE Transactions on Information Theory
Design of capacity-approaching irregular low-density parity-check codes
IEEE Transactions on Information Theory
Analysis of sum-product decoding of low-density parity-check codes using a Gaussian approximation
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Rate-compatible puncturing of low-density parity-check codes
IEEE Transactions on Information Theory
Nonuniform error correction using low-density parity-check codes
IEEE Transactions on Information Theory
Reliable channel regions for good binary codes transmitted over parallel channels
IEEE Transactions on Information Theory
On Achievable Rates and Complexity of LDPC Codes Over Parallel Channels: Bounds and Applications
IEEE Transactions on Information Theory
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Irregular low-density parity-check (LDPC) code design for parallel sub-channels with different qualities is investigated. Such channels appear in many communication systems, e.g., orthogonal frequency-division multiplexing systems. When channel knowledge is available at both the transmitter and receiver, following the literature, we consider allotted LDPC codes which carefully assign different parts of the code to sub-channels. To reduce the number of design parameters and allow for efficient design, semi-regular allotted codes have been suggested. We first formulate the design of semi-regular codes as a mixed integer linear programming. Relaxing the semi-regularity constraint broadens the search space which results in improved codes and also a more efficient design via linear programming. While information theoretic results suggest that having channel state information--for a fixed power assignment--does not change the capacity, we show that under non-optimal decoding or when the maximum degree allowed in the code is small, allotted codes significantly outperform conventional ones. Finally, for the case that neither side has the channel knowledge (thus capacity-loss is inevitable), we see that the reduced capacity can still be approached by LDPC codes.