The effects of clipping and quantization on the performance of the min-sum algorithm for the decoding of low-density parity-check (LDPC) codes at short and intermediate block lengths are studied. It is shown that in many cases, only four quantization bits suffice to obtain close to ideal performance over a wide range of signal-to-noise ratios. Moreover, we propose modifications to the min-sum algorithm that improve the performance by a few tenths of a decibel with just a small increase in decoding complexity. A quantized version of these modified algorithms is also studied. It is shown that, when optimized, modified quantized min-sum algorithms perform very close to, and in some cases even slightly out-perform, the ideal belief-propagation algorithm at observed error rates.

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Keywords Clipping, Iterative decoding algorithms, Low-density parity-check (LDPC) codes, Max-product algorithm, Max-sum algorithm, Min-sum algorithm, Modified min-sum algorithms, Quantization
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Journal IEEE Transactions on Communications
Zhao, J. (Jianguang), Zarkeshvari, F. (Farhad), & Banihashemi, A. (2005). On implementation of min-sum algorithm and its modifications for decoding low-density parity-check (LDPC) codes. IEEE Transactions on Communications, 53(4), 549–554. doi:10.1109/TCOMM.2004.836563