Performance of Belief Propagation for Decoding LDPC Codes in the Presence of Channel Estimation Error

Noise adaptive LDPC decoding using particle filter

“…However, for an unknown AWGN channel, it is very difficult to estimate the noise power σ 2 without pilot signal or feedback, where the situation whenσ 2 = σ 2 is defined as "signal-to-noise ratio (SNR) mismatch". The effect of the SNR mismatch on LDPC codes is studied in [6][7] [8], which indicated that the BP algorithm is more sensitive to the underestimation of SNR than the overestimation. Moreover, for a time-varying AWGN channel, to generate a real-time estimated noise power is more difficult.…”

“…factor node in region 2 follows (3), where f a (x a ) = 1 if even number of 1's in arguments 0 otherwise 6) Update factor node in region 1, which means to update each particle according to(8) Estimation of noise power for fixed AWGN channel. Estimation of noise power for time-varying AWGN channel.…”

On the Robustness of Iterative Decoders

“…We have to add that it does so only when the channel is perfectly known: in fact, a considerable degradation in sum-product's error performance is observed if not an accurate estimate of σ is used for calculating the LLR values [5]. 2 min-sum, on the other hand, is universal and, at the expense of its inferior error performance, does not require any estimate of σ [13], [14].…”

“…In order to model the uncertainty of the channel, we assume, in line with [5], thatσ, our estimate of σ, is given bŷ…”

“…Second, the channel state information is required for computing the initial bit log-likelihood ratios (LLR), defined as ln (P (x = +1|y)/P (x = −1|y)). With inaccurate LLR values, the code may not perform close to its decoding threshold [5]. The second reason remains valid even if a near-capacity performance is not necessary.…”