Iterative Bounded Distance Decoding of Product Codes with Scaled Reliability

Abstract

We propose a modified iterative bounded distance decoding of product codes. The proposed algorithm is based on exchanging hard messages iteratively and exploiting channel reliabilities to make hard decisions at each iteration. Performance improvements up to 0.26 dB are achieved.

Binary Message Passing Decoding of Product Codes Based on Generalized Minimum Distance Decoding : (Invited Paper)

“…The resulting PC has rate R = 239 2 /256 2 ≈ 0.8716. For comparison purposes, we we also plot the performance of conventional iBDD, AD [10], iBDD-SR [12], iGMDD-SR [15], and TPD based on the Chase-Pyndiah decoding [16]. For all algorithms, a maximum of max = 10 decoding iterations is performed.…”

“…Therefore, in order to reduce the optimization search space, we only consider vectors w with monotonically increasing entries. iBDD-SR also requires scaling factors (see [12], [19]). In this case, the scaling factors can be derived using density evolution [13], [19].…”

“…A thorough complexity analysis of BMP-GMDD should include, besides pure algorithmic aspects, implementation implications in terms of memory requirements, wiring, and transistor switching activity [14], and is beyond the scope of this paper. We however provide a high-level discussion of the complexity and data flow of BMP-GMDD compared to that of conventional iBDD, AD [10], iBDD-SR [12], and iGMDD-SR [15].…”

“…In [11], a decoding algorithm based on marking the least reliable bits was proposed for staircase codes. In [12], we proposed a decoding algorithm based on BDD of the component codes, named iBDD with scaled reliability (iBDD-SR). The algorithm in [12] improves the performance of iBDD by exploiting channel reliabilities as proposed in [13] for LDPC codes, while still only exchanging binary (i.e., hard-decision) messages between component decoders, similar to iBDD.…”

“…In [12], we proposed a decoding algorithm based on BDD of the component codes, named iBDD with scaled reliability (iBDD-SR). The algorithm in [12] improves the performance of iBDD by exploiting channel reliabilities as proposed in [13] for LDPC codes, while still only exchanging binary (i.e., hard-decision) messages between component decoders, similar to iBDD. iBDD-SR improves upon iBDD and AD, and achieves the same throughput of iBDD with a slight increase in energy consumption [14].…”