Analysis and Design of Binary Message Passing Decoders

Abstract

Abstract-Binary message-passing decoders for low-density parity-check (LDPC) codes are studied by using extrinsic information transfer (EXIT) charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations in the L-value domain. A hard decision channel results in the well-know Gallager B algorithm, and increasing the output alphabet from hard decisions to two bits yields a gain of more than 1.0 dB in the required signal to noise ratio when using optimized codes. The code optimization requires adapting the mixing property of EXIT functions to the case of binary message-passing decoders. Finally, it is shown that errors on cycles consisting only of degree two and three variable nodes cannot be corrected and a necessary and sufficient condition for the existence of a cycle-free subgraph is derived.

One and Two Bit Message Passing for SC-LDPC Codes With Higher-Order Modulation

“…III. DECODING ALGORITHMS FOR ONE AND TWO BIT MESSAGE PASSING In this section, we first review the BMP and TMP decoding algorithms introduced in [9] and [12, Sec. III-A].…”

“…In [9], the authors present a one-bit binary message passing (BMP) algorithm for low-density parity-check (LDPC) codes. In particular, the variable node (VN) processor combines the soft channel message with scaled binary messages from the check nodes (CNs), followed by a HD step.…”

Symbol Message Passing Decoding of Nonbinary Low-Density Parity-Check Codes

“…Remark 1. As for the message passing algorithms proposed in [3], [4], DE analysis plays a two-fold role. On one hand, it allows deriving the iterative decoding threshold of the LDPC code ensemble under analysis.…”

“…In [2], algorithm E was proposed, where messages take values in a ternary alphabet. A powerful algorithm, referred to as binary message passing (BMP) was introduced in [3]. Although the exchanged messages are binary, the algorithm is able to exploit soft information from the channel at the VNs.…”

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

“…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].…”