Decoding of Non-Binary LDPC Codes using the Information Bottleneck Method

Abstract

Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-informationmaximizing lookup tables replace the conventional operations of the variable nodes and the check nodes in message passing decoding. Moreover, the exchanged messages are represented by integers with very small bit width. A machine learning framework termed the information bottleneck method is used to design the corresponding lookup tables. In this paper, we extend this decoding principle from binary to non-binary codes. This is not a straightforward extension but requires a more sophisticated lookup table design to cope with the arithmetic in higher order Galois fields. Provided bit error rate simulations show that our proposed scheme outperforms the log-max decoding algorithm and operates close to sum-product decoding.

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

“…For list size 1, the exchanged messages take values in a (q + 1)-ary message alphabet, composed of the elements of F q and an additional erasure message. In [15] a decoding algorithm for q-ary LDPC codes was presented, for which the CN and VN operations are implemented by means of look up tables. It makes use of the information bottleneck method and is practical for small q.…”

On the Information Bottleneck Problems: Models, Connections, Applications and Information Theoretic Views

“…Recent works show that this connection turns out to be useful for a better understanding the fundamental limits of learning problems, including the performance of deep neural networks (DNN) [ 10 ], the emergence of invariance and disentanglement in DNN [ 11 ], the minimization of PAC-Bayesian bounds on the test error [ 11 , 12 ], prediction [ 13 , 14 ], or as a generalization of the evidence lower bound (ELBO) used to train variational auto-encoders [ 15 , 16 ], geometric clustering [ 17 ], or extracting the Gaussian “part” of a signal [ 18 ], among others. Other connections that are more intriguing exist also with seemingly unrelated problems such as privacy and hypothesis testing [ 19 , 20 , 21 ] or multiterminal networks with oblivious relays [ 22 , 23 ] and non-binary LDPC code design [ 24 ]. More connections with other coding problems such as the problems of information combining and common reconstruction, the Wyner–Ahlswede–Korner problem, and the efficiency of investment information are unveiled and discussed in this tutorial paper, together with extensions to the distributed setting.…”

Multi valued parity generator based on Sudoku tables: properties and detection probability

“…The main differences between the given MPGs in this paper and the previous codes are: (i) Although NB‐LDPC and other non‐binary error correction codes provide additional performance gain when symbols with high‐order modulations are sent, they have basically and originally presented for dealing with error in a binary system with the aim of achieving higher throughput by reducing the number of computing stages [25]. The current paper is exclusively devoted to MVL communication systems with higher radixes than 2. (ii) NB‐LDPC has a costly and complex computational decoding [27, 28] while the entire error detection procedure by the presented operators is straightforward in both transmitter and receiver. (iii) The order of a GF is always a prime or a power of a prime number [25] whereas MPGs can be defined for every radix, e.g. base 6. (iv) Non‐binary error correction codes are mostly based on polynomial and GF arithmetic, whereas the new operators are defined by a set of positional rules. (v) Most of the previous non‐binary works using GF aim to provide error correction without presenting any SPC operator.…”