Arithmetic completely regular codes,

Abstract In this paper, we explore completely regular codes in the Hamming graphs and related graphs. We focus on cartesian products of completely regular codes and products of their corresponding coset graphs in the additive case. Connections to the theory of distanceregular graphs are explored and several open questions are posed

On the parameters of codes for the Lee and modular distance

AbstractWe introduce the concept of a weakly metric association scheme, a generalization of metric schemes. We undertake a combinatorial study of the parameters of codes in these schemes, along the lines of [9]. Applications are codes over Zq for the Lee distance and arithmetic codes for the modular distance.Our main result is an inequality which generalizes both the Delsarte upper bound on covering radius, and the MacWilliams lower bound on the external distance, yielding a strong necessary existence condition on completely regular codes.The external distance (in the Lee metric) of some self-dual codes of moderate length over Z5 is computed

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

Recently, a novel lookup table based decoding method for binary low-density parity-check codes has attracted considerable attention. In this approach, mutual-information maximizing 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.Comment: This paper has been presented at IEEE International Conference on Communications (ICC'19) in Shangha