We study the performance of nonbinary low-density parity-check (LDPC) codes over finite integer rings over two channels that arise from the Lee metric. The first channel is a discrete memory-less channel (DMC) matched to the Lee metric. The second channel adds to each codeword an error vector of constant Lee weight, where the error vector is picked uniformly at random from the set of vectors of constant Lee weight. It is shown that the marginal conditional distributions of the two channels coincide, in the limit of large block length. Random coding union bounds on the block error probability are derived for both channels. Moreover, the performance of selected LDPC code ensembles is analyzed by means of density evolution and finite-length simulations, with belief propagation decoding and with a low-complexity symbol message passing algorithm and it is compared to the derived bounds.

翻译：我们研究了由李公制生成的两条频道上非二进制低密度对等检查(LDPC)代码的性能。 第一个频道是一个与李公制相匹配的离散的无内存通道(DMC),第二个频道在每个代码词中添加了一个恒定的李重误矢量,其中误矢量从恒定的李重矢量的一组矢量中以随机方式统一选择。 显示两个频道的边际有条件分布在大块长度的界限内是相交的。 两个频道都从块误差概率上得出随机编码结合的界限。 此外,选定的 LDPC 代码组合的性能通过密度进化和长度模拟手段进行分析,同时进行信仰传播解码和低兼容性符号信息传递算法的测试,并与衍生的界限进行比较。