The Capacity Region of Frequency-Selective Gaussian Interference Channels Under Strong Interference

Abstract

Practical applications that employ coding for large alphabets often partition the alphabet set into two or more layers and encode each symbol by using some suitable prefix coding for each layer. In this paper, we formulate the problem of finding an alphabet partitioning for the de- sign of a two-layer semiadaptive code as an optimization problem, and give a solution based on dynamic programming. However, the complexity of the dynamic-programming approach can be quite prohibitive for a long se- quence and a very large alphabet size. Hence, we also give a simple greedy heuristic algorithm whose running time is linear in the length of the input sequence, irrespective of the underlying alphabet size. Although our dy- namic programming and greedy algorithms do not provide a globally op- timal solution for the alphabet-partitioning problem, experimental results demonstrate that superior prefix coding schemes for large alphabets can be designed using our new approach. One such setting is developed in this paper, for the purpose of analyzing the distribution of short cycles and the structure of stopping and trapping sets in Tanner graphs of LDPC codes based on idempotent and symmetric Latin squares. The parity-check matrices of LDPC codes based on Latin squares have a special form that allows for connecting the combinatorial parameter of the codes with the number of certain subrectangles in the Latin squares. Subrectangles of interest can be easily identified, and in certain instances, completely enumerated. The presented study can be extended in several different directions, one of which is concerned with modifying the code-de- sign process in order to eliminate or reduce the number of configurations bearing a negative influence on the performance of the code. Another ap- plication of the results includes determining to which extent a configura- tion governs the behavior of the bit-error rate curve in the waterfall and error-floor regions.