Distance preserving maps and combinatorial joint source channel coding for large alphabets
In this paper we present several results regarding distance preserving maps between nonbinary Hamming spaces and combinatorial (adversarial) joint source channel coding. In an (a, b) map from one Hamming space to another, any two sequences that are at least a relative distance apart, are mapped to sequences that are relative distance at least b apart. The motivation to study such maps come from (D, d) joint source channel coding (JSCC) schemes, where any encoded sequence must be recovered within a relative distortion D, even in the presence of d proportion of adversarial errors. We provide bounds on the parameters of both (a, b) maps and (D,d) JSCC for nonbinary alphabets. We also provide constructive schemes for both, that are optimal for many cases.
2016 IEEE International Symposium on Information Theory (ISIT)