A look-up table (LUT) is arranged as a plurality of rows each indexed by an index value and storing at least a coefficient for each index value for use in processing digital data. The LUT contains repeated sections in which m coefficients stored for successive index values form a cycle. The number m is not an integer power of 2. For example the LUT may be used when converting a digital count to a gain in dB, in which case m may be 6 or 12, the coefficients representing dB or fractional-dB steps in gain. The LUT contains n additional blank rows inserted after every repeated section of m rows storing the cycle of m coefficients, n being 1 or more and (m+n) being an integer power of two (such as 8 or 16). By feeding an initial index value through encoding logic which takes account of the additional rows, it can be ensured that these are never indexed. Thus, a sparse-coded LUT is provided. Although each repeated section is increased in size, the actual size of the LUT in terms of circuit area or programming logic is reduced because the repeating length is now a power of two.