Efficient Non-Recursive Design of Second-Order Spectral-Null Codes

A new efficient design of second-order spectralnull (2-OSN) codes is presented. The new codes are obtained by applying the technique used to design parallel decoding balanced (i.e., 1-OSN) codes to the random walk method introduced by some of the authors for designing 2-OSN codes. This gives new non-recursive efficient code designs, which are less redundant than the code designs found in the literature. In particular, if k ∈ IIN is the length of a 1-OSN code then the new 2-OSN coding scheme has length n = k + r ∈ IIN with an extra redundancy of r ≃ 2 log
₂
k + (1/2) log
₂
log
₂
k - 0.174 check bits, with k and r even and n multiple of 4. The whole coding process requires O(k log k) bit operations and O(k) bit memory elements.