Half-Product Codes

A class of codes, half-product codes, derived from product codes, is characterized. These codes have the implementation advantages of product codes and possess a special structural property which leads them to have larger (at least 3/2 times more) minimum distance than product codes. With the same length and rate, they have better scaling in the error floor than product codes. They also have a larger minimum stopping-set size under iterative decoding which provides better scaling. The main results of this thesis are summarized as follows: 1. Encoding and decoding methods of half-product codes are described. 2. The minimum distance of these codes is derived, and proved to be at least 3 2 times larger than that of the product codes for the same rate and block length. 3. The performance of iterative decoding in the error floor region is analyzed by enumerating the minimum stopping-set patterns for these codes. The results are compared with product codes.

Simulations are also performed to compare the half-product codes with product codes. We conclude that half-product codes scale better in the error floor than product codes in the region where the minimum stopping-sets dominate the error floor, and that they have same threshold as product codes when rate is same and code length is increased to infinity.