Analysis of thresholds for braided block codes in BEC

Low-density parity-check (LDPC) codes, invented by Gallager [2], who described and analyzed a block variant of the codes, arouse great interest of researchers. These codes are widely used in practice since they can be decoded by using relatively simple iterative decoding algorithms. Several modifications of these codes are known, in particular, generalized LDPC codes [3]. In contrast to Gallager’s LDPC codes, using single parity-check codes as component codes, the generalized LDPC codes use as component codes arbitrary block codes. The convolutional version of Gallager’s codes, called convolutional LDPC codes, was described in [4]. These codes have better decoding reliability performance then the related LDPC block codes. Particularly, if the density of the parity-check matrices of convolutional LDPC codes increases, then their threshold (see below) tends to the Shannon limit [5], [6]. Braided block codes [1] and braided convolutional codes [7] can be considered as special constructions of generalized LDPC convolutional codes.