Free-Ride BCH Codes for Fine-Grained Rate Adaptation: Construction, Decoding, and Analysis

Abstract

In this paper, we propose free-ride BCH (FR-BCH) codes to enable fine-grained rate adaptation on conventional BCH codes. At the transmitter, a small number of extra bits are superimposed onto the BCH codeword via random or structured superpositions. At the receiver, all candidate extra-bit patterns are enumerated by a parallel trial-and-error decoder, in which interference is canceled per path and an OSD-like decoder is executed. In particular, we propose an effective global early stopping rule that terminates all paths whenever a reliable path is identified, thereby reducing the number of searches (i.e., tested TEPs) in the parallel decoder. For performance analysis, we derive finite-blocklength characterizations for extra-bit reliability (an upper bound and a refined predictor) and present a decoder-specific saddlepoint-based analysis that accurately estimates both the frame error rate (FER) and the average number of searches for the proposed decoder. Simulation results show that: 1) FR-BCH codes with the proposed decoder outperform the considered BCH-subcode and shortened-BCH codes; 2) the proposed decoder matches well with the derived finite-length bounds and saddlepoint-based estimates; and 3) the proposed FR-BCH codes closely approach the conventional finite-length bounds across nearly all rates (e.g., continuously from <inline-formula> <tex-math notation="LaTeX">$K=8$ </tex-math></inline-formula> to <inline-formula> <tex-math notation="LaTeX">$K=127$ </tex-math></inline-formula> at <inline-formula> <tex-math notation="LaTeX">$n=128$ </tex-math></inline-formula>), thus overcoming the coarse rate granularity of native BCH codes.