Design of the BCJR decoding algorithm with reduced space complexity

Given an M-state (recursive) convolutional encoder, we show that, in theory, computing the forward alpha probabilities of the BCJR decoding algorithm can be done with 2M memory elements. Building on this idea we propose new design with reduced space complexity for the original BCJR algorithm. Initial experiments with rate-1/2 1025-bit-long Turbo Codes show possibility for compressing the size of memory for the alpha probabilities for about 97%.