In successive cancellation (SC) polar decoding, an incorrect estimate of any prior unfrozen bit may bring about severe error propagation in the following decoding, thus it is desirable to find out and correct an error as early as possible. In this paper, we first construct a critical set S of unfrozen bits, which with high probability (typically >99%) includes the bit where the first error happens. Then we develop a progressive multi- level bit-flipping decoding algorithm to correct multiple errors over the multiple-layer critical sets each of which is constructed using the remaining undecoded subtree associated with the previous layer. The level in fact indicates the number of independent errors that could be corrected. We show that as the level increases, the block error rate (BLER) performance of the proposed progressive bit flipping decoder competes with the corresponding cyclic redundancy check (CRC) aided successive cancellation list (CA-SCL) decoder, e.g., a level 4 progressive bit-flipping decoder is comparable to the CA-SCL decoder with a list size of L=32. Furthermore, the average complexity of the proposed algorithm is much lower than that of a SCL decoder (and is similar to that of SC decoding) at medium to high signal to noise ratio (SNR).

In this paper, we propose a Distributed Turbo Product Code (DTPC) over cooperative network using block Bose Chaudhuri Hochquenghem (BCH) codes as component codes. The source broadcasts extended BCH coded frames to the destination and nearby relays. After decoding the received sequences, each relay constructs a product code by arranging the corrected bit sequences in rows and re-encoding them vertically using BCH as component codes to obtain an Incremental Redundancy (IR) for source's data. To obtain independent vertical parities from each relay in the same code space, different circular interleavers are proposed to interleave BCH rows before reencoding vertically. A modified turbo product decoder to cope with Multiple Vertical Parities (MVP) is used at the destination to iteratively decode the systematic data from the source and the vertical parities generated by the relays. Simulation results in Additive White Gaussian Noise (AWGN) channel using network scenarios show 0.3-0.5dB gain improvement in Bit Error Rate (BER) performance over the non-cooperative Turbo Product Codes (TPC).

We present a method to reduce the number of test patterns (TPs) decoded in the Chase-II algorithm for turbo product codes (TPCs) constructed with multi-error-correcting extended Bose-Chaudhuri-Hocquengem (eBCH) codes. We classify TPs into different conditions based on the relationship between syndromes and the number of errors so that TPs with the same codeword are not decoded except the one with the least number of errors. For eBCH with code length of 64, simulation results show that over 50% of TPs need not to be decoded without any performance degradation.

In this paper, Chase decoding algorithm for turbo product codes (TPCs) built with multi-error-correcting codes is investigated. A method is proposed to reduce the decoding of test patterns (TPs) as well as the calculation of syndromes and metrics. In the beginning, syndromes and metrics of the first half of TPs are calculated recursively. After decoding of one TP, according to the error bit positions, other TPs that will have the same decoded codeword are identified and rejected from decoding. In the mean time, if these TPs fall into the range of second half of TPs, their syndromes and metrics need not to be calculated either. Simulations results for TPCs built with eBCH(64,51,6,2) or eBCH(64,45,8,3) are presented to demonstrate the efficiency of the proposed method. Moreover, this method that reduces the inherent redundancy in Chase decoding does not cause any degradation in coding gain.