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...n of an inverse accumulator with one or more rate-adaptive base codes. The base codes considered in [18] are simple product codes and extended Hamming codes, yielding overall Product Accumulate codes =-=[22]-=- and extended Hamming Accumulate codes [23]. Both of these systems incur decoding complexity of up to O(n log n) since that is the soft decoding complexity for the base codes. In this section, we cons...

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...m in code design and opportunities to combine the advantages of parallel and serial concatenated systems. Several different hybrid concatenated structures have been proposed in literature, e.g., [7], =-=[8]-=-, [9]. Also, in [10], an inner code was used to improve the distance properties of an outer turbo code. In this paper we show that the minimum distance of HCCs that consist of an outer MPCC serially c...

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...video coding, we usually expect high compression ratio, so the channel coding methods used must be high-rate code. Product accumulate code has been proven to have good performance with high code rate =-=[11]-=-. Product accumulate code [11] is a serial concatenation of a single-parity-check-based product code, and a rate-1 recursive convolutional code. It provides similar coding performance to turbo code, b...

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... Identifier 10.1109/TCOMM.2009.02.060165 codes, are proposed in [10]. The encoders of zigzag codes are also very simple and can be decoded using low-complexity soft-in/soft-out decoders. Recently, in =-=[12]-=-, the authors proposed two classes of product accumulate (PA) codes, termed PA-I and PA-II codes. The PA codes are constructed based on the serial concatenation of an outer product code, an interleave...

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...ulate (RA) codes [9], by replacing the repetition codes in RA codes with other “base codes.” If the new base codes are products of single parity checks, the SCA code is a product-accumulate (PA) code =-=[10]-=-. If the new base codes are extended Hamming codes, the resulting SCA code is what we call an “extended-Hamming-accumulate” (EHA) code [11, 12]. Low complexity decoders of PA and EHA codes have both b...

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...uct accumulate (PA) codes (Part I), and then we move to the general case where an arbitrary (random) LDPC code is concatenated with an accumulator (Part II) [3]. Product accumulate codes, proposed in =-=[4]-=- and depicted in Figure 1, are a class of serially concatenated codes, where the inner code is a differential encoder, and the outer code is a parallel concatenation of two branches of single-parity2...

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...hs to a cascade of such graphs for erasure channels. In [93–95], the LDPC codes were designed based on finite geometry and algebra. Low-density generator matrix (LDGM) codes were explored in [96]. In =-=[97]-=-, product accumulate codes were proposed, which comprises the serial concatenation of a single-parity-check (SPC)-based product code, an interleaver, and a rate-1 recursive convolutional code. All the...

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... TPC/SPC codes are: minimum distance dH = 4, no length-4 cycles, linear-time encodable and decodable (i.e., low complexity implementation), and high code rate for relatively short codewords [8], [9], =-=[10]-=-. In magnetic recording systems, where the sector size is fixed, the use of LDPC with shorter code words provides benefits in an iterative architecture. This is because the combination of interleaving...

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... variety of different systems, including low-density parity-check (LDPC) codes with message-passing decoding, turbo codes with turbo decoding, product accumulate (PA) codes with iterative PA decoding =-=[10]-=-, and convolutionally-coded inter-symbol interference (ISI) channel with turbo equalization. In all of these systems, we have observed the Z-crease phenomenon. To study the per-block system behavior a...