List decoding

About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.

Low-complexity iterative joint source-channel decoding for variable-length encoded Markov sources

Abstract: In this paper, we present a novel packetized bit-level decoding algorithm for variable-length encoded Markov sources, which calculates reliability information for the decoded bits in the form of a posteriori probabilities (APPs). An interesting feature of the proposed approach is that symbol-based source statistics in the form of the transition probabilities of the Markov source are exploited as a priori information on a bit-level trellis. This method is especially well-suited for long input blocks, since in contrast to other symbol-based APP decoding approaches, the number of trellis states does not depend on the packet length. When additionally the variable-length encoded source data is protected by channel codes, an iterative source-channel decoding scheme can be obtained in the same way as for serially concatenated codes. Furthermore, based on an analysis of the iterative decoder via extrinsic information transfer charts, it can be shown that by using reversible variable-length codes with a free distance of two, in combination with rate-1 channel codes and residual source redundancy, a reliable transmission is possible even for highly corrupted channels. This justifies a new source-channel encoding technique where explicit redundancy for error protection is only added in the source encoder.

Coding and decoding system using crc check bit

Abstract: A coding and decoding system which uses CRC check bits is disclosed. When a coding apparatus performs coding, symbol interleaving is performed after coding by an outer code of a concatenated code, and coding by an inner code is performed after CRC check bits are added. Then, upon decoding by a decoding apparatus, error detection using the CRC check bits is performed after decoding of the inner code. After symbol deinterleaving is performed, decoding of the outer code by erasure decoding or error correction is performed depending upon the number of symbols included in a frame in which an error has been detected.

New Scalable Decoder Architectures for Reed–Solomon Codes

Abstract: In this paper, we devise new scalable decoder architectures for Reed–Solomon (RS) codes, comprising three parts: error-only decoding, error-erasure decoding, and their decoding for singly extended RS codes New error-only decoders are devised through algorithmic transformations of the inversionless Berlekamp–Massey algorithm (IBMA) We first generalize the Horiguchi–Koetter formula to evaluate error magnitudes using the error locator polynomial $\Lambda(x)$ and the auxiliary polynomial $B(x) $ produced by IBMA, which effectively eliminates the computation of error evaluator polynomial We next devise an enhanced parallel inversionless Berlekamp–Massey algorithm (ePIBMA) that effectively takes advantage of the generalized Horiguchi–Koetter formula The derivative ePIBMA architecture requires only $2t+1$ ( $t$ denotes the error correction capability) systolic cells, in contrast with $3t$ or more cells of the existing regular architectures based on IBMA or the Euclidean algorithm Moreover, it may literally function as a linear-feedback-shift-register encoder New error-erasure decoders are devised through algorithmic transformations of the inversionless Blahut algorithm (IBA) The proposed split parallel inversionless Blahut algorithm (SPIBA) yields merely $2t+1$ systolic cells, which is the same number as the error-only decoder ePIBMA The task is partitioned into two separate steps, computing the complementary error erasure evaluator polynomial followed by computing error-erasure locator polynomial, both utilizing SPIBA Surprisingly, it has exactly the same number of cells and literally the same complexity and throughput as the proposed error-only decoder architecture ePIBMA; it employs 33% less hardware and at the same time achieves more than twice faster throughput, than the serial architecture IBA we further propose a unified parallel inversionless Blahut algorithm (UPIBA) by incorporating the key virtues of the error-only decoder ePIBMA into SPIBA The complexity and throughput of the rderivative UPIBA architecture are literally the same as ePIBMA and SPIBA, while performing almost equally efficiently as ePIBMA on error-only decoding and as SPIBA on error-erasure decoding UPIBA also inherits the dynamic power saving feature of ePIBMA and SPIBA Indeed, UPIBA renders highly attractive for on-the-fly implementation of error-erasure decoding We finally demonstrate that the proposed decoders, ie, ePIBMA, SPIBA, and UPIBA, can be magically migrated to decode singly extended RS codes, with negligible add-ons, except that an extra multiplexer is added to their critical paths To the author's best knowledge, this is the first time that a high-throughput decoder for singly extended RS codes is explored

Decoding LDPC codes with mutual information-maximizing lookup tables

Abstract: A recent result has shown connections between statistical learning theory and channel quantization In this paper, we present a practical application of this result to the implementation of LDPC decoders In particular, we describe a technique for designing the message-passing decoder mappings (or lookup tables) based on the ideas of channel quantization This technique is not derived from sum-product algorithm or any other LDPC decoding algorithm Instead, the proposed algorithm is based on an optimal quantizer in the sense of maximization of mutual information, which is inserted in the density evolution algorithm to generate the lookup tables This algorithm has low complexity since it only employs 3-bit messages and lookup tables, which can be easily implemented in hardware Two quantized versions of the min-sum decoding algorithm are used for comparison Simulation results for a binary-input AWGN channel show 03 dB and 12 dB gains versus the two quantized min-sum algorithms On the binary symmetric channel also a gain is seen

List decoding of Reed-Muller codes up to the Johnson bound with almost linear complexity

Abstract: A new deterministic list decoding algorithm is proposed for general Reed-Muller codes RM(s,m) of length n = 2m and distance d = 2m-epsi. Given n and d, the algorithm performs beyond the bounded distance threshold of d/2 and has a low complexity order of nmepsi-1 for any decoding radius T that is less than the Johnson bound