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A construction of big convolutional codes from short codes called block Markov superposition transmission (BMST) is proposed. The BMST is very similar to superposition blockMarkov encoding (SBME), which has been widely used to prove…
In this paper, we propose systematic block Markov superposition transmission of repetition~(BMST-R) codes, which can support a wide range of code rates but maintain essentially the same encoding/decoding hardware structure. The systematic…
Tail-biting convolutional codes extend the classical zero-termination convolutional codes: Both encoding schemes force the equality of start and end states, but under the tail-biting each state is a valid termination. This paper proposes a…
In this paper, we consider the asymptotic and finite-length performance of block Markov superposition transmission~(BMST) of short codes, which can be viewed as a new class of spatially coupled~(SC) codes with the generator matrices of…
We consider the concatenation of a convolutional code (CC) with an optimized cyclic redundancy check (CRC) code as a promising paradigm for good short blocklength codes. The resulting CRC-aided convolutional code naturally permits the use…
This paper presents a variable-length decision-feedback scheme that uses tail-biting convolutional codes and the tail-biting Reliability-Output Viterbi Algoritm (ROVA). Comparing with recent results in finite-blocklength information theory,…
Recently, rate-$1/\omega$ zero-terminated and tail-biting convolutional codes (ZTCCs and TBCCs) with cyclic-redundancy-check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RCU) bound for short…
In this paper, we present the block Markov superposition transmission of BCH (BMST-BCH) codes, which can be constructed to obtain a very low error floor. To reduce the implementation complexity, we design a low complexity iterative…
In this paper, a modified extrinsic information transfer (EXIT) chart analysis that takes into account the relation between mutual information (MI) and bit-error-rate (BER) is presented to study the convergence behavior of block Markov…
Motivated by the need to communicate short control messages in 5G and beyond, this paper carefully designs codes for cyclic redundancy check (CRC)-aided list decoding of tail-biting convolutional codes (TBCCs) and polar codes. Both codes…
In this work we propose a novel decoding algorithm for tailbiting convolutional codes and evaluate its performance over different channels. The proposed method consists on a fixed two-step Viterbi decoding of the received data. In the first…
We present in this paper a special class of unit memory convolutional codes (UMCCs), called semi-random UMCCs (SRUMCCs), where the information block is first encoded by a short block code and then transmitted in a block Markov (random)…
Hadamard transform~(HT) as over the binary field provides a natural way to implement multiple-rate codes~(referred to as {\em HT-coset codes}), where the code length $N=2^p$ is fixed but the code dimension $K$ can be varied from $1$ to…
Recently, rate-1/n zero-terminated (ZT) and tail-biting (TB) convolutional codes (CCs) with cyclic redundancy check (CRC)-aided list decoding have been shown to closely approach the random-coding union (RCU) bound for short blocklengths.…
The multidimensional convolutional codes are an extension of the notion of convolutional codes (CCs) to several dimensions of time. This paper explores the class of two-dimensional convolutional codes (2D CCs) and 2D tail-biting…
Cyclic redundancy check (CRC) codes combined with convolutional codes yield a powerful concatenated code that can be efficiently decoded using list decoding. To help design such systems, this paper presents an efficient algorithm for…
We present extensions to Raghavan and Baum's reliability-output Viterbi algorithm (ROVA) to accommodate tail-biting convolutional codes. These tail-biting reliability-output algorithms compute the exact word-error probability of the decoded…
We propose in this paper a new coding scheme called twisted-pair superposition transmission (TPST). The encoding is to "mix together" a pair of basic codes by superposition, while the decoding can be implemented as a successive cancellation…
In this paper, we provide a new approach to the analytical estimation of the bit-error rate (BER) for convolutional codes for Viterbi decoding in the binary symmetric channel (BSC). The expressions we obtained for lower and upper BER bounds…
We present a stochastic first-order optimization algorithm, named BCSC, that adds a cyclic constraint to stochastic block-coordinate descent. It uses different subsets of the data to update different subsets of the parameters, thus limiting…