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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 list decoding algorithm. The most significant features of the TPST code are its predictable performance that can be estimated numerically from the basic codes and its flexible construction in the sense that it can be easily adapted to different coding rates. To construct good TPST codes in the finite length regime, we propose two design approaches-rate allocation and partial superposition. By taking tail-biting convolutional codes (TBCC) as basic codes, we show by numerical results that the TPST codes can have near-capacity performance in the short length regime., Comment: submitted to IEEE Transactions on Information Theory

In this paper, we propose a systematic low density generator matrix (LDGM) code ensemble, which is defined by the Bernoulli process. We prove that, under maximum likelihood (ML) decoding, the proposed ensemble can achieve the capacity of binary-input output symmetric (BIOS) memoryless channels in terms of bit error rate (BER). The proof technique reveals a new mechanism, different from lowering down frame error rate (FER), that the BER can be lowered down by assigning light codeword vectors to light information vectors. The finite length performance is analyzed by deriving an upper bound and a lower bound, both of which are shown to be tight in the high signal-to-noise ratio (SNR) region. To improve the waterfall performance, we construct the systematic convolutional LDGM (SC-LDGM) codes by a random splitting process. The SC-LDGM codes are easily configurable in the sense that any rational code rate can be realized without complex optimization. As a universal construction, the main advantage of the SC-LDGM codes is their near-capacity performance in the waterfall region and predictable performance in the error-floor region that can be lowered down to any target as required by increasing the density of the uncoupled LDGM codes. Numerical results are also provided to verify our analysis., Comment: submitted to IEEE Transactions on Information Theory

In this paper, we formulate a new problem to cope with the transmission of extra bits over an existing coded transmission link (referred to as coded payload link) without any cost of extra transmission energy or extra bandwidth. This is possible since a gap to the channel capacity typically exists for a practical code. A new concept, termed as accessible capacity, is introduced to specify the maximum rate at which the superposition transmission of extra bits is reliable and has a negligible effect on the performance of the coded payload link. For a binary-input output-symmetric (BIOS) memoryless channel, the accessible capacity can be characterized as the difference between the channel capacity and the mutual information rate of the coded payload link, which can be numerically evaluated for very short payload codes. For a general payload code, we present a simple lower bound on the accessible capacity, given by the channel capacity minus the coding rate of the payload code. We then focus on the scenarios where low-density parity-check (LDPC) codes are implemented for the payload link. We propose to transmit extra bits by random superposition for encoding, and exhaustive search (with the aid of statistical learning) for decoding. We further propose, by establishing an auxiliary channel (called syndrome channel) induced from "zero-forcing" over the binary field, to transmit extra bits with structured codes such as repetition codes and first-order Reed-Muller (RM) codes. Numerical results show that up to 60 extra bits can be reliably transmitted along with a rate-1/2 LDPC code of length 8064., Comment: submitted to IEEE Transactions on Information Theory

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) superposition manner. We propose a successive cancellation list decoding algorithm, by which a list of candidate codewords are generated serially until one passes an empirical divergence test instead of the conventional cyclic redundancy check (CRC). The threshold for testing the correctness of candidate codewords can be learned off-line based on the statistical behavior of the introduced empirical divergence function (EDF). The performance-complexity tradeoff and the performance-delay tradeoff can be achieved by adjusting the statistical threshold and the decoding window size. To analyze the performance, a closed-form upper bound and a simulated lower bound are derived. Simulation results verify our analysis and show that: 1) The proposed list decoding algorithm with empirical divergence test outperforms the sequential decoding in high signal-to-noise ratio (SNR) region; 2) Taking the tail-biting convolutional codes (TBCC) as the basic codes, the proposed list decoding of SRUMCCs have comparable performance with the polar codes under the constraint of equivalent decoding delay., Comment: Submitted to IEEE Transactions on Information Theory. arXiv admin note: substantial text overlap with arXiv:1902.09808

This paper is concerned with block Markov superposition transmission (BMST) of tail-biting convolutional code (TBCC). We propose a new decoding algorithm for BMST-TBCC, which integrates a serial list Viterbi algorithm (SLVA) with a soft check instead of conventional cyclic redundancy check (CRC). The basic idea is that, compared with an erroneous candidate codeword, the correct candidate codeword for the first sub-frame has less influence on the output of Viterbi algorithm for the second sub-frame. The threshold is then determined by statistical learning based on the introduced empirical divergence function. The numerical results illustrate that, under the constraint of equivalent decoding delay, the BMST-TBCC has comparable performance with the polar codes. As a result, BMST-TBCCs may find applications in the scenarios of the streaming ultra-reliable and low latency communication (URLLC) data services., Comment: 5 pages, 6 figures, submitted to ISIT2019

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 sliding-window decoding algorithm, in which only binary and/or erasure messages are processed and exchanged between processing units. The error floor can be predicted by a genie-aided lower bound, while the waterfall performance can be analyzed by the density evolution method. To evaluate the error floor of the constructed BMST-BCH codes at a very low bit error rate (BER) region, we propose a fast simulation approach. Numerical results show that, at a target BER of $10^{-15}$, the hard-decision decoding of the BMST-BCH codes with overhead $25\%$ can achieve a net coding gain (NCG) of $10.55$ dB. Furthermore, the soft-decision decoding can yield an NCG of $10.74$ dB. The construction of BMST-BCH codes is flexible to trade off latency against performance at all overheads of interest and may find applications in optical transport networks as an attractive~candidate., Comment: submitted to IEEE Transactions on Communications

A new Chase-type soft-decision decoding algorithm for Reed-Solomon codes is proposed, referred to as tree-based Chase-type algorithm}. The proposed tree-based Chase-type algorithm takes the set of all vectors as the set of testing patterns, and hence definitely delivers the most-likely codeword provided that the computational resources are allowed. All the testing patterns are arranged in an ordered rooted tree according to the likelihood bounds of the possibly generated codewords, which is an extension of Wu and Pados' method from binary into $q$-ary linear block codes. While performing the algorithm, the ordered rooted tree is constructed progressively by adding at most two leafs at each trial. The ordered tree naturally induces a sufficient condition for the most-likely codeword. That is, whenever the tree-based Chase-type algorithm exits before a preset maximum number of trials is reached, the output codeword must be the most-likely one. But, in fact, the algorithm can be terminated by setting a discrepancy threshold instead of a maximum number of trials. When the tree-based Chase-type algorithm is combined with Guruswami-Sudan (GS) algorithm, each trial can be implement in an extremely simple way by removing from the gradually updated Grobner basis one old point and interpolating one new point. Simulation results show that the tree-based Chase-type algorithm performs better than the recently proposed Chase-type algorithm by Bellorado et al with less trials (on average) given that the maximum number of trials is the same.