Spinal codes are known to be capacity achieving over both the additive white Gaussian noise (AWGN) channel and the binary symmetric channel (BSC). Over wireless channels, Spinal encoding can also be regarded as an adaptive-coded-modulation (ACM) technique due to its rateless property, which fits it with mobile communications. Due to lack of tight analysis on error probability of Spinal codes, optimization of transmission scheme using Spinal codes has not been fully explored. In this work, we firstly derive new tight upper bounds of the frame error rate (FER) of Spinal codes for both the AWGN channel and the BSC in the finite block-length (FBL) regime. Based on the derived upper bounds, we then design the optimal transmission scheme. Specifically, we formulate a rate maximization problem as a nonlinear integer programming problem, and solve it by an iterative algorithm for its dual problem. As the optimal solution exhibits an incremental-tail-transmission pattern, we propose an improved transmission scheme for Spinal codes. Moreover, we develop a bubble decoding with memory (BD-M) algorithm to reduce the decoding time complexity without loss of rate performance. The improved transmission scheme at the transmitter and the BD-M algorithm at the receiver jointly constitute an "encoding-decoding" system of Spinal codes. Simulation results demonstrate that it can improve both the rate performance and the decoding throughput of Spinal codes.

中文翻译：

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脊柱代码优化：错误概率分析和传输方案设计

众所周知，在加性高斯白噪声（AWGN）信道和二进制对称信道（BSC）上，脊柱码都能实现容量。在无线信道上，由于脊柱编码的无速率特性，它也可以被视为自适应编码调制（ACM）技术，使其适合于移动通信。由于缺乏对脊柱码错误概率的严格分析，因此尚未充分探索使用脊柱码的传输方案的优化。在这项工作中，我们首先在有限块长（FBL）体制下为AWGN信道和BSC导出了新的Spinal码帧错误率（FER）的严格上限。基于导出的上限，然后设计最佳传输方案。具体来说，我们将速率最大化问题公式化为非线性整数规划问题，并通过迭代算法解决其双重问题。由于最佳解决方案表现出增量尾部传输模式，因此我们提出了一种改进的脊髓代码传输方案。此外，我们开发了带有存储器的气泡解码（BD-M）算法，以降低解码时间的复杂度，而不会降低速率性能。发射机处的改进的传输方案和接收机处的BD-M算法共同构成了脊髓代码的“编码-解码”系统。仿真结果表明，它可以同时提高码率性能和解码吞吐量。我们开发了带有存储器的气泡解码（BD-M）算法，以降低解码时间的复杂度，而不会降低速率性能。发射机处的改进的传输方案和接收机处的BD-M算法共同构成了脊髓代码的“编码-解码”系统。仿真结果表明，它可以同时提高码率性能和解码吞吐量。我们开发了带有存储器的气泡解码（BD-M）算法，以降低解码时间的复杂度，而不会降低速率性能。发射机处的改进的传输方案和接收机处的BD-M算法共同构成了脊髓代码的“编码-解码”系统。仿真结果表明，它可以同时提高码率性能和解码吞吐量。