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Short Block-length Codes for Ultra-Reliable Low-Latency Communications
Mahyar Shirvanimoghaddam, Mohamad Sadegh Mohamadi, Rana Abbas, Aleksandar Minja, Chentao Yue, Balazs Matuz, Guojun Han, Zihuai Lin, Yonghui Li, Sarah Johnson, Branka Vucetic
TL;DR
URLLC requires very high reliability and very low latency, making short-block coding a central design challenge. The paper reviews and compares candidate codes, decoders, and research directions, finding that existing schemes remain imperfect relative to finite-blocklength benchmarks while highlighting promising approaches.
Problem
URLLC needs short blocks for low latency, but conventional codes show deficiencies at short lengths and reliability cannot readily be increased through retransmission.
Method
The paper reviews and compares Polar, Turbo, LDPC, convolutional, and BCH codes by reliability, rate performance, and decoding complexity, while discussing improvement directions.
Results
More than 90% of the normal-approximation benchmark and BLERs as low as 10−6 have been demonstrated for PBRL-LDPC codes.
Takeaways & Limitations
Low-complexity ML-like decoders for fundamentally better short-block codes, such as BCH codes, remain an important research direction.
Abstract
from arXiv · showhide
This paper reviews the state of the art channel coding techniques for ultra-reliable low latency communication (URLLC). The stringent requirements of URLLC services, such as ultra-high reliability and low latency, have made it the most challenging feature of the fifth generation (5G) mobile systems. The problem is even more challenging for the services beyond the 5G promise, such as tele-surgery and factory automation, which require latencies less than 1ms and failure rate as low as $10^{-9}$. The very low latency requirements of URLLC do not allow traditional approaches such as re-transmission to be used to increase the reliability. On the other hand, to guarantee the delay requirements, the block length needs to be small, so conventional channel codes, originally designed and optimised for moderate-to-long block-lengths, show notable deficiencies for short blocks. This paper provides an overview on channel coding techniques for short block lengths and compares them in terms of performance and complexity. Several important research directions are identified and discussed in more detail with several possible solutions.
I. INTRODUCTION
URLLC targets highly reliable, delay-sensitive services, creating a physical-layer trade-off between latency and reliability. This paper reviews short-block channel codes and compares their performance and complexity to identify improvement directions.
- Factory automation and tele-surgery require reliability of (1 −10−9) with end-to-end latency below 1ms.
- Power-electronics industrial control targets latency below 0.1msec and reliability of (1 −10−9).
- Short packets reduce latency but cause severe coding-gain loss, while widening bandwidth is not always feasible.
- At small block lengths, candidate codes such as LDPC, Polar, TB-CC, and Turbo can differ substantially despite similar large-block performance.
- The paper compares short-block codes by rate efficiency at relevant reliabilities and identifies research directions because existing candidates remain below the normal-approximation benchmark.
1) Latency:
URLLC latency is the time to deliver a data block over the radio interface, combining transmission, propagation, processing, and retransmission components. Its tight budget motivates flexible coding while keeping retransmissions low.
- User-plane latency includes transmission, propagation, processing, and retransmission time.
- The transmission-time component is required to be on the order of a hundred microseconds, below the 1ms considered in 4G.
- Reliability is the probability of transmitting K information bits successfully within the desired user-plane latency at a given channel quality.
- URLLC coding schemes should support bit-level codeword-size and rate flexibility while minimizing retransmissions to limit latency.
- 3GPP specifies reliability of (1 −10−5) for a 32-byte packet within 1ms, with or without HARQ.
4) Performance Benchmark:
The normal approximation separates finite-blocklength channel effects from additional code-and-decoder gaps. It provides the benchmark for assessing short-block codes, whose performance approaches it as block length increases.
- The normal approximation benchmarks short-block performance by incorporating the coding-gain loss caused by fewer channel observations.
- R is code rate, C channel capacity, V channel dispersion, ε average BLER, and Q(.) the standard normal distribution’s cumulative distribution function.
- As information block length increases, the gap to Shannon’s limit decreases.
- At short blocks, LTE Turbo and TB-CC codes show considerable gaps to the normal approximation, partly reflecting suboptimal decoding algorithms.
- The normal approximation is reported as tight for moderate block lengths above 100 bits, while Shannon capacity itself assumes infinite block length.
III. CANDIDATE SHORT BLOCK LENGTH CHANNEL CODES FOR URLLC
The paper introduces fixed-rate short-block codes and decoding approaches suitable for URLLC, emphasizing BCH codes and near-maximum-likelihood OSD decoding. BCH codes offer strong distance properties but limited block-length and information-length flexibility.
- BCH Codes: BCH codes are cyclic error-correcting codes whose guaranteed correction capability t is set during design.Their minimum distance satisfies d_min >= 2t + 1.
- OSD Decoding: OSD is a near-maximum-likelihood soft-decision decoder for binary linear block codes.It reorders channel outputs by reliability, forms a systematic generator matrix, and tests error patterns of increasing weight.
- OSD Decoding: Recent OSD advances reduce decoding complexity, making OSD suitable for short block-length codes.The decoder retains the candidate codeword with the smallest Euclidean distance after reprocessing.
- BCH Codes: BCH codes have large minimum distances that help avoid performance floors at low BLER.This distance property supports their strong short-block reliability, while their lengths and information sizes remain constrained.
B. Convolutional Codes
Convolutional codes use encoder memory to obtain large minimum distances, but their decoding complexity generally grows exponentially with memory. Tail-biting avoids the short-block rate loss of zero-tail termination and is therefore considered for URLLC.
- Convolutional Code Structure: A rate R = k/n convolutional encoder uses k inputs, n outputs, and memory order m in a linear sequential circuit.Inputs remain in the encoder for m time units after entering.
- Convolutional Code Structure: Increasing convolutional-code memory can improve minimum distance and reduce error probability, but decoding complexity generally scales exponentially with memory.This creates a direct reliability-complexity tradeoff for short-block designs.
- Tail-Biting Convolutional Codes: Tail-biting convolutional codes eliminate the rate loss caused by zero-tail termination at short block lengths.They are consequently considered in 5G standardization for URLLC.
- Turbo Codes: Turbo codes perform close to Shannon’s limit for large blocks but show a gap exceeding 1 dB at short and moderate block lengths with iterative decoding.Their short-block behavior differs substantially from their long-block performance.
- LDPC Codes: Binary LDPC codes can perform poorly at short-to-moderate lengths because of many short cycles in their bipartite graphs.Protograph-based LDPC codes improve this regime but remain behind BCH codes under OSD or large-memory TB-CCs, while retaining low iterative-decoding complexity.
E. Polar Codes
Polar codes construct reliable synthesized channels through channel polarization and decode them using successive-cancellation-based methods. For short blocks and low rates, proposed Polar schemes can outperform LDPC codes, although list decoding increases implementation complexity.
- Polar-Code Construction: Polar coding transforms N binary-input channels into synthesized channels with capacities near zero or one.Information is sent over near-perfect channels, while unreliable channels receive known frozen symbols.
- Decoding: Successive cancellation decoding has O(N log N) complexity, but its recursive implementation can impose substantial latency.For sufficiently large lengths, its block error probability decays exponentially in the square root of block length.
- Decoding: Successive-cancellation list decoding retains multiple likely paths instead of making only one symbol-wise decision.CRC-aided SCL adds CRC error detection to improve list-decoding performance.
- Short-Block Performance: Polar codes have been selected for short-block eMBB control channels and are proposed for URLLC because they outperform LDPC codes at short lengths and low rates without observed error floors.They also provide 1-bit granularity across coding rates and block sizes.
- Evaluation: The paper compares candidate codes on a BI-AWGN channel using BLER as the reliability metric.Simulations run at each SNR and code rate until 100 decoder-output codeword errors are obtained.
A. Reliability
At short block length, BCH codes approach the normal-approximation benchmark most closely, while competing codes trade some performance for lower complexity. Polar list size strongly affects this tradeoff, and BCH decoding becomes especially costly at low rates.
- Reliability: At R = 1/2 and N = 128 under MLD, extended BCH closely approaches the normal approximation and reaches BLER 10^-7 with a 0.1 dB gap.TB-CC with memory m = 14 is also competitive, while F256 LDPC has nearly the same performance as that TB-CC.
- Rate Performance: BCH codes outperform other existing codes across the evaluated SNRs and remain close to the normal approximation at BLER 10^-4 for N = 128.The paper attributes this result to their better distance spectrum and uses OSD with maximum re-factoring order 5.
- Complexity Tradeoffs: Polar decoding with list size 32 significantly outperforms list size 4, but requires substantially greater complexity to store and rank additional candidates.This illustrates the reliability-complexity cost of increasing the list size.
- Complexity Tradeoffs: Short-block LDPC codes offer very low-complexity iterative BP decoding and slightly outperform CA-Polar with SCL list size 4.BCH decoding is much more complex, especially when lower rates require higher OSD reprocessing orders.
C. Complexity vs. Performance
Short-block decoding complexity depends on more than block length, creating a performance–complexity tradeoff for URLLC codes. The paper identifies further improvements as essential for meeting both reliability and latency requirements.
- Complexity considerations: Turbo and LDPC decoders can achieve near-capacity performance at large block lengths with reasonable, parallelizable complexity.Their belief-propagation complexity scales linearly with block length.
- Complexity considerations: For short blocks, parameters beyond block length significantly affect decoding complexity, including memory order for Viterbi-decoded tail-biting convolutional codes.The complexity measure used is the number of binary operations.
- Performance–complexity tradeoff: Polar codes with SCL decoding reach BLER 10^-4 within a 0.5 dB gap to the normal approximation at roughly 10^3 operations per bit.Reducing the list size lowers complexity but degrades performance.
- Research directions: The paper identifies three main directions requiring major improvements to achieve ultra-high reliability and low latency.Recommendations are provided for each direction.
A. Developing Low Complexity OSD Decoders
The paper examines ways to reduce OSD decoding complexity while preserving short-block rate efficiency and compares complexity–performance behavior across candidate codes. It also situates self-adaptive coding as a route toward low-latency transmission without transmitter-side CQI.
- Developing Low Complexity OSD Decoders: BCH codes outperform existing Polar, Turbo, and LDPC codes under OSD, while sufficient conditioning and segmentation can substantially reduce OSD complexity.These reductions maintain rate efficiency similar to the original OSD decoder.
- Developing Low Complexity OSD Decoders: Fig. 6 compares algorithmic complexity and performance for rate-1/2 codes of block length N = 128 at BLER 10^-4.Decoder complexity is obtained from [14].
- Developing Low Complexity OSD Decoders: Bounded-complexity OSD enables a performance–complexity tradeoff, motivating low-complexity ML-like decoders for stronger short-block codes such as BCH.The paper presents this as a direction for improving URLLC channel-code performance.
- Self-adaptive coding: Current rate-adaptive schemes target BLER 10^-2 and rely heavily on retransmissions, with each LTE retransmission taking about 7∼8 ms.The resulting delay is described as unacceptable for URLLC.
- Self-adaptive coding: Self-adaptive codes determine code rate during transmission and adapt to channel conditions without transmitter-side CQI.PBRL-LDPC codes have demonstrated more than 90% of the normal-approximation benchmark and BLER as low as 10^-6.
1) The design of a self-adaptive joint coding and modulation scheme:
The paper proposes jointly designing PBRL-LDPC coding with real-domain rateless modulation to improve self-adaptive transmission, while also identifying space-frequency coding as an unresolved URLLC design challenge. Its broader comparison finds BCH strongest under optimal decoding and highlights practical Polar performance near the normal-approximation benchmark.
- The design of a self-adaptive joint coding and modulation scheme: Jointly designing binary PBRL-LDPC codes with real-domain rateless codes such as AFC can significantly improve performance.The proposal replaces the Raptor component with rateless coding over the real domain.
- Reducing pilot sequence length for channel estimation at the receiver side: Rateless transmission requires pilot symbols because the receiver must know the channel, and pilot overhead causes larger losses for smaller information blocks.The paper links this issue to the need for shorter pilot sequences.
- Space-Frequency Channel Coding: Current systems mainly use spatial resources for multiplexing rather than diversity, while short-block URLLC requires channel-code designs that account for space and frequency diversity.The paper states that no universal framework currently designs such codes for different low-latency reliability levels.
- Conclusions: BCH codes provide the highest reliability under optimal decoding, while Polar codes with SCL achieve reliability 1−10^-4 within a 0.5 dB gap to the normal approximation.The conclusion also notes that reduced-complexity OSD and BCH codes may improve results at similar complexity.